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EPJ Web of Conferences 100, 0400 5 (2015)
DOI: 10.1051/epjconf/ 201510004 00 5
© Owned by the authors, published by EDP Sciences, 2015
Numerical Solutions of Schõn-Klasens model for luminescence efficiency
Erdem Uzuna and Mehmet Emin Korkmaz
Karamanoglu Mehmetbey University, Faculty of Kamil Ozdag Science, Department of Physics, 70100, Karaman, Turkey
Abstract. Phosphors exhibit luminescence following irradiation and the absorption of energy depends upon the relative probabilities
of the radiative and non-radiative transitions. In general, the luminescence efficiency of a phosphor is related to the probability of a
luminescence transitions and probability of a non-radiative transitions. Several experimental measurements of the luminescence
efficiency have shown it to be strong temperature dependent over given temperature ranges. In literature, Schõn-Klasens model has
been offered to explain the temperature dependence of luminescence efficiency. In this study, theoretical basis and some numerical
Solutions of the model was discussed. The brief information about mathematical principies of the model was given and differential
equations expressing the charge carrier transitions were derived. Numerical Solutions of the equations were performed by using
Mathematica 8.0 Computer code. All the analysed parameters were chosen realistically. According to the simulations, glow curves
intensities were decreased by the appropriate pe and qi, ratio.
1 Introduction
A number of models are available in the literature for the
explanation of the thermoluminescence (TL) event. The
theoretical explanation of TL is based on the electron band
theory of an insulating or semiconducting solid. It consists of a
set of localized energy leveis in the forbidden band, which
arises due the presence of impurities and other point defects.
The energy leveis act as traps and recombination centres in the
TL process [15]. All TL phenomena are govemed by the
process of the electron hole recombination. It should be noted
that rather complex processes are taking place in the traffic of
charge carrier between trapping States and luminescent
recombination centres. Almost all of TL models have been
based on the consideration of charge release from electron trap
only. In this paper, we assumed that not only electrons but also
holes are mobile in the same temperature interval. The model
introduced originally by Schon and colleagues [6,7] and used
by Klasens [8]. According to the model holes also contribute
to TL emitting like electrons. Fig. 1 show that energy leveis,
charge carrier transitions and related parameters suggested by
the Schõn-Klasens model [4].
According to the model charge carrier traffic are given in
Eq.1-4. The 4 equations set also describe the simultaneous
release of holes during the thermal stimulation of the trapped
electrons [1-4].
dn/dt=-se n cxp(-Ee/k T)+Ate nc (N-n)-Arh nv n
(1)
dnc/dt=sen exp(-Ee/k T)-Ate nc (N-n)-Are nc m
(2)
dm/dt=-.s,m exp(-Eh/k T)+Ath nv (M-m)-Are nc m (3)
dnJdt=s\, m exp(-Eh/k T)-Ath nv (M-m)-Arh nv n
a
(4)
, ValanceBand , „
,
Figure 1. Generalized energy leveis scheme and allowed transitions
for Schon - Klasens model [4].
In here, the instantaneous concentration of electrons in the
conduction band is denoted by nc (m“3) and that of holes in the
valence band by nv (m“3) respectively. N (m“3) denotes here
the total concentration of electron trapping States which is a
constant and n (m“3) the instantaneous concentration of filled
electrons trap which is a variable. Ee (eV) and Se (s-1) are the
activation energy and frequency factor of the electron trap,
respectively, k is the Boltzmann constant (eV K -1) and Ate (m3
s-1) is the trapping (re-trapping during heating) probability of
electrons from the conduction band. M (m“3) denotes here the
total concentration of hole trapping States which is a constant
and m (m“3) the instantaneous concentration of filled holes trap
which is a variable. Eh (eV) and Sh (s-1) are the activation
energy and frequency factor of the hole trap, respectively. Ath
(m3 s-1) is the probability of capturing hole in M, whereas Are
(m3 s-1) is the recombination probability of free electrons with
captured holes. Arh (m3s-1) is the recombination probability of
free holes with captured electrons in electron trap.
At the same time, the equations to keep to the right
neutralization condition expressed inEq5.
Corresponding author: [email protected]
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dn/dt+ dnc/dt= dm/dt+ dn/dt
(5)
curve are the same for the given trap parameters in Table 1.
If all recombination events are radiative and produce
photons and all photons are detected, TL glow curve is
expressed byEq.6. [1-4].
ITL= ^ellLn +^hlTLh
(6)
For the equations set approximate Solutions were given by
Brâunlich and Scharmann [9]. These authors considered four
extreme cases, involving the rates of electron and hole
retrapping and their comparison with the corresponding
recombination rates. The model also solved numerically by
Mckeever et.al. [10] without any of the assumptions of the
Brâunlich and Scharmann and reached the same conclusions.
In addition to these the model was solved numerically by Uzun
[11] for various trapping and recombination probabilities.
Figure 2. Thermoluminescence intensity comes from only electrons
(black line), holes (red line) and glow curve (green line)
Table 1. Trap parameters for Fig.2
2 Methodology
In this study, we assumed that material irradiated before
heating stage and has electrons in electron trap (n.,) and holes
in hole trap (mo). In this case it is important assumption that
there are not any charge carriers in the conduction and valence
bands. This is followed by a heating stage. During this stage M
and N are assumed to be rather far from the valence band and
conduction band, respectively. Electrons from N may be
thermally released into the conduction band and then either retrap in N or recombine with holes in M. At the same time holes
from M may be thermally released into the valence band and
then either re-trap in M or recombine with electrons in N. For
a given set of trapping parameters, differential equations
goveming the process during the excitation stage were
numerically solved by using a special code in the Mathematica
8.0 [12] Computer program with an explicit Runge-Kutta
method [13]. During the Solutions temperature was changing
with a constant heating rate (0) and therefore instantaneous
temperature is expressed by Eq. 7.
T= To + p t
(7)
Where To is the initial temperature at the beginning of heating
stage and t is the time (s). Both recombination into N and M
are considered to be radiative, but separable. Thus, the intensity
in photons per m3 per second of one spectral component of TL
is proportional to the rate of change of N, i.e. Eq. 1 and the
second spectral component is assumed to be proportional to the
rate of change of M, namely, Eq. 3. The shape, position and
intensity of the glow curve are related to a various trapping
parameters of the trapping States responsible for the TL
emission.
3 Results
Thermoluminescence intensities come from only electrons and
only holes movement were determined and glow curve was
calculated. Results are given in Fig. 2 and parameters used in
the simulations were given in Table 1. It can be seen from the
Fig. 2 that contributions of the electrons and holes on glow
The effect of the radiative recombination ratios of the
electrons and holes on glow curves are show in Fig.3-5. Trap
parameters used in the simulations were given in Table 2.
Parameters
Values
Ee=Eh (eV)
1.00
Se=Sh (s' 1)
1012
M=N (cm'3)
IO10
m=n (cm'3)
IO10
Ate=Ath
10'9
Are=Arh
10'7
1.00
Figure 3.rpContributions
different
values.
of the electrons on glow curve for
04005-p.2
TESNAT 2015
Figure 6. The effect ofthe rp on IM. Maximum intensities of the glow
curve, electron and hole contributions are shown as black triangle,
red and blue circles, respectively.
Figure 4. Contributions ofthe holes on glow curve for different
rp, values.
According to simulations;
i. When Ee=Eh and Pe^Ph, glow curve is shaped by both
electrons and holes movement. In addition to this,
contributions of them to glow curve are the same ratios.
ii. When Ee=Eh and ne>Ph, glow curve shaped by both
electrons and holes movement. But in this case
contribution of electrons is bigger than holes depending
on pe/ph ratio.
iii. When ph=0, glow curve is shaped by only electrons.
iv. When qe=0, glow curve is shaped by only holes.
v. When qe=l, it means that all electron-hole (electron is
mobile and hole is still) recombination are radiative and
vice versa if pe=0.
References
TfC)
Figure 5. Glow curves for different rp values.
Table 2. Trap parameters for Fig.3-5.
Parameters
Values
1
1.00-0
The effect of the radiative recombination ratios of the
electrons and holes on maximum thermoluminescence
intensities of the glow curves are show in Fig.6.
4Conclusions
In this study Schõn-Klasens model has been solved by
numerically. In the Solutions and ph parameters were chosen
as variables and others were constant. By using these
parameters, Eq.l to Eq.6 are solved by numerically but no
simplifying assumptions had been made.
Simulations show that according to Schõn-Klasens model,
in which electron and hole can be released by thermally,
thermoluminescence glow curve is shaped by charge carrier
movement resulting recombination. This
1.
R.
Chen,
S.W.S.
McKeever.
Theory
of
Thermoluminescence and Related Phenomena (Word
Scientifíc, Singapore, 1997)
2. R. Chen, D.J. Lockwood, J. Electrochem. Soc., 149 9
(2002)
3. C. Furetta, Handbook of Thermoluminescence (Word
Scientifíc, New Jersey, 2003)
4. S.W.S. Mckeever, R.Chen, Rad. Meas., 27 5/6 (1997)
5. S.W.S. McKeever, Thermoluminescence of Solids
(CambridgeUniversityPress, London, 1985)
6. N. Riehl, M. Schon, Z. PhysikA, 114, 11-12 (1939)
7. M. Schon, Z. Physik A, 119, 7-8 (1942)
8. H.A. Klasens, Nature, 158 (1946)
9. P. Brâunlich, A. Scharmann, Phys. Status Solidi (b) 18
(1966)
10. S.W.S. Mckeever, et al., Phys. Rev. B, 32 6 (1985)
11. E.Uzun,JCBPSC,5 2 (2015)
12. Wolfram Mathematica 8, Wolfram Research Inc., Version
Number 8.0.0.0, Platform Microsoft Windows(64),
Registered Org: Karamanoglu Mehmetbey University.
13. https://reference.wolfram.com/language/tutorial/NDS
olveExplicitRungeKutta.html
process is different from the other models’ process because,
now hole is not a stable charge carrier.
04005-p.3
EPJ Web of Conferences 100, 04003 (2015)
DOI: 10.1051/epjconf/ 201510004003
© Owned by the authors, published by EDP Sciences, 2015
Parameters affecting of Akkuyu's safety assessment for severe core
damages
Yusuf Kavun1'2'a and Muzaffer Karasulu3
1,
2
3
Celal Bayar University, Faculty of Art and Science, Department of Physics, 45030, Manisa, Turkey
Akdeniz University, Faculty of Science, Department of Physics, 07058, Antalya, Turkey
Akdeniz University, Faculty of Science, Department of Space Science and Technologies, Antalya, Turkey
Abstract. We have looked at all past core meltdowns (Three Mile Island, Chemobyl and Fukushima incidents) and
postulated the fourth one might be taking place in the future most probably in a newly built reactors anywhere of the
earth in any type of NPP. The probability of this observation is high considering the nature of the machine and human
interaction. Operation experience is a very significant parameter as well as the safety culture of the host nation. The
concems is notjust a lack of experience with industry with the new comers, but also the infrastructure and established
institutions who will be dealing with the Emergencies. Lack of trained and educated Emergency Response Organizations
(ERO) is a major concem. The culture on simple fire drills even makes the difference when a severe condition occurs in
the industry. The study assumes the fourth event will be taking place at the Akkuyu NGS and works backwards as
required by the "what went wrong " scenarios and comes up with interesting results. The differences studied in depth to
determine the impact to the severe accidents. The all four design have now core catchers. We have looked at the operator
errors(like in TMI); Operator errors combined with design deficiencies(like in Chemobyl) and natural disasters( like in
Fukushima) and found operator errors to be more probable event on the Akkuyu's postulated next incident. With respect
to experiences of the operators we do not have any data except for long and successful operating history of the Soviet
design reactors up until the Chemobyl incident. Since the Akkuyu will be built, own and operated by the Russians we
have found no alarming concems at the moment. At the moment, there is no body be able to operate those units in Turkey.
Turkey is planning to build the required manpower during the transition period. The resolution of the observed parameters
lies to work and educate, train of the host nation and exercise together.
1.
Introduction
Conceivable accidents in a Light Water Reactor can be
classifíed as, a) Abnormal Operational Transients; b) Design
Basis Accidents; and c) Severe accidents. It is expected that a
substantial core damage occurs if not mitigated, material release
into the containment may cause over-pressurization and breach
of the containment. The severe accident may result in release of
fission products to the environment beyond the acceptable limits
of known standards (10CFR100) [1]. When it happens you may
have a mess in operational peoples hand and requires special
training and cultural behavior to deal with it. This requires long
training and behavioral attitudes on adherence to procedures to
follow, selection and performing the most appropriate action
require long training hours workload share among the peers and
safety culture of the organization build over the time with
several exercises. Levei of degradation during severe accidents
usually refer to operating crew work habits and control room
environment during the accident management while trying to
put plant under recovery
operation with suffícient enough core cooling water to keep core
covered, if the mitigating measures are not effective, a severe
accident progresses in the following stages. Three Mile Island
(TMI) occurred following the loss of 125-V DC bus 32 followed
by an operator error causing total loss of Auxiliary Feed Water
(AFW) [6]. The initial abnormal event progressed into a severe
accident due to lack of design knowledge by the operators which
a
caused a wrong decision on defeating the AFW as to not fill the
pressurizer. At the time the industry believed that a severe
accident was not credible. Since then, there have been many
improvements to the safety systems, operations, procedures,
control room environment, education and fínally On The Job
(OTJ) in the nuclear technology. However, severe accidents
should not be entirely discounted not just its probability is not
zero but it involves a complex technology plus the human factor
In other words, does not matter how fast can the machine
(Lamborghini) goes but the driver may not be ready. There have
been several analysis and many methodologies on severe
accidents that based on several well-known phenomena. Such
as; Core, RCS (Reactor Coolant System), Steam Generator (SG)
phenomena must be mustered [7]. The summary of these
phenomena will be provided in section 2 and operators’ safety
culture as well as entire organization’s attitude towards safety
and the established safety culture plays enormous roll in
accident evaluation, operator training must require to be
revisited.
In this paper we studied all the phenomena but particularly
SG phenomenon, because of the design differences among the
subject existing PWRs fírst [8]; Then, we combined the human
factor to all of these to conclude that the new comers in the
technology with a horizontal SG designs may require to be more
attendant in increased probabilities of severe accidents.
Different cultures have shown different behaviors during
severe accident conditions on any operations [5]. Carvalho, and
Corresponding author : [email protected]
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EPJ Web of Conferences
his co-workers claim that human factor is culturally differs
under conditions depending of their behavior under the
pressured situation [3]. They were investigated cultural and
cognitive issues related to the work of nuclear power plant
operators during their time on the job, in the control room, and
during simulator training (emergency situations), in order to
show how these issues impact on plant safety. They have
modeled the operators’ behavior, their work deals with the use
of operational procedures, the constant changes in the focus of
attention and the dynamics of the conflicting activities. They
have observed that the safety implications of the control room
operators’ cognitive and cultural issues go far beyond the formal
organizational structures usually implied. They have found that
that the competence required for the operators are concemed
with developing the possibility of constructing situation
awareness, managing conflicts, gaps and time problems created
by ongoing task procedures, and dealing with distractions,
developing skills for collaborative work. These are all both
developmental, psychological and degree of training and
knowledge accumulation by the control room staff.
providing small amount of water to the core may only aggravate
the oxidation process rather than cool the core. The water flow
rate must be high enough to accomplish the compensate for
decay power and oxidation, remove stored energy in the reactor
core due to elevated temperatures in an uncovered core and refíll
the vessel. The require flow rate to cool down an uncovered core
and refíll the vessel is shown in the Fig. 1 as three regions.
Figure 1: Minimum water injection rate required to recover the water
levei after the core is uncovered (SAG-2, CA-1) [9].
2. Methodology and analysis
The reactor core, coolant system and steam generator
phenomena were studied to explain to the structure of the
durability and strength. Energy sources, core uncover, melting
and relocation are important to RC phenomena. As a result of
decay power, some físsion products can be gas form after
shutdown and thus decreases exponentially as if function of
duration. Zr and Stainless Steel (SS) can cause the oxidation
when react oxygen in steam at high temperatures so release
energy [5]. As the RCS is unspoiled, generated hydrogen may
be distinctive for oxidation. If there is vessel breach and core is
relocated into the containment so there will be additional
generation of H2. If the Hydrogen concentration increase global
combustion of H2 is highly probable. Along with combustion
deflagration and detonation cause the damage on concentration.
During loss of coolant accident, the failures occurred can
combine with blackout and loss of turbine auxiliary feed water
pump, core damage compose in two hours [5]. The differences
between inner and outer surfaces’ maximum temperature of clad
can oxidize that molten Zr penetrates the oxide layer and
candles the fuel rods, leaving less Zr in the upper hot sections.
As a result of breached and LOCA (loss of coolant accident)
físsion products may be escaping the RCS following core
damage. The next line of defense is to cool and contain the core
in the RCS and reduce the rate of físsion product release from
RCS. To perform these situations, quenching and coolability of
in vessel debris occupies an important place. If the reactor is
partially uncovered and temperatures enough for oxidation,
in VVER reactors [2]. The horizontal design means that during
SG phenomenon dry out will be reached earlier than the vertical
design leading the core meltdown earlier. The horizontal steam
generators on the other hand, do not face such problems as
primary water stress- corrosion cracking, fouling and denting
which are the known problems for the vertical design that leads
to SGs degradation the horizontal steam generator also uses a
“corridor” layout for the heat-exchange tubes in the tube bundle.
Horizontal SG design is a proven design with incrementai
improvements such as effective sludge removal from the steam
generator bottom, the use of secondary side ethanolamine water
Region 1: More Flow needed
Region 2: Expected success. Suffícient to cool the reactor core
and to reflood the vessel in 45 minutes.
Region 3: Uncertain. Core may be eventually cooled, but it may
take as long as 2 hours, during which time the core may already
relocate into the lower plenum, compact and lose coolable
geometry, and cause a vessel breach.
The required injection flow rate is almost independent of the
RCS pressure, whereas the pump flow rates are strongly
dependent of the RCS pressure. As the injection is provided, the
RCS pressure rises due to evaporation, even if the PORVs (Pilot
Operated Relief Valve) are open. The pressure stabilizes at the
intersection of the pump curved and PORV curve at the reflood
[4]. Also, under thermal attack molten core debris in the lower
plenum, two modes of fail will consist of absence of effective
cooling [5]. Local Failure may occur through the melting of the
instrument guide tubes. If the vessel is pressurized and not
submerged, the molten core material may be ejected at a high
speed. Creep-rupture failure occurs when a component is
subjected for some time interval to high-temperature and highpressure that need to more than one hour after debris is collected
in the lower plenum. Lastly SG phenomena is important to our
studies which we will be combined design differences
(horizontal vs. vertical) with the mentioned cultural differences.
At Akkuyu NPP, AES 2006 design utilizes horizontal steam
generators which are traditionally used
chemistry and elimination of copper-bearing components on the
secondary side, enable an expected Service life of 60 years to be
achieved. All of the other available 3rd generation PWRs; like
Westinghouse's AP1000, Areva's EPR or Ament; Rosatom’s
AES 2006, and Mitsubishi's AJP1200 are almost the same
designs except for some differences in core-fuel, horizontal
steam Generators (SG) designs, and some differences in
Emergency Response System (ERS) in AES-2006 [2]. Now
with the earlier core meltdown due to horizontal SGs of Akkuyu
combined with a less experience crew (assumed the operations
has been transferred to the local operators with minimal
04003-p.2
TESNAT 2015
operating experience as well as culture differences). This makes
the Akkuyu’s risk of a severe accident scenario is somewhat a
little bit higher than the other options. The metrics of culture
difference requires to be established by the risk analysis.
Therefore, the total risk difference has not been qualifíed in this
part of study. The cultural issues focuses on control of Mis
(micro incidents) by operators. The operator’s attention tums to
information while reading signals on identifying if there are
overruns. After this moment, the agent focuses on this situation
and here is a strong relationship between reading activity,
reading instruments, displays etc. [3]. The reading activities
provides to strategies for continuously solving problems. To this
strategies, operators move to different location to apply instant
strategies in the control room. In almost all MI known behaviors
of the system by operators that will increase confídence in
nuclear power plants. Therefore, to understand the functioning
of the system is to realize and what is happening during the
operation are one of the most important safety process for NPP.
[6]
[7]
[8]
[9]
3. Conclusion
In this study, we focused on the adequacy of operational
effíciency with the advanced technology of nuclear power
plants. Conceivable accidents in a LWR can be classifíed and
mentioned the operational impact for competence of the
operator to emphasize just how important. In this process,
defíned phenomena and safety culture are important to
understand how things are going in NPP. As a result of all of
them, with respect to experiences of the operators, we do not
have any data except for a long and successful operating history
of the Soviet design reactors up until the Chemobyl incident.
Since the Akkuyu will be built, own and operated by the
Russians we have found no alarming concems at the moment.
The plant will be transferred to Turkey when its paid
(approximately 15 years), up until that transfer time we cannot
make any assumptions as to some serious incidents be taking
place, because if it does it will ruin the good reputation of
Russians as the best seller of the technology. We assume that
Russians will assign their best operators to operate the plant.
Turkey is planning to build the required manpower during the
transition period. In general, for the host countries the most
important issue found was the build up their qualifíed operating
personnel.
References
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[2]
[3]
[4]
[5]
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IAEA, Status of advanced light water reactor designs,
Vienna, Áustria, (2004)
V.R.P. Carvalho, L.I. dos Santos, M.C.R. Vidal, Safety
implications of cultural and cognitive issues in nuclear
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(2006)
C.A. Kadak, 22.091/22.903, Nuclear Reactor Safety
Lectures,
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accident management, Vienna, Áustria programmes in
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M. Hashim, Y. Ming, A. Saeed, Review of Severe
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EPJ Web of Conferences 100, 04004 (2015)
DOI: 10.1051/epjconf/ 20151000400 4
© Owned by the authors, published by EDP Sciences, 2015
Comparison of a designed virtual oscilloscope with a real oscilloscope
Gozde Tektasa and Cuneyt Celiktas
Ege University, Faculty of Science, Physics Department, 35100, Bornova, Izmir, Turkey
Abstract. A virtual oscilloscope based on LabVIEW software was designed. Sinus, square and triangle shaped signals produced by
a function generator were analyzed with a real and a virtual oscilloscope. Amplitude, rise time and fali time values of a signal were
determined for different time/division values in both type oscilloscopes. Obtained values in the virtual oscilloscope were compared
with those of the real oscilloscope. It was deduced from the results that amplitude, rise time and fali time values and signal shapes
were compatible with each other.
1 Introduction
2 Material and methods
LabVIEW, Laboratory Virtual Instrument Engineering
Workbench, is a programming environment in which programs
are created by using a graphical notation. It is based on
graphical programming. LabVIEW software can command
plug-in data acquisition devices to acquire or generate signals.
It also facilitates data transfer over a GPIB (General Purpose
Interface Bus) or a serial port [1]. Its graphical nature makes it
ideal for test and measurement, instrument control, data
acquisition and data analysis applications [2].
An oscilloscope is a voltage sensitive electronic instrument
that is used to visualize certain voltage signals. An
oscilloscope can display the variation of a voltage signal in
time on the oscilloscope’s screen [3]. Time and amplitude
values of the signal can be determined by means of the
oscilloscope.
A virtual instrument consists of a Computer, a software
and a hardware. They are combined and confígured to emulate
the function of traditional hardware instrumentation. Virtual
instruments are extremely ílexible, powerful and cost-effective
[1].
An oscilloscope can be used for amplitude, rise time and
fali time measurements of a signal. The amplitude is the height
of a pulse in volt unit as measured from its maximum value to
its instantaneous baseline. The rise time is the time it takes for
the pulse to rise from 10 to 90% of its íull amplitude. The fali
time is the time it takes for the pulse to fali from 90 to 10% of
its full amplitude [4].
Since a virtual oscilloscope which is a kind of virtual
instruments can be developed by LabVIEW software, it was
designed through the program in this study. Sinus, square and
triangle shaped signals were analyzed with a real and a virtual
oscilloscope. Amplitude, rise time and fali time values of the
signals obtained from the real and virtual oscilloscopes were
compared. According to the obtained results, the virtual
oscilloscope was in highly compatible with the real
oscilloscope in terms of amplitude and time measurements and
the signal shapes.
In this study, a GW Instek 2204 type oscilloscope as a real
oscilloscope and a Hung Chang sweep function generator
(9205C) as a signal source were used. Block diagram for the
measurement is shown in Figure 1.
a
Figure 1. Block diagram for the measurement. (DSO: Digital
Storage Oscilloscope, VI: Virtual Instrument, GPIB: General
Purpose Interface Bus).
As can be seen in the block diagram, after sinus, triangle
and square signals which were selected altemately from the
function generator were displayed in the real oscilloscope; they
were transferred from the real oscilloscope to the virtual
oscilloscope by GPIB connection. Time/division values ranged
from 1 ps to 250 ps of the real and the virtual oscilloscopes
were analyzed. During the measurement, volt/division value of
each oscilloscope was kept steady on 2V. Frequency of the
function generator was set about 155 kHz for the 1.0, 2.5, 5.0
and 10 ps time/division values. Since the signals stayed out of
the oscilloscope screen for the 25, 50, 100 and 250 ps
time/division values, its frequency was decreased about to 13
kHz. In both oscilloscopes, time/division values were switched
separately, and then amplitude, rise time and fali time values
of the signals were determined.
Corresponding author: [email protected]
This
is anavailable
Open Access
article distributed under the termsorofhttp://dx.doi.org/10.1051/epjconf/201510004004
the Creative Commons Attribution License 4.0, which permits unrestricted use,
Article
at http://www.epj-conferences.org
EPJ Web of Conferences
For 25 ps time/division value, as an example, signal images
obtained from the virtual and the real oscilloscope are shown
inFig.2.
Sinus signal was fírst selected from the generator.
Amplitude, rise time and fali time values of the signal versus
different time/division values ranging from 1.0 ps to 250 ps are
given in Table 1.
Triangle signal was secondly used. Obtained data from the
real and the virtual oscilloscopes are presented in Table
2.
Finally, the square signal was displayed in the virtual and
the real oscilloscopes, and the data from the oscilloscopes can
be seen in Table 3.
Figure 2. (a) Sinus, (b) triangle and (c) square signal shapes for 25 ps time/division in the virtual oscilloscope and the real oscilloscope.
Table 1. Amplitude (Vamp), rise time (TR) and fali time (TF) values for the sinus signal in the real and the virtual oscilloscopes.
Real Oscilloscope
Virtual Oscilloscope
Time/Division(ps)
Vamp(V)
TR (ps)
TF (ps)
Vamp (V)
TR(ps)
TF (ps)
1.0
5.760
1.824
1.772
5.760
1.824
1.772
2.5
5.760
1.883
1.800
5.760
1.883
1.800
5.0
5.760
1.864
1.799
5.759
1.864
10.0
5.760
1.938
1.929
5.760
1.938
1.798
1.929
25.0
5.680
21.750
20.860
5.681
21.750
20.870
50.0
100.0
5.840
5.760
21.810
21.330
21.980
22.300
5.840
5.760
21.820
21.340
21.990
22.300
250.0
5.840
24.240
23.990
5.840
24.250
23.990
Table 2. Amplitude (Vamp), rise time (TR) and fali time (TF) values for the triangle signal in the real and the virtual oscilloscopes.
Real Oscilloscope
Virtual Oscilloscope
Time/Division(ps)
Vamp(V)
TR(ps)
TF (ps)
Vamp (V)
TR(ps)
TF (ps)
1.0
4.960
2.388
2.424
4.960
2.388
2.424
2.5
3.840
1.871
1.927
3.840
1.871
1.927
5.0
5.120
10.0
4.720
25.0
3.440
50.0
100.0
4.320
4.080
250.0
3.760
2.504
2.431
5.120
2.504
2.431
2.255
2.218
4.720
2.255
2.218
20.260
19.800
3.440
20.270
19.800
24.900
22.920
23.940
24.070
4.320
4.080
24.900
22.920
23.940
24.070
21.360
21.980
3.759
21.360
21.980
Table 3. Amplitude (Vamp), rise time (TR) and fali time (TF) values for the square signal in the real and the virtual oscilloscopes.
Real Oscilloscope
Virtual Oscilloscope
Time/Division(ps)
Vamp(V)
TR(PS)
TF (ps)
Vamp (V)
TR(PS)
TF (ps)
1.0
5.20
76.68
86.85
5.20
76.69
86.83
2.5
5.28
143.40
144.20
5.28
143.40
144.20
5.0
5.20
165.00
162.50
5.20
165.10
162.50
10.0
5.20
550.90
550.00
5.20
550.90
549.80
25.0
5.20
787.80
787.80
5.20
787.90
787.90
50.0
100.0
5.28
5.28
1625.00
3200.00
1600.00
3200.00
5.28
5.28
1625.00
3200.00
1600.00
3200.00
04004-p.2
TESNAT 2015
250.0
5.28
8123.00
8123.00
5.28
8124.00
8124.00
3 Results and discussion
Sinus, triangle and square signals from a function generator were used to compare the results from both real and virtual
oscilloscopes. Amplitude, rise time and fali time values of the signals were determined from both oscilloscopes. According to the
results in the Table 1, Table 2 and Table 3, amplitude, rise time and fali time values from the virtual oscilloscope were hig hly
accorded with those of the real oscilloscope. Besides, it was observed that signal shapes in both type oscilloscopes were mostly
the same as each other. It was concluded that the designed virtual oscilloscope can be used as a real oscilloscope for the
determination of amplitude, rise time and fali time values.
References
1. J. Travis and J. Kring, LabVIEW for Everyone: Graphical
Programming Made Easy and Fun (Third Edition, Prentice
Hall, U.S.A., 2006)
2. R. Bitter, T. Mohiuddin and M. Nawrocki, LabVIEW
Advanced Programming Techniques (Second Edition, Taylor
and Francis Group, Boca Raton, Florida, 2007)
3. NotesonOscilloscope,
http://www.eee.metu.edu.tr/~ee214/documents/Note sOnOscilloscopes.pdf
4. R.W. Leo, Techniques for Nuclear and Particle Physics Experiments (Springer-Verlag Berlin Heidelberg, Germany, 1987)
04004-p.3
EPJ Web of Conferences 100, 04001 (2015)
DOI: 10.1051/epjconf/ 201510004001
© Owned by the authors, published by EDP Sciences, 2015
Investigation of temperature dependence of semiconductor detectors
used in medicine for radiation measurements
Simay Ozleyis Altunkok1, Nina Tuncel2'a and Nazim Ucar1
1
2
Süleyman Demirel University School of Science, Department of Physics, Sparta, Turkey
Akdeniz University School of Science, Department of Physics, Antalya, Turkey
Abstract. In this study, the temperature dependence of p-type semiconductor diodes that are a part of in-vivo dosimetry system
was assessed in Co-60 photon energy. The collimator and gantry angle on zero degree, SSD 100 cm, field size 20x20 cm 2 was
selected. The IBA EDP-5, EDP-10 and EDP-20 diode types that included in this study have different thickness of build-up material
so the depth of measurements at water equivalent phantom by FC65-p ion chamber was selected at 5, 10 and 20 mm. Along the
process the room and phantom temperature was measured and recorded (19°C). The special water fílled PMMA phantom was
used for diode set-up on its surface and a thermometer for determine phantom temperature was employed. Each type of diodes
irradiated separately for one minute and the signal to dose sensitivity and calibration was performed at room temperature (19°C)
by OmniPro- InViDos software with DPD-12 electrometer. Examination was repeated from 33°C to 20°C temperatures. The
temperature correction factors were found from slope of the linear drawings for each diode types. The obtained correction factor
for EDP-5 and EDP-10 was 0.29 %°C/cGy and 0.30 %°C/cGy respectively, that higher than recommended factor (%0.25°C/cGy).
While the more fluctuation for EDP-20 was realized.
1 Introduction
In vivo dosimetry is effective method for fínding several types
of common errors, such as errors in data transfer or manual
adjustments of the treatment plan in radiation therapy [1-3]. It
is therefore, a recommended quality assurance (QA) procedure
[4-6]. The use of diodes for in vivo dosimetry is described in
several publications [7-9]. Both n-type or p-type Silicon diodes
are commercially available, but only the p-Si type is suitable
for radiotherapy dosimetry, since it is less affected by radiation
damage and has a much smaller dark current. Diodes are used
in the short circuit mode with an electrometer, since this mode
exhibits a linear relationship between the measured charge and
dose. They are relative dosimeters and should be calibrated by
applying several correction factors if used as an absolute
dosimeter. For instance, the sensitivity of diode on temperature
could be calculated by S=M/D equation. M is the total charge
collected by diode during the irradiation and D is the absorbed
dose. Diodes for entrance and exit dose measurements on
patient skin are provided with build-up encapsulation and
hence must be appropriately chosen, depending on the type and
quality of the clinicai beams [10]. The real-time in-vivo
dosimetry by diode allows checking the prescribed dose for
dynamic beam immediately and makes it possible to correct
the treatment errors interactively [11-13]. Since 1994, Howlett
et al. [14] have shown that the entrance dose measurement by
a
utilizing p-type diodes at photon beams is an effective method
of providing an independent verifícation of dose delivery
accuracy. Diodes show a variation in dose response with
temperature (particularly important for long treatments),
dependence of signal on the dose rate (for different source-skin
distances), angular (directional) dependence and energy
dependence even for small variation in the spectral
composition of radiation beams (important for the
measurement of entrance and exit doses) [10].
In this study, the temperature dependence of p-type
semiconductor diodes that are a part of in-vivo dosimetry
system was assessed in Co-60 photon energy.
2 Materials and methods
The dose measurements in Theratronix Co-60 treatment unit,
model Theratron 1000-E, were performed (Fig. 1). The mean
energy of two gamma ray counterpart with two beta decay is
evaluated 1.25 MeV as mono energy gamma for this
radioisotope. For in-vivo entrance dose measurements, the
diode is calibrated under a standard condition before it is used
as an absolute dosimeter. The main correction factors which
influence the diode response during the entrance dose
measurements are temperature, field size, source to skin
distance (SSD),
Corresponding author: [email protected]
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution,
and reproduction in any medium, provided the original work is properly cited.
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510004001
EPJ Web of Conferences
gantry angle (beam direction) and presence of other beam
modifiers such as wedges and trays. The collimator and gantry
angle was set on zero degree, and the field size at 100 cm SSD
was 20x20 cm2. So, by using this field the irradiation of diode
groups was applicable at the same time for assessing
temperature dependence. The IBA 3G- pSi diode detectors that
included in this study were EDP- 5, EDP-10 and EDP-20 (Fig.
2). The diode die (chip) usually has inherent build-up material
placed around the die. The build-up material type and its
thickness are chosen in such a way that the effective depth of
the measurements is closer to the depth of the maximum dose
of the megavoltage photon energy used. The inherent build-up
material is usually made of high Z material so that the physical
thickness can be less than that of water- equivalent thickness
[9]. The build-up material of EDP-5 is 5mm thickness
polystyrene with epoxy encapsulation. For EDP-10 and EDP20 build-up material is stainless steel with epoxy encapsulation
that is equivalent to 10 and 20 mm water thickness
respectively. So, the depth of measurements at water
equivalent phantom was 5, 10 and 20 mm.
temperature reached to 33 oC, then the measurements were
started. The manufacturer, IBA, recommended the global
correction factor as %0.25°C/cGy. The software did not use
this factor if the input temperature stood in 19°C. By this way,
the dose readings of diodes reflect the dependence to
temperature separately. This examination was repeated at
30°C, 26°C, 24°C, 23°C, 22°C, and 20°C temperatures. The
dose response of each diode based on temperature was tailored.
3 Results
The dose response of each diode types regarding to
temperature which irradiated at Co-60 treatment unit was
evaluated by a linear function. The equations and their
regression parameter were obtained. Then, the temperature
correction factor of each diode occurred by calculation of the
slope of each line. The linear equations and their regressions
for four diodes of EDP-5, two diodes of EDP-10, and four
diodes of EDP-20 types have been shown in Fig. 3 (a), (b) and
(c), respectively. The average of the slope value was calculated
as %0.29, %0.30 and %0.18°C/cGy for EDP-5, EDP-10 and
EDP- 20 respectively (Table 1).
Table 1. The temperature correction factor for each diode type
Diod
Types
EDP-5
EDP-10
Figure 1. Theratronix Co-60 treatment unit.
EDP-20
Serial No.
Corr. Factor
(%°C/cGy)
4505
4506
4507
4508
4955
4957
5401
5402
5403
5404
0.29
0.29
0.27
0.29
0.29
0.30
0.25
0.13
0.19
0.14
Mean
0.29
0.30
0.18
4 Discussion and conclusion
Figure 2. The IBA special phantom with thermometer and EDP-5,
10 and 20 type diodes.
Along the dose measurement process the room and
phantom temperature was measured by external in-touch
thermometer and recorded as 19°C. The special water filled
PMMA phantom produced by IBA was used for diode set-up
on its surface and a thermometer for determine phantom
temperature was employed. Each type of diodes was irradiated
separately for one minute and the signal to dose sensitivity and
calibration was performed at room temperature (19°C) by
OmniPro- InViDos software with DPD-12 electrometer. By
using IBA FC65-p ion chamber and Dose 1 electrometer the
absolute dose was obtained at 5 cm and then the dose at request
depths were calculated. For temperature dependence
examination the hot water added to special phantom while its
The sensitivity variation with temperature of dosimetry diodes
is well-known and the temperature-dependence in p-type
silicon detectors has also been well described in the literature
[15-16]. The diode response variation over time to normal
body temperature exposure was evaluated using a 20x20 cm 2
field size at a 100 cm SSD at Co-60 gamma energy. Under
normal conditions, the body skin temperature is approximately
around 33°C. Therefore, the diodes which were initially at
normal room temperature 19°C were placed on the surface of
special phantom. The water temperature was raised to a
temperature equal to 33°C and was allowed to stay in thermal
equilibrium with the surrounding. This experiment simulates
clinically the thermal effect on the diode when it comes in
contact with patient skin. In these experimental conditions, the
temperature of the water bath is different from the temperature
of the diode. Even after the equilibrium, the temperatures
might differ from each other. In our clinicai setting, the diode
does not stay in contact with the patient skin for more than 2
minutes. But in the especial cases such as total body irradiation
the test dose delivery was took placed after the diode was
placed on the surface over a period duration of 3-5 minutes and
then the total dose delivery was performed. For the next
04001-p.2
TESNAT 2015
position the test dose delivery were done when they were yet
placed on the surface so the total duration of diodes in touch
with skin was more than 30 minutes. Therefore, based on our
experimental results we concluded that for these diode series
and under the especial experimental and clinical conditions,
the temperature correction factors are important.
Acknowledgement
The Authors would like to thanks all our collaborators from
radiation oncology department in Akdeniz University.
References
1.
2.
3.
4.
G. Leunens, et al., Radiother. Oncol. 23, 4 (1992)
A. Noel, et al., Radiother. Oncol. 34, 2 (1995)
J.H. Lanson, et al., Radiother. Oncol. 52, 1 (1999)
ICRU Report 24., International Commission on Radiation
Units and Measurements, Oxford: Universitypress,
(1976)
5. NACP, Recommendations by the Nordic Association of
Clinicai Physics (NACP). Acta Radiol. Oncol. 19,
1(1980)
6. G.J. Kutcher, et al., Med. Phys. 21, 4 (1994)
7. J. Van Dam and G. Marinello, Booklet no:l, ESTRO,
Brussels(1994)
8. D.P. Huyskens, R. Bogaerts, J. Verstraete, et al., Booklet
no:5, ESTRO, Brnssels (2001)
9. AAPM Report 87, Medicai Physics Publishing, Madison
(2005)
10. J. Izewsk and G. Rajan, Chapter 3: Radiation
Dosimeters,quality assurance of externai beam
radiotherapy. In: Radiation Oncology Physics: A
Handbook for Teachers and Students. (Ed. E.B.
Podgorsak) STI/PUB/1196. pp. 71-99. IAEA, Vienna,
Áustria (2005)
11. G. Rikner, E. Grusell, Phys. Med. Biol. 28, 11 (1983)
12. G. Rikner, Ph.D. Thesis, Uppsala University, Sweden
(1983)
13. G. Rikner and E. Grusell, Phys. Med. Biol. 32, 9 (1987)
14. S. Howlett, L. Duggan, S. Bazley, T. Kron, Medicai
Dosimetry 24, 1 (1999)
15. E. Grusell and G. Rikner, Phys. Med. Biol. 31, 5 (1986)
16. J. Van Dam, G. Leunens, and A. Dutreix, Radiother.
Oncol. 19,4(1990)
Figure 3. The dose temperature dependence curve and the
linear function of each diode to temperature for (a) EDP-5, (b)
EDP-10, and (c) EDP-20 type.
The temperature correction factors were found from slope of
the linear drawings for each diode types. These factors for
EDP-5 and EDP-10 was 0.29 %°C/cGy and 0.30 %°C/cGy
respectively, that higher than recommended factor 0.25
%°C/cGy by OmniProInViDos manufacturer. While the more fluctuation for EDP20 was realized.
According to our experience the heat equilibrium that
detected indirectly does not reflect the diode temperature based
on the variety on design of each diode type. It will be
recommended to applying the direct temperature of each diode
that electronically measured by system as an input to software.
On the other hand it will be preferred to rewrite the software
that is able to accept the temperature for each diode type and
then separate temperature calibration factor for each diode will
be calculated and possessed.
04001-p.3
EPJ Web of Conferences 100, 04002 (2015)
DOI: 10.1051/epjconf/ 201510004 002
© Owned by the authors, published by EDP Sciences, 2015
Determination of environmental gamma radiation in Bitlis
Sultan Sahin Bala and Sule Karatepe
Bitlis Eren University, Physics Department 13000, Bitlis , Turkey
Abstract. In this study; the environmental gamma radiation at the various points (16 points) in the districts of and in Bitlis,
where it was located in the Turkey Eastem Anatolia region, were measured. The environmental gamma radiation measurement
was made from two leveis (the ground and one meter above the surface) by using portable gamma survey meter which consisted
of 2"x2" scintillation detector (Nal(Tl)). The obtained data were discussed in considering the geological structure of the region
and the other factors.
1 Introduction
There are two main contributions determining the levei of
exposure to natural radiation. The fírst of these are highenergy cosmic rays reaching to the earth's atmosphere. The
other is that there are radioactive elements in the crust of the
World (environment, even in the human body) [1]. The
contribution of natural radiation of cosmic rays varies with
altitude. As one climbs up from sea levei to remain constant in
certain latitude [2].
The basic leveis of natural radiation varies depending on
the geological and geographical features of area. Soil and rock
mineralogical structure with geographical altitude affects the
basic radiation leveis in the region [3].
Natural radionuclides as 238U, 232Th and 40K in the soil
causes to be radioactive of the soil. Natural radionuclides are
mostly found in high concentrations in volcanic rocks
(especially in granite), pegmatites and hydrothermal deposits.
Water constantly interact with the soil and rocks around it.
Therefore, the transfer possibility of interacting waters with
them of the natural radionuclides in the soil and rocks is very
high [4].
Soils contain an amount of radiation due to radioactive
isotopes contained in incurred main material. Radionuclides
that are naturally present in the earth's crust formation and their
degradation products form the major part of the environmental
radiation with spread gamma rays. X, y and z as Long-lived
radionuclides as 238U, 232Th and 40K is beginning of source of
the radiation of terrestrial origin. The mass activity
concentration of these natural radionuclides varies according
to the type of soil and rock [5-7]. The mass activity
concentration is radiation intensity corresponds to the absorbed
dose in the air on 1 m height from the ground [5]. Thus, the
measured radiation dose in the air is closely related to
concentrations of radionuclides in the soil.
In this study Environmental gamma measurements was
a
conducted in Bitlis. Bitlis was founded as the cities of the
valley on that a natural passageway connects the Southeastem
Anatolia to Eastem Anatolia on the borders of the up Firat and
the up Murat regions of the Eastem Anatolia Region [8].
Figure 1. The map of the Bitlis and its counties
2 Experimental
The environmental gamma measurements in the various
locations (16 points) in Bitlis was made by Dose Rate Meter
that it is containing scintillation counter having to 2"x2" NaI
(Tl) crystal at ground and lm high leveis [9]. The city center
and its counties were easily screened because used system is
portable.
3 Results and Discussion
Environmental gamma measurements were taken monthly
periods on the ground and lm above the ground leveis.
Locations of 16 points on the Bitlis, where environmental
gamma measurements were conducted are presented in Table
1. The measurements made 1 m above the soil levei and the
ground are presented in Table 2.
Corresponding author: [email protected]
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution,
and reproduction in any medium, provided the original work is properly cited.
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510004002
EPJ Web of Conferences
Table 1. Location of environmental gamma measurement
points.
Latitude (North)
38.33451
38.32286
38.33052
38.41749
38.41745
38.41175
38.58592
38.39302
38.39928
38.48519
38.63133
38.84262
38.78785
38.74583
38.66603
38.63527
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
XII
XIII
XIV
XV
XVI
Longitude (East)
42.00472
42.01657
42.01483
41.91641
41.91586
42.11722
42.00056
42.26883
42.26320
42.32428
42.44054
42.82970
42.69599
42.45415
42.30422
42.24807
According to the data in Table 2; the measurements made
in 1 m above the soil levei and the ground from June to
November are shown in Figs. 2-4.
Figure 2. Environmental gamma variation at ground (n) and lm
levei (o) on the 16 points in the June and the July.
Table 2. Formatting sections, subsections and subsubsections.
I
II
III
IV
V
Ground
0.250
0.251
0.237
0.242
0.196
lm
0.244
0.237
0.244
0.233
0.186
Ground
0.256
0.284
0.247
0.254
0.204
lm
0.237
0.266
0.238
0.239
0.196
August
(pSv/h)
Ground
lm
0.308
0.302
0.354
0.346
0.269
0.258
0.271
0.271
0.219
0.218
VI
VII
VIII
IX
0.388
0.245
0.251
0.219
0.382
0.225
0.238
0.214
0.399
0.280
0.290
0.291
0.384
0.263
0.274
0.286
0.436
0.295
0.311
0.332
0.448
0.302
0.307
0.312
0.442
0.294
0.268
0.313
0.442
0.286
0.257
0.303
0.382
0.256
0.265
0.292
0.369
0.241
0.247
0.268
0.361
0.245
0.239
0.268
0.352
0.231
0.227
0.246
X
XI
0.316
0.313
0.291
0.300
0.352
0.333
0.344
0.323
0.377
0.319
0.359
0.322
0.334
0.403
0.316
0.379
0.316
0.364
0.300
0.347
0.300
0.322
0.264
0.299
XII
XIII
XIV
0.360
0.196
0.325
0.341
0.187
0.289
0.353
0.156
0.301
0.343
0.139
0.295
0.303
0.156
0.308
0.306
0.151
0.287
0.350
0.147
0.306
0.343
0.143
0.279
0.335
0.144
0.285
0.306
0.128
0.276
0.352
0.139
0.286
0.320
0.132
0.281
XV
XVI
0.346
0.404
0.321
0.375
0.324
0.478
0.302
0.453
0.337
0.527
0.307
0.485
0.300
0.435
0.307
0.401
0.291
0.416
0.272
0.397
0.296
0.380
0.256
0.367
June (pSv/h)
July (pSv/h)
September (pSv/h)
October (pSv/h)
Ground
0.250
0.260
0.223
0.264
0.197
lm
0.247
0.249
0.219
0.262
0.202
Ground
0.230
0.259
0.198
0.242
0.165
lm
0.216
0.242
0.186
0.225
0.157
04002-p.2
November
(pSv/h)
Ground
lm
0.205
0.205
0.288
0.255
0.195
0.193
0.226
0.207
0.146
0.140
TESNAT 2015
Figure 3. Environmental gamma variation at ground (n) and
lm levei (o) on the 16 points in the August and the September.
Figure 4. Environmental gamma variation at ground (n) and
lm levei (o) on the 16 points in the October and the November.
It is understood from Table 2, Figs. 2-4 that the values in
ground levei, where gamma radiation is directly emitted from
the soil, were higher than the values that were measured atlm
levei. It was seen that the measured environmental gamma
values on XVI point measurement point in the both ground and
1 m levei were highest and the measured environmental
gamma values on XIII point were the lowest. However, it was
found that 68.8 % of the measured environmental gamma
values on measurement points in the both ground and 1 m levei
were highest value in August and their 75 % were the lowest
value in November.
XVI numbered measuring point is located higher than the
other measuring points. The height of this point is 2.935 m and
XVI point is determined on a mountain that it is volcanic
mountain that stood the latest activity in Turkey. To be this way
of results is the expected case because the contribution to
natural radiation of cosmic rays varies with height, this
contribution remains constant moving up sea levei on certain
latitude [2], more elevation locations are exposed to more
radiation than less elevation locations [10].
Cosmic radiation is consists of electromagnetic radiation
or released particles at different energy and different charges.
Their origins are also different. Their density decreases when
it reaches the upper layers of the atmosphere to sea levei [2,11].
Being the lowest of environmental gamma values measured at
the measurement point XIII may be caused by less effect of
electromagnetic waves (this point is further away from the
other point of to residential areas) and not intense
electromagnetic reflections.
According to UNSCEAR (1993, 2000) report, the global
average of the measured gamma dose rate ranged from 10 to
200 nGyh'1. In this study, the averages of measurements taken
at ground levei are 291.01 nGyh'1 and the averages of
measurements taken at 1 m levei are 277.68 nGyh' 1. When the
obtained results are compared with gamma dose rate average
values world; it is seen that the gamma dose rates in counties
of it and Bitlis is at a levei above the world average. The cause
of the high leveis of gamma dose rates may be geological
features of the region, the absence of fault zones and the
residential area of higher altitudes. The radioactivity on the
fault zone is generally higher than other places, and
radioactivity can be changed with the seismological aspects of
activity of the fault [7].
4 Conclusions
Environmental gamma values were measured low progressed
towards the winter season due to not to perpendicular and of an
angle the sun's rays begin to come to earth.
Environmental gamma values measured at 1 m distance
gives information about the concentration of radioactivity in
the soil of the measurement point [7]. According to this study,
the average gamma dose rate values of Bitlis and counties were
measured approximately 0.28 pSvh'1.
Acknowledgement
This work was supported by BEBAP with project number is
2014.06.
References
1.
2.
3.
S. Kaya, S.M. Karabudak, U. Çevik, GUSTIJ, 5 (1), 2433 (2015)
UNSCEAR, Sources and effects of ionizing radiation.
Report to General Assembly, with Scientific Annexes
(United Nations, 2000)
M. Degerlier, V. Peçtemalci, Ç.Ü J. Sei. Eng., 5, 27
(2012)
4. S. §ahin Bal, M. Dogru, IZYEF, 71 (2012)
5. G. Karahan, PhD Thesis (ITU, Nuc. Ener. Ins., 1997)
6. H.L. Beck, II. USERDA Conf.-720805-P2, 101-104
(1982)
7. S. §ahin, Ph.D. Thesis (FU, Ins. of Sei. Tech., 2009)
8. H. Gür, F. Yildirim Sonmez, M. Ay, Bitlis Province
Environmental Status Report (2012)
9. LUDLUM Model 44-10 Gamma Scint. (Ludlum
Meas.Inc., 2012)
10. S. §ahin, S. Niksarlioglu, M. Yilmaz, FUJS, 22 (2), 101-
04002-p.3
EPJ Web of Conferences
107 (2010)
11. UNSCEAR, Sources and effects of ionizing radiation.
Report to General Assembly, with Scientific Annexes
(United Nations, 1993)
04002-p.4
EPJ Web of Conferences 100, 0300 5 (2015)
DOI: 10.1051/epjconf/ 20151000300 5
© Owned by the authors, published by EDP Sciences, 2015
An investigation on some of the tumor treatment cases using x-rays and
electron beams
Burcu Ucar1, Ibrahim Yigitoglu1’3, IpekArsIan Kabalay2, Duygu Altiparmak1 and Sinem Kilicaslan1
1
2
Gaziosmanpasa University, Faculty of Science and Arts, Department of Physics, 60240 Tokat, Turkey
Gaziosmanpasa University, Faculty of Medicine, Department of Radiation Oncology, 60100 Tokat, Turkey
Abstract. In this work, we discussed some of the applications which X-rays and electron beam used in radiotherapy for tumor
treatments. This study has been performed at Radiation Oncology Department, Medicine Faculty in Gaziosmanpasa University
by using the VARIAN CLINICA DHX linear accelerator which is operated in the range of 6 MeV - 15 MeV. Processes for the
treatments that X-rays used for pancreas, bladder and prostate tumors and the processes that the electron beam used for some of
the derm tumors are studied. Effects of X-rays and electron beams to treatments process are examined and the obtained results
are presented comparatively.
1 Introduction
Radiation can be defined as particle radiation and the
electromagnetic waves. Alpha, beta, nêutron and heavy ions
are particle radiation. The wave radiations (photons) are
gamma, X-ray, ultraviolet, visible light, infrared and radio
waves [1].
The discovery of X-rays leads to important developments
in physics and medicai Science. It is also give rise so called
nuclear physics and radiology. X-rays was discovered in 1895
by Wilhelm Conrad Rontgen. In order to produce X- rays fírst
free electrons must be produced then they must be accelerated
and must be collided to a target [2]. It is discovered in 1900
that X- rays are harmful to human tissue but also it is
recognized that it can be used to scale down the malignant
tumor or even to remove it all from the body [3]. The electrons
are also used in radiotherapy for treatment purposes.
Radiotherapy is the method used in treating cancerous
tissue with electromagnetic waves and particle radiation. The
aim of radiotherapy is to apply the maximum dose the
cancerous tissue and apply the minimum dose to criticai organs
to protect the criticai organ around the cancerous tissue as
possible.
In order to make a good treatment planning in radiotherapy
the concept of tumor volume terms should be known. This
volume terms is expressed by the concept ICRU 50
(International Commission on Radiation Units and
Measurements) and ICRU 62 (1999) protocols [4].
The concept of this volume; Gross Tumor Volume (GTV),
Clinicai Target Volume (CTV), Planning Target Volume
(PTV), Treated Volume (TV), Irradiated Volume (IV), Organ
at Risk (OAR) and Planning Organ at Risk Volume (PRV).
a
Figure 1. The schematic view ofICRU50 and ICRU62 volume
terms.
In addition, the determined dose during radiotherapy can
be administered to patient accurately and to obtain the planned
dose distribution the appropriate position to the patient must
be given, patient movements must be minimized and it is
required that the patients always must be in the same position
during the treatment [5].
2 Material and methods
X-Ray beam with 6 MV and 15 MV energies and electron
bundles between 6 MeV and 18 MeV was produced by Varian
Clinac DHX model 5576 linear accelerator device in
Gaziosmanpasa University Medicai Faculty Oncology
Department.
Radiotherapy process, used in X-ray treatment for 5
"prostate câncer" patients and 4 "bladder câncer" patients
while the electron beam treatment is applied to 4 "derm
câncer" patients. The absorbed dose amount was checked and
the amount of X-ray that criticai organs were exposed checked
and compared.
Linear Accelerator devices are used for producing X- ray
by increasing the electron energy by using high frequency
electromagnetic fíelds through a long tube [6].
[email protected]
This
is anavailable
Open Access
article distributed under the termsorofhttp://dx.doi.org/10.1051/epjconf/201510003005
the Creative Commons Attribution License 4.0, which permits unrestricted use,
Article
at http://www.epj-conferences.org
EPJ Web of Conferences
High energy electron bundles can be used for treatments of
surface tumors while the X-rays that are reproduced by the
electrons hitting to a target are used for the treatment of the
tumors that located deeper in the body [7].
In this study two different cases where the X-rays and case
where the electron bundles are investigated.
3 Results
In this work by obtaining IMRT planning dose-volume
histograms for fíve prostate, four bladder and four derm
patients, the irradiation of target volume (PTV) and absorbed
dose of criticai organs around are compared. In this
comparison the mean dose, min. and the max. dose values are
investigated. The homogeneity index which is a measure of
dose homogeneity is the ratio of the maximum absorbed dose
of the whole target volume to the 95 % maximum absorbed
dose.
PTV
HI = max
(1)
Figure 3. The IMRT planning dose-volume histogram for the fífth
patient. The line colors red, orange, brown, and yellow present CTV,
PTV66, rectum and bladder, respectively.
Table 1. The min, max and mean dose distributions for prostate
patients.
PTV
Patient
No
PTV95
PTVmm is max. dose values of PTV and PTV-, the
iiidx
ninety fíve percent ofPTV is the dosage value [4].
VJ
1
2
3
4
5
Y
3.1 The prostate tumor
In this treatment a 6 MV photon beam is applied 5 different
prostate tumor patients, choosing 7 area locations in order to
protect criticai organs by using the IMRT planning technic A
daily dose of 2 Gy to all patients has been implemented for 33
days. The iso-dose curves for the fífth prostate patient can be
seen in Fig. 2 [8].
Volume
(cmA3) Min dose
(cGy)
372
6404
390
6323
320
6452
303
6049
379
4730
Max dose
(cGy)
6992
6971
7163
7036
7072
Mean dose
(cGy)
6829
6902
6911
6745
6690
seen in Fig. 4.
Figure 4. The treatment planning using IMRT technic for the fírst
bladder patient.
The histogram in Fig. 5 for the fírst patient the PVT min
dose is 4855 cGy, max dose 5280 cGy and the mean dose 5072
cGy [9],
Figure 2. The treatment planning using IMRT technic for the fífth
prostate patient.
The histogram in Fig. 3 for the fífth prostate patient the
PVT min dose is 4730 cGy, max dose 7072 cGy and the mean
dose 6690 cGy [9].
The PTV min, max and mean volume dose distributions for
the 5 prostate patients can be seen simultaneously in Table 1.
3.2 The bladder tumor
In the treatment of 4 different bladder tumor patients, a 6 MV
photon beam is applied, choosing 7 area locations in order to
protect criticai organs and the IMRT planning technic is used.
A daily 2 Gy dose for all patients has been implemented for 25
days. The iso-dose curves for the fírst bladder patient can be
03005-p.2
TESNAT 2015
Figure 5. The IMRT planning dose value histogram for the first patient.
The line colors red, brown, orange, pink, and yellow present bladder,
rectum, prostate, LN and PTV-rectum respectively.
Figure 6. The treatment planning using IMRT technic for the third
derm patient.
The PTV min, max and mean volume dose distributions for
the 4 bladder patients can be seen simultaneously in Table 2.
Table 3. The hemogenic index values for PTV obtained ífom prostate
and bladder patients.
Table 2. The min, max and mean dose distributions for bladder
patients. ____________________________________________
HI (PTV)
Patient No
Prostate
Bladder
1
1.02
1.04
2
1.00
1.01
3
1.03
1.06
4
1.04
1.03
Mean
1.02
1.04
PTV
Patient No Volume
(cm3)
Min dose
(cGy)
Max dose
(cGy)
1
2
372
390
6404
6323
6992
6971
Mean dose
(cGy)
6829
6902
3
4
320
303
6452
6049
7163
7036
6911
6745
5
379
4730
7072
6690
Figure 7. The IMRT planning dose-value histogram for the
third patient. The line colors red present marker.
Table 4. Wire dose distributions in derm patients
TEL
Volume
Min dose
Max dose
Mean dose
Patient No (cmA3)
(cGy)
(cGy)
(cGy)
1
4.2
1712
3311
2629
2
5.2
23
3558
1915
Table 5. Marker dose distributions in derm patients
MARKER
Patient Volume
No
(cmA3)
1
1.8
2
3.5
Min dose
(cGy)
0
Max dose
(cGy)
3747
Mean dose
(cGy)
2685
2539
3988
3554
3.3 The derm tumor
4 Discussion
In the treatment of 4 different derm tumor patients, using the
IMRT planning technic, a 6 MV photon beam is applied, and
only one area location is selected. A daily 3 Gy dose of electron
treatment for 10 days for all patients has been implemented.
The data obtained from the third patient can be seen inFig. 6.
Thehistogramobtainedfromthemarker points inFig. 7 for
the third patient, the min dose is 4855 cGy, max dose 5280 cGy
and the mean dose 5072 cGy respectively.
The min, max, and the mean absorbed dose distributions
with wire belong to the patients who have practice surgery
before can be seen in Table 4.
The min, max, and the mean absorbed dose distributions
with marker belong to the patients who have not practice
surgery before can be seen in Table 5.
In this work, we discussed some of the applications which Xrays and electron beam used in radiotherapy for tumor
treatments. In this respect we apply X-rays on to prostate and
bladder tumors and electron beam on to derm tumors.
A 6 MV photon beam is applied 5 different prostate tumor
patients, choosing 7 area locations in order to protect criticai
organs by using the IMRT planning technic. A daily dose of 2
Gy to all patients has been implemented for 33 days. In Table
1 PTV, rectum and bladder min., max. and mean volume dose
distributions obtained from 5 prostate patients can be seen
simultaneously.
In the treatment of 4 different bladder tumor patients we
have used the same conditions as in prostate case except this
treatment have taken 25 days long. The
03005-p.3
EPJ Web of Conferences
obtained results belong to bladder tumor treatment can be seen in Table 2.
The minimum dose means the maximum dose absorbed by all the target volume (100 %). It is crucial that the maximum dose
is very close to the minimum dose to homogenize the PTV. It can be concluded that the maximum dose is so close to the minimum
dose which is planned to be irritated to the whole target volume when the Table 1 and Table 2 are compared. The criticai organs
absorbed few dose during the applications. The homogeneity index values for all prostate and bladder patients can be seen in Table
3. The mean homogeneity index value for prostate patients is HU1.02 while for bladder patients this quantity takes HU1.04 value.
It can be concluded from Table 3 that a hemogenic dose distribution is obtained. These values show good agreement with the
reference value HI=1 [4].
In the treatment of derm tumors the electron beam is applied to the patients. The absorbed electron beam doses can be seen in
Table 4 and Table 5. The results in Table 4 belongs to the patients who have practiced surgery before while the results in Table 5
belongs to the patients who have not practiced any surgery so far.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
J.E. Martin, Physics for Radiation Protection 2nd ed. ( Wiley- Vch Verlag, 2011)
G. Yulek, Radyasyon Fizigi ve Radyasyondan Korunma (SekYaymlan, 1992)
R. Uzel, Radyasyon Onkolojisininin Dünyada ve Ülkemizde Geliyme Süresi ve Bugünkü Durumu. Kanser Gündemi (1999)
ICRU 62 (International Commission on Radiation Units and Measurements). Prescribing, recording and reporting photon
beam therapy, ICRU, 4-13, (Washington).
H.Z. Kuru, E. Tavlayan, N. Olacak, D. Yalman ve B.A. Aras, Türk Onkoloji Dergisi , 27(3), 119-132 (2012)
F.M. Khan, The Physics of Radiation Therapy, 3nd. (Williams and Wilkins, 2003)
F.M. Khan, The Physics of Radiation Therapy, 2nd. (USA, 1994)
A. Suetens, et. al., Journal of Radiation Research, 56 (1), 11-21 (2015)
T. Ohno, et. al., Journal of Radiation Research, 56 (1), 128-133 (2015)
03005-p.4
EPJ Web of Conferences 100,0300 6 (2015)
DOI: 10.1051/epjconf/ 20151000300 6
© Owned by the authors, published by EDP Sciences, 2015
Problems in detection and measurement in nuclear medicine
Fatma Aysun Ugur3
Osmaniye Korkut Ata University, Department of Physics, Osmaniye, 80000, Turkey
Abstract. Nuclear Medicine studies are performed with a variety of types of radiation measurement instruments,
depending on the kind of radiation source that is being measured and the type of information sought. For example, some
instruments are designed for in vitro measurements on blood samples, urine specimens, and so forth. Others are designed
for in vivo measurements of radioactivity in patients. All these instruments have special design characteristics to optimize
them for their specific tasks, as described in this study; however, some considerations of design characteristics and
performance limitations are common to all of them. An important consideration for any radiation measurement
instrument is its detection efficiency. Maximum detection efficiency is desirable because one thus obtains maximum
Information with a minimum amount of radioactivity. Also important are instrument’s counting rate limitations. There
are finite counting rate limits for all counting and imaging instruments used in nuclear medicine, above which accurate
results are obtained because of data losses and other data distortions. Non penetrating radiations, such as B particles,
have special detection and measurement problems. In this study, some of these general considerations have been
discussed.
1 Introduction
Radioisotopes have made their unique contributions to
medicine because it is possible to detect the disintegration of
individual nuclei and hence to locate submicroscopic quantities
of a given material in body tissues or fluids. The physical
amount of radioactive tracer required to follow, for example, a
metabolic process is so small that it does not alter the process
itself[l].
The extreme sensitivity of radiation detection equipment is
a cardinal factor in the tracer procedures of nuclear medicine.
Hence, the choice and use of nuclear instrumentation plays a
vital part in the value and accuracy of the results obtained in
radioisotope tests [1].
2 Materials and Methods
Nuclear medicine studies are performed with a variety of
radiation measurement instruments, depending on the kind of
radiation source that is being measured and the type of
information sought. The practice of in vivo counting now
frequently faces the problem of the detection and the
quantitative assessment of low energy photon emitting
radionuclides in the body.
In general, it is desirable to have as large a detection
efficiency as possible, so that a maximum counting rate can be
obtained from a minimum amount of activity. Detection
efficiency is affected by several factors, including the
following:
a) The geometric efficiency, which is the efficiency with
which the detector intercepts radiation emitted from the source.
This is determined mostly by detector size and the distance
from the source to the detector.
b) The intrinsic efficiency of the detector, which refers to the
efficiency with which the detector absorbs incident radiation
a
events and converts them into potentially usable detector
output signals. This is primarily a function of detector
thickness and composition and of the type and energy of the
radiation to be detected.
c) The fraction of output signals produced by the detector that
are recorded by the counting system. This is an important factor
in energy-selective counting, in which a pulse-height analyzer
is used to select for counting only those detector output signals
within a desired amplitude (energy) range.
d) Absorption and scatter of radiation within the source itself,
or by material between the source and the radiation detector.
This is especially important for in vivo studies, in which the
source activity generally is at some depth within the patient [2].
It has been shown in a previous study [3] that currently
used concepts such as efficiency and background have to be
employed in a more precise way when the measurement of low
energy photons is considered. The counting efficiency
associated with a counting geometry and the point efficiency is
preferably used instead of intrinsic efficiency, which does not
consider the anisotropy of the detectors in use.
Too often, the efficiency is considered as the key parameter
to describe a counting device so that the detector with the
highest volume is often selected in several applications. This is
not correct in lower energy photon
Corresponding author: [email protected]
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510003006
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use,
EPJ Web of Conferences
range: a volume increase or an increased number of detectors
in an array always leads to an increase of the continuum. This
is proportional to the total volume of the detector, but the
effíciency is only increased when the added volume is
effectively active in detection of the photons exiting the body.
If the added volume only increases the continuum, the
detection limits are increased. In other words, a detection
volume that does not collect the examined photons, increases
the continuum without bringing information from the
investigated sources. It is better to look for a low detection limit
in the examined region than for a high effíciency in full energy
range. This means that the detector's size can advantageously
be tailored in accordance with the applications [4].
intrinsic effíciency (that is, the fraction of the incident rays
detected) and the effíciency for total absorption, called the
photofraction (Fig. 3).
For a scintillation detector using a sodium iodide crystal,
both the total and the photofraction effíciency are determined
by the energy of the radiation and the size of the crystal [1].
Figure 1. Intrinsic effíciency versus y-ray energy for Nal(Tl)
detectors of different thicknesses.
The size of the detector can be tailored to each application in
order to improve the response in terms of the ratio "Effíciency/
detection limit": the thickness can be adapted to the energy
range in order to decrease the detection limits (Fig. 1). Extra
thickness increases the continuum without bringing
information conceming the examined photopeak. A detector
thickness can be considered adapted to the energy when 50 to
90% of the incident photons are absorbed in the detector. The
same effect can be considered when the diameter is increased
in the measurement of a local deposition. The use of small
detector arrays instead of a large single one will provide an
opportunity to examine the spectrum from each detector
separately, to localize the deposition, to correct calibration
factor according to the burden geometry and to repeat the
burden calculation procedure with a better detection limit. (Fig2)
Figure 2. Examples of detector profiles with different complications
for the computations of total detection effíciency.
Radiation striking the sensitive portion of a detector may
be wholly or partially absorbed or it may pass right through the
detector. If a Geiger tube is used, the signal from the detector
is independent of the energy of the radiation, so that partial or
total absorption produce the same results. In a scintillation
detector the size of the detector output pulse is a function of the
energy lost by the gamma ray in the crystal. Therefore, for
scintillation detectors it is necessary to know both the total
Images of the distribution of radioactive material in organs
of patients are formed by looking at many small areas, either
one after the other (scanning), or simultaneously (a camera
technique). The quality, and hence the diagnostic value of the
resulting image or scan depends to a large extent on the size
and sharpness of outline of each of the areas or picture elements
and on the statistical accuracy of the data obtained from each
picture element. Obviously, the spatial defínition, often called
resolution, is improved if the size of each picture element is
reduced, just as a printed picture looks better if a fíner screen
is used on the printing plate. Making the picture element
smaller means that fewer counts will be recorded for that area
in a given time unless the dose to the patient is increased. Thus,
a compromise must be reached between spatial defínition and
Figure 3. Photofraction versus y-ray energy for cylindrical
Nal(Tl) detectors of different sizes.
the statistical validity of the information.
Determining the absolute effíciency (percentage of
disintegrations detected) of a radiation detector in a given
physical setup is a complex problem because of the many
factors of geometry and detector performance that must be
considered. For this reason, most radiation measurements are
relative rather than absolute; that is, they involve obtaining
count-rate data on an unknown sample (or patient) and on a
standard of the same radioisotope under as nearly identical
conditions as possible [2]. For example, a dose is measured
before administration to a patient, a subsequent blood sample
is counted later at the same position relative to the detector, and
the ratio of the two net count- rates represent the clinicai data.
In order to be able to make both the standard and the unknown
measurements as similar as possible, one must understand and
control all factors affecting the counting effíciency.
The fírst factor that must be considered is the portion of the
radiation produced in the sample or organ which interacts with
other atoms in the source and never gets outside. This process
03006-p.2
TESNAT 2015
is called self- absorption. Obviously, the standard and the
unknown should have similar self- absorption properties.
The attenuation by the tissues is indeed so important that
the measurement is affected by a serious lack of accuracy; this
can vary between 100 and 700% [1]. A heterogeneous
deposition can be difficult to quantify or can even be
undetectable [2,3]. This diffículty leads to reconsideration of
the counting strategy and also to defíning precisely the
concepts that are used. This is necessary if radionuclides such
as 1251, 241Am and 67Ga are to be assessed in vivo with a
reasonable sensitivity.
Background radiation is present at all times in all places. It
comes in part from cosmic radiation and in part from naturally
occurring radioactive material incorporated in the building. For
example, granite contains detectable amounts of uranium
daughter products. In addition, background radiation may also
come from nearby sources of radioactive material such as a
cobalt-60 therapy installation, a radium safe, a supply of
therapeutic
or
multiple
diagnostic
doses
of
radiopharmaceuticals, or patients who have received
radioisotope therapy doses [1].
For this reason the detector should be well shielded on all
sides except the one facing the patient or the sample being
measured. For clinicai work the shielding should be at least the
equivalent of 3/4 inch of lead for 1-inch diameter scintillation
detectors and should go up from there to 2 inches of lead or
more for 3-inch diameter scintillation detectors. It is very
important that this shielding against the general background
extend to the back of the sensitive portion of the detector, since
background radiation can come from all directions and can be
scattered back even if one principal component, such as cosmic
radiation, comes mainly from one direction [1].
The background count-rate of an unshielded scintillation
detector varies with the volume of the crystal while its counting
effíciency of radiation of a given energy coming from a point
source varies with the frontal area of the crystal. Thus, there is
no point in choosing a crystal which is thicker than required for
the almost total absorption of the radiation being measured. A
1-inch thick crystal is adequate for measuring 131I if all detected
rays are counted, while a 2-inch thick crystal are used (2-inch
diameter or more) better rations of effíciency to limit the
counted rays to those falling in the photopeak (total absorption)
[1].
Detectors must be shielded not only against background
radiation, but also against radiation coming from parts of the
patient's body other than the one under study at the moment. If
a whole organ, such as a thyroid or kidney is being measured,
then the front opening should be conical and subtend a solid
angle
just
large
enough
to
enablethedetectorrequiresa36°collimatorto
"see"
alarge
thyroid at a distance of 20cm. At a distance of 35 cm the same
detector needs a 20° collimator. This type of collimator is
called a Hat fíeld collimator because it has rather uniform
sensitivity across its opening.
The background is an important parameter: it depends on
the energy range of the measured photons. In the measurement
of low energy photon emitters, consideration of background is
crucial because any shielding produces, by fluorescence, a shift
of the continuum towards the low energy region. For this
reason, shielding can be avoided and the counting can be
carried out in many places without shielding when the
background is fírst controlled. This technique allows much
longer counting periods, but depends on the required detection
limits and on the examined energies. The environment has an
effect on the continuum and then on the detection limits of a
counting system. If the source is covered by inactive material,
as for example the thyroid is covered by neck tissue, then
absorbed in the covering material must also be taken into
account. It is possible that a gamma ray may be only partially
absorbed in the source or its covering matters and that it may
emerge with reduced energy and a change in direction as a
scattered ray. For this reason, the standard must be arranged to
have scattering conditions similar to those of the unknown, or
all scattered radiation must be eliminated from the
measurement by using an energy discriminator.
Of all of the radiation emerging from the source only a
fraction will be directed toward the detector. This fraction is
determined by the solid angle subtended by the detector with
respect to the source. It is ruled by the “inverse square law,”
since doubling the distance between a point source and detector
reduces the solid angle by a factor of 4[1].
Not all of the radiation within the subtended solid angle
reaches the sensitive portion of the detector because of
absorption in the air and in the detector cover. This is important
primarily in the case of beta and low energy gamma and x
radiation.
Because of their relatively short ranges in solid materiais,
beta particles create special detection and measurement
problems. These problems are especially severe with lowenergy beta particle emitters, such as 3H and 14C. The preferred
method for assay of these radionuclides is by liquid
scintillation counting techniques; however, these techniques
are not applicable in all situations, such as when surveying a
bench top with a survey meter to detect 14C contamination.
A survey meter can be used to detect surface contamination
by beta particle emitters provided it has an entrance window
suffíciently thin to permit the beta particles to enter the
sensitive volume of the detector. Effícient detection of low
energy beta emitters requires a very thin entrance window,
preferably fabricated from a low-density material. A typical
entrance window for a survey meter designed for 3H and 14C
detection is 0.03 mm thick Mylar (~1.3 mg/cm 2 thick). Mica
and beryllium also are used. Such thin Windows are very
fragile, and usually they are protected by an overlying wire
screen. Beta particles that are more energetic (e.g., from 32P)
can be detected with much thicker and more rugged entrance
Windows; for example, 0.2 mm-thick aluminum (~50mg/cm2)
provides approximately 50% detection effíciency for 32P.
GM and proportional counters sometimes are used to assay
the activities of beta emitting radionuclides in small trays
(planchets) or similar sample holders. Two serious problems
arising in these measurements are self- absorption and
backscattering. Self-absorption depends on the sample
thickness and the beta particle energy. For 14C and similar low
energy beta emitters, self-absorption in a sample thickness of
only a few mg/cm2 is suffícient to cause a signifícant reduction
of counting rate. Backscattering of beta particles from the
sample and sample holder tends to increase the sample
counting rate and can amount to 20% to 30% of the total sample
counting rate in some circumstances. Accurate assay of beta
emitting radioactive samples by externai particle counting
techniques requires careful attention to sample preparation. If
only relative counting rates are important, then it is necessary
to have sample volumes and sample holders as nearly identical
03006-p.3
EPJ Web of Conferences
as possible.
Bremsstrahlung counting can be employed as an indirect
method for detecting beta particles using detectors that
normally are sensitive only to more penetrating radiations such
as x-rays and gammarays. Bremsstrahlung counting also was
employed in some early studies using 32P for the detection of
brain tumors and still used occasionally to map the distribution
of 32P labeled materiais administered for therapeutic purposes.
Bremsstrahlung counting is effective only for relatively
energetic beta particles and requires perhaps 1000 times greater
activity than a gamma ray emitter because of the very low
effíciency of bremsstrahlung production.
Detection effíciencies can be determined experimentally
using calibration sources. A calibration source is one for which
the activity or emission rate is known accurately. This
determination is made by the commercial supplier of the
source.
3 Conclusions
Radiation measurement systems are subject to various types of
malfunctions that can lead to sudden or gradual changes in their
performance characteristics. For example, electronic
components and detectors can fail or experience a progressive
deterioration of function, leading to changes in detection
effíciency, increased background, and so forth. To ensure
consistently accurate results, quality assurance procedures
should be employed on a regular basis for all radiation
measurement systems. These would include (1) daily
measurement of the system’s response to a standard radiation
source (e.g., a calibration “rod standard” for a well counter or
a “check source” for a survey meter) (2) daily measurement of
background leveis; and (3) for systems with pulse-height
analysis capabilities, a periodic (e.g., monthly) measurement of
system energy resolution.
Acknowledgements
The study was supported by Osmaniye Korkut Ata University
with (OKÜBAP-2014-PT3-046) and (OKÜBAP-2014-PT3047) project.
References
1.
2.
3.
4.
G. J. Hine, Instrumentation in Nuclear Medicine, 2013
(Page, 30-38).
S. R. Cherry, J. A. Sorenson, M. E. Phelps, Physics in
Nuclear Medicine, 155-160 (2012)
G. H. Kramer, L. C. Bums “ Effect of Radionuclide
Distributions on Lung Counting Effíciency". Radiation
Prot. Dosim. 61 (1-3), 145-147 (1995)
J. L. Genicot, Radiation Protection Dosimetry ,Vol. 89,
Nos 3-4, pp. 339-342 (2000) Nuclear Technology
Publishing.
03006-p.4
EPJ Web of Conferences 100, 03003 (2015)
DOI: 10.1051/epjconf/ 201510003003
© Owned by the authors, published by EDP Sciences, 2015
Comparison of dose distributions calculated by the cyberknife Monte Cario and
ray tracing algorithms for lung tumors: a phantom study
Canan Koksal1'a, UgurAkbas1, Murat Okutan1, Bayram Demir2, Ismail Hakki Sarpun3
1
Istanbul University, Oncology Institute, Department of Medical Physics, Istanbul, Turkey
lstanbul University, Science Faculty, Department of Physics, Istanbul, Turkey
3Afyon Kocatepe University, Science and Art Faculty, Department of Physics, Afyon, Turkey
2
Abstract: Commercial treatment planning Systems with have different dose calculation algorithms have been developed for
radiotherapy plans. The Ray Tracing and the Monte Cario dose calculation algorithms are available for MultiPlan treatment planning
system. Many studies indicated that the Monte Cario algorithm enables the more accurate dose distributions in heterogeneous regions
such a lung than the Ray Tracing algorithm. The purpose of this study was to compare the Ray Tracing algorithm with the Monte
Cario algorithm for lung tumors in CyberKnife System. An Alderson Rando anthropomorphic phantom was used for creating
CyberKnife treatment plans. The treatment plan was developed using the Ray Tracing algorithm. Then, this plan was recalculated
with the Monte Cario algorithm. EBT3 radiochromic films were put in the phantom to obtain measured dose distributions. The
calculated doses were compared with the measured doses. The Monte Cario algorithm is the more accurate dose calculation method
than the Ray Tracing algorithm in nonhomogeneous structures.
1 Introduction
CyberKnife (Accuray Inc, Sunnyvale, CA, USA) is a frameless
stereotactic radiosurgery system which provides to deliver the
high doses to the target using a 6 MV linac mounted on a
robotic arm in a single or a small number of fractions. In this
system, the uncertainties of the target location are reduced by
getting X-ray images during treatment. The system
automatically tracks, detects, and corrects for tumor and
patient movement. For tracking tumor, there are some methods
such as bony structure tracking, fíducial tracking, and soft
tissue tracking. There are 12 fíxed circular collimators (5 mm
to 60 mm in diameter) and IRIS variable collimator to shape
the beams. IRIS collimator automatically changes the size
ofthe variable aperture [1].
In clinic implementations, the Computer based treatment
planning systems (TPS) are used to obtain planned dose
distributions on patient. Commercial TPS with have different
dose calculation algorithms have been developed for ideal
treatment plans. The Ray Tracing (RT) and the Monte Cario
(MC) dose calculation algorithms are available for MultiPlan
TPS (Accuray Inc, Sunnyvale, CA, USA). The RT algorithm,
which is a correction-based algorithm, calculates doses using
measured beam data such as the off-center ratio, tissuephantom ratio, and collimator output factor at reference
conditions and uses an effective path length for heterogeneity
corrections. This calculation method does not compute
electron transport. The MC algorithm uses a virtual source
which is similar a linac head to simulate each treatment beam
interaction with médium. The MC algorithm takes into account
the electronic disequilibrium. Many studies indicated that the
MC algorithm yields the more accurate dose distributions in
heterogeneous regions such a lung than the other dose
calculation algorithms. In MultiPlan TPS, the MC algorithm is
a
used with uncertainty leveis and its range leveis are from 0.1%
to 4%. The less number of photon simulation is performed if
the higher uncertainty levei is assigned [2,3].
The dose prediction which is generated by dose calculation
algorithms is very important for a successful treatment. AAPM
recommends that the dose calculation should be kept within
%3 [4]. In this study, it was investigated which algorithm
provides the more accurate dose predication using fílm
dosimetry for lung tumor.
2 Materials and Methods
2.1 Treatment Planning
An Alderson Rando anthropomorphic phantom was used for
creating Cyberknife treatment plans. The phantom’s computed
tomography (CT) images were acquired with 1 mm slice
thickness and transferred to the MultiPlan TPS. The gross
tumor volume (GTV) and criticai structures were contoured.
The planning target volume (PTV) was generated with 5 mm
margin beyond the GTV. The
Corresponding author: [email protected]
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510003003
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use,
EPJ Web of Conferences
treatment plan was developed using the RT algorithm through
the sequential optimization process (Fig. 1). The fíxed circular
collimators were used. Then, the high resolution plan was
recalculated using the MC algorithm with same beam
parameters (Fig. 2) and the Gaussian smoothing algorithm was
used (o=0.6). In addition, 2% uncertainty levei was applied for
a reasonable optimization time. The prescription dose was 600
cGy for GTV. The plans were normalized to the isodose line
which covers 100% of the GTV.
calibration curve was obtained for measurements (Fig. 3).
2.3 Measurements and Plan Evaluation
The EBT3 films were put into the phantom to obtain measured
dose distributions. The phantom was irradiated using spine
tracking method. The reference point doses calculated by TPS
and measured point doses with films were compared. There
were 4 reference points and their locations were shown in Fig
4. In addition, the treatment plans calculated by the RT and the
MC algorithms were evaluated in terms of the target coverage,
dose conformity, and dose homogeneity by analyzing the dosevolume histograms. The conformity index (Cl) is the ratio of
prescription isodose line (PIV) to the tumor volume (TV). Cl
equal to 1 corresponds to ideal conformation.
CI= PIV/TV
(1)
The new conformity index (nCI) formulated by Paddick and
expressed as following equation:
nCI= (TV*PIV)/(TVpiv)2
Figure 1. Calculated dose distributions with the RT algorithm
(2)
where TVpiv is the target volume covered by the prescription
isodose line. Conforming of the prescribed isodose volume to
the target shape takes into account in this equation. The
homogeneity describes the uniformity of dose within the target
volume. The HI formula is:
HI= Dmax/Dpx
(3)
where Dmax is the maximum dose in the treatment volume and
DRX is the prescription dose [5].
Figure 2. Calculated dose distributions with the MC algorithm
2.2 Film Dosimetry
In this study, the calibration curve was created for film
dosimetry. Gafchromic EBT3 (ISP, International Specialty
Products, ABD) fílms were cut in 2x2 cm 2 size
Figure 4. The locations of the reference points in PTV
Figure 3. Calibration curve with 6 MV and placed at depth of 5
cm, in a solid water phantom. The source to film distance was
100 cm. Films were oriented perpendicular to the central axis
of beam and irradiated with a dose range of 10 - 800 cGy
using a 6 MV photon energy. The field size was 10x10 cm2 at
the isocenter. Films were scanned using a flatbed scanner
(Epson 10000XL America Inc., Long Beach, CA) on
following day. The optical densities of exposed films were
converted to the doses using the Mephysto mee software
program (PTW-New York Corp., Hicksville, NY) and the
3 Results
The values of reference point doses calculated by the RT and
the MC algorithms and measured with EBT3 films
03003-p.2
TESNAT 2015
were shown in Table 1. The differences between the reference
point doses calculated by the MC algorithm and measured with
fílms were within 3%. The reference point doses calculated by
the RT algorithm were found higher than the MC algorithm.
For point 1, point 2, point 3, point 4, the RT algorithm
computed doses values of 10.05%, 12.35%, 11.59%, and
8.26% greater than the MC algorithm, respectively.
In addition, dose conformity index, homogeneity index,
and new conformity index were shown in Table 2. The RT
algorithm produced lower Cl and HI than the MC algorithm.
In this study, the prescription isodose line dropped from 69%
for the RT algorithm to 62% for the MC algorithm.
Table 1. Point doses were calculated by RT and MC algorithms and
measured with EBT3 fílms.
Reference
RT(TPS) RT(Film) MC(TPS) MC(Film)
Points
Point 1 (cGy)
810
746
736
758
Point 2 (cGy)
837
754
745
766
Point 3 (cGy)
828
762
742
764
Point 4 (cGy)
799
741
738
756
Table 2. Dosimetric parameters
PTV
RT
MC
Cl
1.12
1.21
HI
1.15
1.23
nCI
1.45
1.61
the MC algorithm using the same patient data and treatment
parameters. They indicated that the MC algorithm predicts the
more accurate dose distributions than the RT algorithm. The
results in this investigation are consistent with literature.
In conclusion, the RT algorithm is overestimated the target
doses in heterogeneous médium such a lung. The MC
algorithm predicts the more accurate dose than the RT
algorithm because the MC algorithm computes overall photon
and electron scatter, particularly heterogeneous médium.
However, the MC optimization time is a restrictive parameter
in clinics.
References
1. W. Kilby, J.R Dooley, G. Kuduvalli, S. Sayeh, C.R.
Maurer, Technol Câncer Res Treat, 9, 433-452 (2010)
2. F. Crop, Ghent University Faculty of Medicine and Health
Sciences, Department of Radiotherapy and Nuclear
Medicine, PhD Thesis (2008)
3. S.C. Sharma, J.T. Ott, J.B. Williams, D. DiCKow, J Appl
Clin Med Phys, 11, 170-175 (2010)
4. AAPM ReportNo 54, Woodbury, 22-25 (1995)
5. F. Alejandro, S.O. Iciar, S.R. Alberto, Med Dosim, 39, 1-6
(2014)
6. E. Wilcox, G.M. Daskalov, H. Lincoln, R.C. Shumway,
B.M. Kaplan, J.M. Colasanto, Int J Radiat Oncol Biol Phys,
77, 277-84 (2010).
7. W.C. Vincent, T.W. Kwok-wah, T. Shun-ming, J Appl
Clin Med Phys,14, 68-78 (2013)
4 Conclusion
CyberKnife is a stereotactic radiosurgery, which achieves sparing of criticai structures adjacent to the tumors using small fíelds.
This system enables steep dose gradients at the target-normal tissue boundary while delivering the high doses to the target.
Therefore, the accurate dose calculation is very crucial in stereotactic radiosurgery.
The dose calculation algorithms are used to predict dose distributions in TPS. In MultiPlan TPS, there are the RT and the MC
algorithms. In this study, the calculated doses by the RT and the MC algorithms were compared with the measured doses using
fílm dosimetry for lung tumor. For this investigation, 4 reference points were specifíed in the target and these point doses were
evaluated. The RT algorithm fíndings were average 10% higher than the MC algorithm fíndings.
Wilcox et al. [6] found that the RT algorithm over predicts dose to the PTV and recommended using the MC algorithm for
stereotactic radiosurgery of pulmonary targets.
A retrospective study on 33 patients was performed by Vincent et al [7]. The treatment plans were generated using the RT
algorithm. Then the plan recalculated with
03003-p.3
EPJ Web of Conferences 100, 03004 (2015)
DOI: 10.1051/epjconf/ 20151000300 4
© Owned by the authors, published by EDP Sciences, 2015
A systematic quality assurance study in bone densitometry devices
Duygu Tuncman1'a, Hatice Kovan2, Bilal Kovan3, Bayram Demir1 , CuneytTurkmen3
Istanbul University, Science Faculty, Physics Department, 34134, Istanbul, Turkey
Okmeydani Training and Research Hospital, Nuclear Medicine Department, 34400, Istanbul, Turkey 3Istanbul University, Istanbul Medical
Faculty, Nuclear Medicine Department, 34093, Istanbul, Turkey
1
2
Abstract. Osteoporosis is the most common metabolic bone disease and can result in devastating physical, psychosocial,
and economic consequences. It occurs in women after menopause and affects most elderly. Dual-energy x-ray
absorptiometry (DXA) is currently the most widely used method for the measurement of areai Bone Mineral Density
(BMD) (g/cm2) .DXA is based on the variable absorption of X-ray by the different body components and uses high and
low energy X-ray photons. There are two important values in the assessment of the DXA. These values are T-score and
Z-score. The T-score is calculated by taking the difference between a patient’s measured BMD with the mean BMD of
the young normal population, matched for gender and ethnicity, and then by dividing the difference with the standard
deviation (SD) of the BMD of the young normal population. T-score and also Z-score are directly depends on the Bone
Mineral Density (BMD). BMD measurements should be made periodically in a patient life. But mostly, it is not possible
with the same device. Therefore, in this study, for the quality assurance ofbone densitometry devices, we evaluated the
BMD results measured in the different Bone Densitometry (DXA) devices using a spine phantom.
following procedure of the patient, but mostly it is not possible
with the same devices. Therefore, in this study, for the quality
Osteoporosis is the most common metabolic bone disease and can assurance of bone densitometry devices, we evaluated the BMD
result in devastating physical, psychosocial, and economic of spine phantom which are measured in the several Bone
consequences. It occurs in women after menopause and affects Densitometry (DXA).
most elderly but may also be found in men and rarely in children.
Osteoporosis is an insidious illness [1]. Therefore a patient should
be periodically measured bone mineral density (BMD). Dual- 2 Material and Method
energy x-ray absorptiometry (DXA) is currently the most widely In this study, we totally evaluated 23 DXA devices manufactured
used method for the measurement of areai bone mineral density three different corporations .These DXA devices were in 23
(g/cm2) because of its low cost, minimal radiation exposure, different hospitals located Istanbul, Turkey.
accessibility, and ease of use. DXA uses two X-ray beams which
Before the measurements, daily calibrations were made for all
are different energy leveis. These leveis contain low and high devices and measurements were then performed in each hospital.
energy X-rays. Each X-rays pass through specific tissues. If bone, A spine phantom anthropomorphic was used in the
fat or lean tissue components exist, DXA cannot directly estimate measurements. For the phantom, total Area is 52.39 cm3, total
the relative proportion of all three components. DXA can directly BMC is 52.24 gr and phantom’s BMD is then calculated as 0.997
estimate the proportion of fat and lean tissue without bone. gr/cm3. After choosing the spine phantom imaging protocol, the
Besides, DXA determines the proportion of bone and soft tissue phantom values were entered to the device computer as a patient
for structure that contain bone. There are two important values in with 20 years old, women patient (some devices accepts as white
the assessment ofthe DXA. These values are T- score and Z-score. women, some other devices accepts as Asian women), 50 kg
T score is used to evaluate bone density on young people weight and 160 cm height. The phantom was placed in the device
moreover Z score is used to evaluate bone density based on age bed according to the patient's position and imaging procedures
and gender. T-score and also Z-score are directly depends on the were then performed.
Bone Mineral Density (BMD) [2]. In a patient life, BMD
measurements have been made several times because of the
1 Introduction
a
e-mail : [email protected]
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use,
distribution, and reproduction in any medium, provided the original work is properly cited.
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510003004
EPJ Web of Conferences
3 Results and Discussion
Osteoporosis is often occurring silently and patients don’t know
that they have osteoporosis till their bones suddenly strain or
bump. There are certain risk factors linked to development of
osteoporosis. It develops quickly therefore BMD values should
be measured periodically. World Health Organization (WHO)
defines low bone mass and osteoporosis as follows:
1. In case the T-score is in the range of 0 to -1 SD, the subject
is healthy;
2. In case the T-score is in the range of -1 to -2.5 SD, the
subject is osteopenic (low bone mass);
3. In case the T-score is less than -2.5 SD, the subject is an
osteoporotic patient;
4. In case the T-score is less than - 2.5 SD with fragility
fracture, the subject is severely osteoporotic. [3]
In this study, we evaluated the BMD results measured in the
different Bone Densitometry (DXA) devices using a spine
phantom. Two values (Area and BMC) were directly measured
by means of the device computer and the values of BMD were
calculated by using these measurements values [4-5]. Also Zscore and T-score values of phantom were calculated using
BMD values by the device computers using the above formulas;
T-score = (patient’s measured BMD - mean BMD of young
normal population) / (Standard Deviation of BMD of young
normal population).
Tablel. Area, BMC, BMD, T-score and Z-score of the first
group DXA devices.
Device
1.Device
2.Device
3.Device
4.Device
5.Device
6.Device
7.Device
8.Device
9.Device
10.Device
Area
(cm2)
52.75
52.78
52.52
52.19
51.86
52.04
51.99
51.04
51.57
50.79
BMC
(g)
52.99
52.82
52.23
52.27
51.52
52.04
51.76
51.68
51.65
51.57
BMD
(g/cm2)
1.005
1.001
0.994
1.010
0.994
1.000
0.996
1.013
1.001
1.015
T
Score
-0.40
-0.40
-0.50
-0.30
-0.50
-0.40
-0.50
-0.30
-0.20
-0.30
Z
Score
-0.20
-0.40
-0.50
-0.10
-0.48
-0.20
-0.20
-0.10
-0.20
-0.10
there are 0.6 value difference between third device of the first
group DXA devices (-0.5) and third device of the third group
DXA devices (0.10). When Z-score is analyzed among the each
group DXA devices, similar differences are seen. For example,
there are 0.7 value difference between seventh device of first
group DXA devices (-0.20) and seventh device of third group
DXA devices (0.50).
Table 2. Area, BMC, BMD, T-score and Z-score of the second
group DXA devices.
Device
Area
(cm2)
1.Device 51.70
2.Device 51.02
BMC
(g)
57.32
55.21
BMD
(g/cm2)
1.109
1.082
T
Score
-0.42
-0.45
Z
Score
-0.37
-0.42
Table 3. Area, BMC, BMD, T-score and Z-score of the third
group DXA devices.
Device
Area
(cm2)
l.Device 48.74
2.Device 48.09
3.Device 48.70
4.Device 48.77
5.Device 48.47
6.Device 49.21
7. Device 48.66
8.Device 48.94
9.Device 49.26
lO.Device 48.74
ll.Device 49.70
BMC
(g)
56.28
55.47
56.20
56.01
55.59
56.10
55.81
56.19
56.16
56.43
56.15
BMD
(g/cm2)
1.154
1.153
1.154
1.148
1.146
1.138
1.146
1.148
1.140
1.157
1.129
T
Score
0.00
0.00
0.10
-0.30
0.00
-0.10
-0.10
0.00
-0.10
-0.30
-0.10
Z
Score
0.00
0.00
0.10
-0.30
0.00
0.40
0.50
0.00
0.40
0.20
-0.10
4 Conclusion
Osteoporosis has become a chronic disease of our time. This
disease should be kept under control. These studies showed that
BMD, T-score and Z-score values point out important changes
from device to device even using the same phantom. These
changes can affect the type of treatment (as osteopenic,
osteoporotic, severely osteoporotic) [6]. Therefore, using the
same device for the treatment accuracy is extremely important.
The Z-score is similarly calculated, comparing a patient to
age matched group;
Z-score = (patient’s measured BMD - mean BMD of agematched group) / (Standard Deviation of BMD of age-matched
group).
Each trademark group DXA devices values (T-score, Zscore and BMC, BMD) for 23 different DXA devices were
given Table 1, Table 2, and Table 3. When tables are analyzed
it is seen that given values have important different variation for
each group DXA devices. In generally, while BMD values of
first group DXA devices are close to (0.997 g / cm 3), BMD
values of second group DXA devices have higher value than
physical BMD value of the spine phantom. On the other hand,
BMD values of third group DXA devices have higher value than
physical BMD value of spine phantom. When T- scores of the
spine phantom are analyzed, T-scores of first group DXA
devices are close to each other and the other two groups show
the same trend with the first group DXA devices. But when the
comparisons are made among the groups, it is seen that there
are some alteration among the T-score values. For example,
References
1. J.A. Kanis, et al., Bone 42, 467-475 (2008)
2. M.G. Blake, I. Fogelman, Postgrad Med J. 83 (982): 509517 (2007)
3. http://www.iofbonehealth.org/sites/default/files/WHO
Technical_Report-2007.pdf
4. M.R Salamat, et al., Adv Biomed Res. 30; 4: 34 (2015)
5. B. Heidari, et al., Med J Islam Repub Iran. 28 (2014)
6. B.V. Halldorsson, et al., Comput Math Methods Med,
(2015)
03004-p.2
EPJ Web of Conferences 100, 03001 (2015)
DOI: 10.1051/epjconf/ 201510003 0 01
© Owned by the authors, published by EDP Sciences, 2015
Dosimetric comparison oftools for intensity modulated radiation therapy
with gamma analysis: a phantom study
UgurAkbas1'a,MuratOkutan1, BayramDemir2, CananKoksal1
1
2
Istanbul University, Oncology Institute, Department of Medical Physics, Istanbul, Turkey
Istanbul University, Science Faculty, Department of Physics, Istanbul, Turkey
Abstract: Dosimetry of the Intensity Modulated Radiation Therapy (IMRT) is very important because of the complex
dose distributions. Diode arrays are the most common and practical measurement tools for clinicai usage for IMRT.
Phantom selection is criticai for QA process. IMRT treatment plans are recalculated for the phantom irradiation in QA.
Phantoms are made in different geometrical shapes to measure the doses of different types of irradiation techniques.
Comparison of measured and calculated dose distributions for IMRT can be made by using gamma analysis. In this study,
10 head-and-neck IMRT QA plans were created with Varian Eclipse 8.9 treatment planning system. Water equivalent
RW3-slab phantoms, Octavius-2 phantom and PTW Seven29 2D-array were used for QA measurements. Gantry,
collimator and couch positions set to 0o and QA plans were delivered to RW3 and Octavius phantoms. Then the positions
set to original angles and QA plans irradiated again. Measured and calculated fluence maps were evaluated with gamma
analysis for different DD and DTA criteria. The effect of different set-up conditions for RW3 and Octavius phantoms in
QA plan delivery evaluated by gamma analysis. Results of gamma analysis show that using RW3-slab phantoms with
setting parameters to 0o is more appropriate for IMRT QA.
1 Introduction
disagreement.
Intensity modulated radiation therapy (IMRT) technique poses
such challenges for measuring quality assurance (QA) of the
complex dose distributions. Treatment plans that modulated by
multi-leaf collimation lead to numerous regions containing
steep dose gradients. For a proper IMRT implementation,
comprehending the use of dosimetric tools to measure the
doses is important.
Point dosimetry may allow validating the IMRT dose
distributions at individual points, but quality assessment of
modulated dose distributions requires two dimensional (2D)
dosimetry at least. Diode arrays are the most common and
practical measurement tools for clinicai usage. Phantom
selection is criticai for QA process. The appropriate phantom
should be determined by the purpose of measurement.
Treatment planning systems calculate dose to patients in regard
to constrains defined at optimization page. These plans are
recalculated for the phantom irradiation in QA. For an accurate
calculation, phantoms should be made of water-equivalent or
known electron-density material. Phantoms are made in
different geometrical shapes to measure the doses of different
types of irradiation techniques [1].
Irradiation of tumor and simultaneous protection of the
organs at risk is the main point of IMRT. Comparison of
measured and calculated dose distributions for IMRT can be
made by using gamma analysis. After creating dose fluence
maps by measuring with dosimetric tool and by calculating
with treatment planning system, the gamma method measures
the closest distance between each reference point and
evaluated dose distribution after scaling by DD (Dosedifference-criteria) and DTA (distance-to-agreement). The
method provides an evaluation of either dosimetric or spatial
2 Materials and Methods
a
2.1 Treatment Planning
Computed tomography (CT) images of 10 nasopharynx câncer
patients were acquired in head gantry and supine position.
Thickness of the CT images is 3 mm. Gross tumor volume
(GTV), clinicai target volume (CTV), planning target volume
(PTV) and organs at risk (OARs) were defined and contoured
by radiation oncologist. Then images were sent to Varian
Eclipse treatment planning system (TPS). 7 field IMRT plans
were created for each patient. 6MV energy was used for each
of 7 fíelds in Varian Trilogy linear accelerator (LINAC).
Analytical anisotropic algorithm (AAA) was used for
calculation. Calculation grid size was chosen 2.5 mm. QA
plans were created in some conditions. Gantry, collimator and
couch positions set to 0 o and QA plans were created for RW3
and Octavius phantoms. Then the positions set to original
angles and QA plans were created for RW3 and Octavius
phantoms. Created QA plans were irradiated under these
conditions.
Corresponding author: [email protected]
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at http://www.epj-conferences.org
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is anavailable
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EPJ Web of Conferences
2.2 Measurements and Gamma Evaluation
5% of maximum dose of measured data set was suppressed.
Gamma results of both phantoms were compared each other.
Irradiations for each condition were measured by using PTW
Seven29 2D-array, which is an ion chamber array with 729 ion
chambers for precise IMRT plan verifícation and LINAC QA.
In Seven29, the vented plane-parallel ion chambers are 5 mm
x 5 mm x 5 mm in size, and the center-to-center spacing is 10
mm. In total there are located 729 chambers in a matrix of 27
x 27, providing a maximum field size of 27 cm x 27 cm. The
array is only 22 mm Hat and 3.2 kg light. The surrounding
material is acrylic (PMMA) [2],
The gamma method provides an evaluation of either
dosimetric or spatial disagreement with measuring the closest
distance between each reference point and evaluated dose
distribution after scaling by Dose- difference-criteria and
distance-to-agreement. The concept of gamma verifícation is
shown in Fig. 1 [3].
Figure 1. The principie of gamma verifícation: x, y, D - spatial and
dose dimensions; DTA; Dmax; Ar, AD - local spatial and dose
divergence of the analyzed point
3 Results
The results of 3 mm DTA - 3% DD and 5 mm DTA - 5% DD
gamma analysis for RW3 slab phantom with all set-up
parameters set to original angles and with all Setup parameters
set to 0o are shown in Table 1 and Table 2, respectively. Also,
the results of 3 mm DTA - 3% DD and 5 mm DTA - 5% DD
gamma analysis for Octavius phantom with all set-up
parameters set to original angles and with all set-up parameters
set to 0o are shown in Table 3 and Table 4, respectively.
Table 1. RW3 Slab Phantom: 3 mm DTA - 3% DD and 5 mm DTA 5% DD Gamma Analysis: Parameters are set to original angles
Table 2. RW3 Slab Phantom: 3 mm DTA - 3% DD and 5 mm DTA 5% DD Gamma Analysis: Parameters are set to 0o
Figure 2. PTW VeriSoft 4.1
For gamma evaluation, dose fluence maps measured by
2D-array and calculated by treatment planning system are
required to compare. This comparison can be made with
software. In our clinic, PTW VeriSoft 4.1 (PTW, Freiburg,
Germany) used (Fig. 2). VeriSoft is software to load, evaluate
and compare dose matrices. VeriSoft is used to compare
measured dose matrices (e.g. 2D- ARRAY matrices or fílms)
and corresponding calculated matrices (from treatment
planning systems). The software can also be used for dose
verifícation in IMRT (Intensity Modulated Radiation
Therapy).
The gamma evaluation was made under the criteria of 3
mm DTA - 3% DD and 5 mm DTA - 5% DD. The dose below
03001-p.2
TESNAT 2015
89.09%; min and max values were found 86.3% and 96.7%,
respectively. Mean value of 5mm DTA-5% DD analysis for
Octavius phantom with set- up parameters were set to 0o was
found 96.55%; min and max values were found 95.7% and
99.2%, respectively.
Table 3. Octavius Phantom: 3 mm DTA - 3% DD and 5 mm
DTA - 5% DD Gamma Analysis: Parameters are set to
originalOctavius
angles Phantom - Gantry, Collimator, Couch set to 0°
4 Conclusion
■ 3mtnDTA-3%DD
■ 5mtn DTA • 5%DD
Table 4. Octavius Phantom: 3 mm DTA - 3% DD and 5 mm DTA 5% DD Gamma Analysis: Parameters are set to 0o
Octavius Phantom - Gantry, Collimator, Couch set to
original angles
100
90
80
70
60
50
40
g 30
’
<
!
20
■ 3mmDTA-3%DD
10
■ 5mmDTA-5%DD
=0
23456789 10
Number ofPatient
Mean value of 3mm DTA - 3% DD analysis for RW3
phantom with original set-up parameters was found 77.63%;
minimum and maximum values were found 74.3% and 83.4%,
respectively. Mean value of 5mm DTA - 5% DD analysis for
RW3 phantom with original set-up parameters was found
92.03%; minimum and maximum values were found 90.2%
and 95.6%, respectively.
Mean value of 3mm DTA-3% DD analysis for RW3
phantom with set-up parameters were set to 0o was found
98.95%; min and max values were found 97.9% and 99.7%,
respectively. Mean value of 5mm DTA-5% DD analysis for
RW3 phantom with set-up parameters were set to 0o was found
99.85%; min and max values were found 99.6% and 100.0%,
respectively.
Mean value of 3mm DTA-3% DD analysis for Octavius
phantom with original set-up parameters was found 84.25%;
min and max values were found 80.4% and 86.4%,
respectively. Mean value of 5mm DTA - 5% DD analysis for
Octavius phantom with original set- up parameters was found
92.97%; min and max values were found 90.2% and 97.2%,
respectively.
Mean value of 3mm DTA-3% DD analysis for Octavius
phantom with set-up parameters were set to 0o was found
Radiation therapy is the main treatment modality for most of
the head and neck câncer. Intensity modulated techniques have
advantage of delivering maximum dose to target while
protecting the normal tissues. Computed tomography
scanning, immobilization, contouring the volumes of interest,
treatment planning, set-up and dose delivery are the parts of
treatment and every step of them extremely important. In
IMRT technique, a successful dose delivery is strongly related
to treatment planning. Treatment plans must be verifíed by QA
plans before irradiation of the patient.
In this study, 10 nasopharyngeal carcinoma patients’
treatment plans were used to create QA plans. 52°, 104°, 156°,
208°, 260° and 312° angles were chosen for 7 fíelds. Dynamic
leaf shaped fíelds make the study more meaningful, because
the dose fluence verifícation becomes more important. For the
gamma analysis, normalization of calculated and recorded
dose matrixes was performed inside regions of homogeneous
dose. Commercially different types of QA tools are available.
In our clinic, we use RW3 slab phantoms and Octavius
phantom for QA.
In all conditions of phantom set-up and gamma analysis
criteria, 5mm DTA-5% DD gave the highest values as
expected. As we seen in tables above, setting set-up parameters
to 0o gave better results compare to original set-up parameters
for both RW3 and Octavius phantoms. The best results were
obtained from RW3 slab phantom by setting gantry, collimator
and couch to 0o.
Spezi et al. [4], compared output factors with 2D- array and
pinpoint chamber measurements and the results were coherent.
Also, output factors agreed with reference dataset for field
sizes ranging from 2x2 cm2 to 27x27 cm2. This can be
considered a very good achievement since it is not trivial to
obtain good output factor response for small radiation fíelds
when using matrices of detectors. Studies reported the diodes
of the 2D array used in IMRT verifícation have angular
dependence which would lower the verifícation accuracy when
the 2D array is used in measuring the actual beams of the
treatment plan. Thus, all the beam gantry angles should be
modifíed to 0 o for the verifícation of the IMRT treatment plan
[5,6]. Li et al. [7], suggested that the 2D array can be used in
the verifícation of the composite dose distribution of IMRT
treatment plan if enough solid water slabs are attached
03001-p.3
EPJ Web of Conferences
around the 2D array and the beam incidence angles are not in the range of 90° or 270° ±5°. Chandraraj et al. [8], reported th at
when stricter gamma index criteria were used, some of the measured planar doses failed to pass the tolerance of 90%.
IMRT is a modem accurate irradiation technology characterized by the highly conformai radiation dose to the planning target
volume and great steep dose gradients [99]. We consider gamma evaluation method as a reliable and effective instrument for IMRT
treatment plan verifícation. The method should be performed by 0 o angles of gantry, collimator and couch in RW3 slab phantoms
with considering angular dependence of 2D-array detectors.
References
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E. Spezi, A.L. Angellini, F.Romani, A. Ferri. Phys. Med. Biol. 50, 3361 - 3373 (2005)
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Q.L. Li, X.W. Deng, L.X. Chen, X.Y. Huang, S.M. Huang. Chin. J. Câncer 29, 617 - 620 (2010)
V. Chandraraj, S. Stathakis, R. Manickam, C. Esquivei, S. Supe, N. Papanikolaou. J. Appl. Clin. Med.Phys. 12,338 -349
(2011)
Y.M. Hu. Radiation Oncology Physics. Beijing: Atomic Press, 538-541 (1999)
03001-p.4
EPJ Web of Conferences 100,03002 (2015)
DOI: 10.1051/epjconf/ 201510003002
© Owned by the authors, published by EDP Sciences, 2015
Gamma radiation exposure of accompanying persons due to Lu-177
patients
Bilal Kovan1'a, Bayram Demir2, Duygu Tuncman2, Veli Capali3, CuneytTurkmen1
1
2
3
Istanbul University, Istanbul Medical Faculty, Nuclear Medicine Department, 34093,Istanbul,Turkey
Istanbul University, Science Faculty, Physics Department, 34134, Istanbul,Turkey
Süleyman Demirel University, Arts and Sciences Faculty, 32260, Isparta, Turkey
Abstract. Neuroendocrine tumours (NET) are cancers usually observed and arisen in the stomach, intestine, pancreas and breathing
system. Recently, radionuclide therapy applications with Lu-177 peptide compound are rapidly growing; especially effective clinicai
results are obtained in the treatment of well-differentiated and metastatic NET. In this treatment, Lu-177-DOTA, a beta emitter
radioisotope in the radiopharmaceutical form, is given to the patient by intravenous way. Lu-177 has also gamma rays apart from
beta rays. Gamma rays have 175 keV average energy and these gamma rays should be under the control in terms of radiation
protection. In this study, we measured the exposure dose from the Lu-177 patient.
1 Introduction
follow-up during one day.
Neuroendocrine tumors (NET) are cancers usually observed
and arisen in the stomach, intestine, pancreas and breathing
system. Recently, radionuclide therapy applications with Lu177 peptide compound are rapidly growing; especially
effective clinicai results are obtained in the treatment of welldifferentiated and metastatic NET. In this treatment, Lu-177DOTA, a beta emitter radioisotope in the radiopharmaceutical
form, is given to the patient by intravenous way. This targeting
radio- peptide is intensely accumulated in the tumor site
containing somatostatin receptor and the tumor is intemally
treated by means of beta rays emitted from Lu- 177. The
treatment is sequentially repeated 4 or 5 times in the 6-8
weekly periods [1].
Lu-177 is a beta emitter with a maximum energy of 0.5 MeV
and it’s a maximal tissue penetration of 2 mm. Lu- 177 halflife is 6.7 days. A part from beta rays, Lu-177 has also emits
two low-energy y-rays at 208 and 113 keV with 10% and 6%
abundance. These gamma rays allow scintigraphy and
subsequent dosimetry with the same therapeutic compound.
Because of the gamma rays of the Lu-177, radiation protection
issue can be became a problem. We measure the dose exposure
resulted from Lu-177 patient to accompanying person [2].
Radiation exposure measurements were performed by using a
portable Ludlum trademark Geiger Muller device. Geiger
Muller was calibrated by Turkish Atomic Energy Authority.
After injection, measurements were performed at 4. hours, 24.
hours, 48. hours, 96. hours and 120. hours. Measurement
distances were 0.2, 0.5 and 1 meter from the patients’
abdominal regions. Measurement results were given in Table
1.
2 Material and Method
In this study, we measured the radiation exposure of four Lu177 patients. Each patient was injected with average 200 mCi
Lu-177 with 500 cc serum during 30 minutes. After the
injection, patient’s stayed in an isolated room for the clinicai
a
3 Results
Neuroendocrine tumours (NETs) develop in the cells of the
neuroendocrine system. There are several types of
neuroendocrine tumors. These types are Gastrointestinal
neuroendocrine tumours, Pulmonary neuroendocrine tumours
and other NETs, known as functioning tumors. One of the
treatment model of the NETs tumours is radiation therapy with
radionuclides. Lu-177 is known to be effective in
neuroendocrine tumours, paragangliomas, neuroblastomas and
certain types of thyroid câncer. Lu- 177 is a radioactive
substance that we can add to a carrier called DOTATATE.
Once in your body, the Lu-177 DOTATATE attaches to
specifíc tumour cells and destroys these cancerous cells. [3]
Lu-177 emits beta rays, besides gamma radiation. It has
gamma rays which can be considered as dangerous in terms of
radiation protection. Injected doses are 200 mCi in the Lu-177
treatment. On the other hand, NETs are advanced câncer type
and these patients need close patient care [4,5]. Therefore,
these people are at risk of exposure to radiation. In this study,
we measured the dose
e-mail: [email protected]
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution,
and reproduction in any medium, provided the original work is properly cited.
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510003002
EPJ Web of Conferences
exposure resulted from Lu-177 patient to accompanying
person. Therefore, measurement distance was selected 0.2, 0.5
and 1 m. Especially 0.2 m measurements are important
because of gamma rays energies of Lu-177. Its energies are
113 and 208 keV. These energies affects to the accompanying
person in the case of close contact. Various values for six
patients are shown in Figs. 1, 2 and
3. Signifícant degradation is observed from the frrst 24 hours
for each distances (0.2 m, 0.5 m and 1 m) when the figures
were analysed. After 24 hours, Lu-177 activity keeps in
organs. Then, this activity decreases slowly. Thus first 24
hours very criticai for accompanying persons. Because of
radiation exposure for accompanying persons, they should
refrain from close contact with their patients. Moreover
patients should be kept in isolated rooms after the injection.
25
Time aftertreatment (hours )
for each distance from accompanying persons to patients.
Periodical measurements should be made after Lu-177
injection. If measurement results allow, patient will discharged
1 meter
0,2 meter
Time after treatment ( hours )
1 Patient
20
2.Patient
Figure 3. Dose rate measurements results at 1 m.
15
10
References
5
from isolated rooms. [6-8]
0
4
24
48
96
Time after treatment (hours )
120
1.
2.
3.
4.
5.
Figure 1. Dose rate measurements results at 0.2 m.
6.
7.
8.
J. Fitschen, et al., Z Med Phys. 21 (4) 266-73 (2011)
G.S. Limouris,Front Oncol. 28 2 20 (2012)
S. Banerjee, et al., Nucl. Med. Biol., 31 753-759 (2004)
B.L.R. Kam, et al., Eur J Nucl Med Mol Imaging. 39
103-11 (2012)
S. Walrand, et al., Eur J Nucl Med Mol Imaging.
2011;38(Suppl 1):S57-S68. doi: 10.1007/s00259- 0111771-7.
G.A. Kaltsas, D. Papadogias, P. Makras, A.B. Grossman,
Endocr Relat Cancer. 12 683-99 (2005)
E.J. Rolleman, et al., Eur J Nucl Med Mol Imaging.
37(5):1018—1031 (2010)
N. Singh, et al., Indian J Nucl Med. 26(3): 135-138
(2011)
Figure 2. Dose rate measurements results at 0.5 m.
4 Conclusion
Lu-177 treatment is sequentially repeated 4 or 5 times in the 6-8 weekly periods, each fraction has 200mCi activity. Totally 8001000 mCi Lu-177 activity was injected to the patient’s body. Gamma rays energies of Lu-177 are considered as important. So it is
important to keep in an isolated room for at least one day after the injection. First 24 hours close contact should be avoided
Mass attenuation coefficient calculations of different detector crystals
by means of FLUKA Monte Cario method
Elif Ebru Ermisa, Cuneyt Celiktas
Ege University, Faculty of Science, Physics Department, 35100, Bornova, Izmir/Turkey
03002-p.2
EPJ Web of Conferences 100,02003 (2015)
DOI: 10.1051/epjconf/ 201510002003
© Owned by the authors, published by EDP Sciences, 2015
Abstract. Calculations of gamma-ray mass attenuation coefficients of various detector materiais (crystals) were carried out
by means of FLUKA Monte Cario (MC) method at different gamma-ray energies. NaI, PVT, GSO, GaAs and CdWÜ4 detector
materiais were chosen in the calculations. Calculated coefficients were also compared with the National Institute of Standards
and Technology (NIST) values. Obtained results through this method were highly in accordance with those of the NIST values.
It was concluded from the study that FLUKA MC method can be an altemative way to calculate the gamma-ray mass
attenuation coefficients of the detector materiais.
demonstrated in MC method. A simple diagram of a MC code
is shown in Fig. 1 [3].
1 Introduction
If gamma-rays are allowed to pass through an absorber, the
result should be simple exponential attenuation of the gammarays. Each of the interaction processes removes the gamma-ray
from the beam either by absorption or by scattering. It can be
characterized by a fíxed probability of an occurrence per unit
path length in the absorber and is called linear attenuation
coefficient [1], i.e.;
I(x>be(1)
with Io: incident beam intensity or photon numbers, t:
thickness of absorber, p: linear attenuation coefficient, I(x): the
intensity transmitting through t thickness [2].
Linear attenuation coefficient varies with the density of the
absorber, even though the absorber material is the same. For
this reason, use of the linear attenuation coefficient is limited
by the fact that it varies with density of the absorber. Therefore,
the mass attenuation coefficient is much more widely used and
is defmed as;
(2)
where p is the density of the absorber [1].
The interaction of radiation with matter can be simulated
by Monte Cario (MC) method. Some input data such as details
of geometry of radiation source, target and médium, type of
radiation, energy and direction of radiation flight, etc. are
a
Figure 1. A simple diagram of a MC Code [3],
FLUKA is one of the well-known MC codes which is
based on FORTRAN language. These are particle transport
and interactions with matter, covering and extended range of
applications spanning from proton and electron accelerator
shielding to target design, dosimetry, detectordesign, etc. [4,5].
ROOT is an object-oriented framework aimed at solving
the data analysis challenges of high-energy physics. It works
by depending on C++. It is additionally used for advanced data
analysis such as MC simulations in the field of subjects [6].
Sidhu et al. investigated the effect of collimator size and
the absorber thickness on gamma-ray attenuation measurement
by using a Nal(Tl) detector [7]. The gamma-ray attenuation
coefficient of various absorber materiais were experimentally
determined by Abdel- Rahman et al. [8]. Singh et al. obtained
gamma-ray mass attenuation coefficients of bismuth borate
glasses by experimental and XCOM methods [9]. The gamma
attenuation coefficients of the materiais were investigated
through an experimental method by Ermis and Celiktas [10].
Corresponding author: [email protected]
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution,
and reproduction in any medium, provided the original work is properly cited.
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510002003
EPJ Web of Conferences
The gamma-ray mass attenuation coefficients of NaI, PVT,
GSO, GaAs and CdWO4 were theoretically determined at 60,
150, 500, 600, 1000 and 1250 keV energies by means of
FLUKA. Obtained attenuation coefficients were compared to
the NIST values. It can be concluded that the results were
highly compatible with each other.
2 Simulation Configuration
In the calculation procedure, FLUKA (ver. 2011.2c) program
which was installed on an Ubuntu (ver. 13.10) operating
system was used to obtain the gamma-ray attenuation
coefficients of sodium iodide (NaI), polvinyltoluene (PVT),
gadolinium silicate (GSO, Gd2SiOs), gallium arsenide
(GaAs), and cadmium tungstate (CdWO4) detector materiais
in this work. 60, 150, 500, 600, 1000 and 1250 keV energy
gamma photons were sent to each detector material,
respectively.
In the calculations, the materiais were first formed in lem
thicknesses. Mono-energetic gamma rays of 60, 150, 500, 600,
1000 and 1250 keV were secondly sent to each detector
material surface. The transmitted photon numbers from the
materiais were then detected. Built-in PRECISIO physics list
was utilized for FLUKA program. The program was run ten
cycles for each material, and the mass attenuation coefficient
values were calculated by means of ROOT (ver. 5.34.18)
which was used to analyze the output files of the program.
The attenuation coefficients of the materiais via FLUKA
were finally compared to the NIST ones.
Figure 2. Gamma-ray mass attenuation coefficients vs. photon
energies for NaI, PVT, GaAs, GSO and CdWO4.
3 Results
Calculated and the NIST mass attenuation coefficients of the
used materiais for 60, 150, 500, 600, 1,000 and 1,250 keVenergy gamma photons are listed in Table 1.
In Fig. 2, the calculated mass attenuation coefficients
versus the photon energies of each detector material are shown.
The graphs of calculated mass attenuation coefficients
versus each gamma-ray energy and absorber densities are
given in Fig. 3, respectively.
Table 1. Calculated mass attenuation coefficients according to
different photon energies.
PVT
ÍW)
G$O IX-4)
0|
CdWO, (p-'.9lW t <■*)
•«ordi
pX.10»
i1.KK
MS
FLVKA MO
FLVKA
MSI
FLVKA MSI
FLVKA
MSI
.UV,
•0
0.1*024» >0
0.18810
00:00'
150
500
400
2*42*0
1*0 4*0
J.704M
•-144)22
«0*01 a 24 0.14580
0.4093'5
«•♦•3038 0*1120
•.252102
«0*00012 0-25*00
0*2)503
«•*•?! 20
0*5410
1*32802
«0*2*124
0*045'0
>0.0001'1
0*0)081
0*04*?
4*400412
•*81234
>•*♦0*10
0.10*005
>•*♦•504
0.10210
•.114)20
>•*♦0425
0.1142*
0 00032
•*042)8
>•*♦•314
0.09523
0*41*4
0*43032
>o*oo::.t
0.0432'
0*0443
0*84142
>0.00043: uri:
!*••
U50
4.45OO0
0**2444
>•*♦0401 0*0223
4««»IS >*
*001)4
>OOOO'* I
0.04*04
0OJM1
•♦50494
<0.000352
0*4104
0.051154
>0*0040' 0*3142
0*24*2*
>•*♦0405
•**2114
>•*•010*
0.03241
•*''404
0*5251
0.050452
>••00314 0.0*122
0*00)12
>•*♦0)9'
0*41012
•0*00)15
0*5)243
>0*00202 0.0*322
1 00400
•*5301*
>0*00239 0*54*3
Figure 3. Gamma-ray mass attenuation coefficients vs. photon
energies of60, 150, 500, 600, 1,000 and 1,250 keV and absorber
densities.
six different gamma-ray (photon) energies.
Calculated mass attenuation coefficients of the absorber
materiais through the theoretical method were listed in Table
1. The NIST values for these detector materiais were also
indicated in the same table.
NIST values and the gamma-ray mass attenuation
coefficients calculated by FLUKA were highly compatible
with each other for each detector material (Table 1). But the
mass attenuation coefficients could not be calculated in lower
energy region (60 keV) and higher material density (Table 1)
because no gamma-ray photons could transmit through the
materiais.
The mass attenuation coefficients of the used detector
materiais were also calculated by means of XCOM program
(ver. 3.1) [11]. This program uses the NIST database. For this
reason, obtained mass attenuation coefficients from this
program were the same with those
4 Conclusion and Discussion
In this work, gamma-ray mass attenuation coefficients of PVT,
NaI, GaAs, GSO, and CdWO4 detector materiais were
theoretically calculated by means of FLUKA MC program at
02003-p.2
TESNAT 2015
of the NIST values. Therefore, XCOM results were not given in the table.
Consequently, the compatibility of the attenuation coeffícient results from FLUKA program with the NIST values leads us
that FLUKA can be used as an altemative way to determine gamma-ray mass attenuation coeffícients of the detector materiais.
Acknowledgement
The Authors thank to Dr. Pilicer for his help in the calculation procedure.
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02003-p.3
EPJ Web of Conferences 100,02004 (2015)
DOI: 10.1051/epjconf/ 201510002004
© Owned by the authors, published by EDP Sciences, 2015
Combined backscatter and transmission method for nuclear density gauge
Seyed Mohammad Golgoun1'a, Dariush Sardari1, Mahdi Sadeghi2, Mohammad Ebrahimi3, Mojtaba Aminipour4 and Mohammad
Reza Davarpanah5
1
Islamic Azad University, Science and Research Branch, Department of Medical Radiation, P.O. Box 14515-775, Tehran, Iran
Nuclear Science and Technology Research Institute, Radiation Application Research School, Tehran, Iran
3Sharif University of Technology, Department of Energy Engineering, P.O. Box 11365-8639, Tehran, Iran
4
Amirkabir University of Technology, Department of Energy Engineering and Physics, P.O. Box 15875-4413, Tehran, Iran
5
Pars Isotope Co., P.O. Box 14376-63181, Tehran, Iran
2
Abstract. Nowadays, the use of nuclear density gauges, due to the ability to work in harsh industrial environments, is very common.
In this study, to reduce error related to the p of continuous measuring density, the combination of backscatter and transmission are
used simultaneously. For this reason, a 137Cs source for Compton scattering dominance and two detectors are simulated by MCNP4C
code for measuring the density of 3 materiais. Important advantages of this combined radiometric gauge are diminished influence of
p and therefore improving linear regression.
1 Introduction
These days, practically every industry uses radiation in some
way. Science and industry use radioisotopes in a variety of
ways to improve productivity and, in some cases, to gain
information that cannot be obtained in any other way. Nuclear
techniques are increasingly used in Science, industry and
environmental management. The continuous analysis and
rapid response of nuclear techniques, many involving
radioisotopes, mean that reliable ílow and analytic data can be
constantly available. This results in reduced costs with
increased product quality.
Although scientists have only known about radiation since
the 1890s, they have developed a wide variety of uses for this
natural phenomenon. Today, to benefít humankind, radiation
is used in veterinary, medicine, academics, and industry, as
well as for generating electricity. In addition, radiation has
useful applications in such areas as agriculture, archaeology
(carbon dating), geology (mining and aggregates) and many
others.
2 Theoretical Principies
The radiometric density gauge is designed for continuous
measurement of the density of liquids, suspensions, slurries of
materiais. Measurement is made without physical contact and
is unaffected by changes of pressure, flow rate and viscosity.
A nuclear gauge is a tool that consists of a radioactive source
a
and a detector. The source emits a directed beam of particles
and a detector would receive this beam. The radiation that
comes from a radioisotope has its intensity reduced by matter
between the radioactive source and a detector which is used to
measure this reduction. This principie can be used to gauge the
presence or the absence, or even to measure the quantity,
density, thickness and moisture of material. The beam of
Gamma rays emitted by a radioactive source, generally 137Cs
or 60Co (depending on application), passes through the testing
material to NaI detector, which converts it into output in the
form of pulse rate. The strength of the pulse rate, in counts per
minute (cpm) depends upon the activity of the source, on a
geometric layout and on the quantity of material through which
the rays have passed. It will be a function of the density of the
Processing material so long as the volume and geometric
disposition of the material remains constant.
In this study we used collimated point 137Cs because it
emits gamma photons of initial energy of 662 keV. In
simulation we considered isotropic radiations and for the 137Cs
source energy, Compton scattering is the dominant interaction
[1,8]. Both photoelectric effect and pair production have mass
attenuation coeffícients that are heavily dependent on
elemental composition that is why only those source energies
within the “Compton window” are useful for densitometry. In
the MCNP4C simulation that will be discussed later, we
selected transmission confíguration and simulated pipe with
three different materiais individually [2].
e-mail: [email protected]
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution,
and reproduction in any medium, provided the original work is properly cited.
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510002004
EPJ Web of Conferences
Calcium
Sodium
Potassium
Magnesium
Hydrogen
Water
Ca
Na
K
Mg
H
H2O
20
11
19
12
1
10
40.08
22.99
39.10
24.31
1.008
18.016
0.4990
0.4785
0.4895
0.4936
0.9921
0.5551
The density of a material is dependent upon its atomic mass
(A), but the count rate in the nuclear density gauge is
dependent on the number of electrons (atomic number (Z)). As
above table, for the most materiais A=2Z [1].
Because the source to detector distance is fixed, ‘X’ in eq.
1 is constant. If the experiment source is 137Cs with energy of
662keV then for variant materiais the mass absorption
coefficient relationship is:
f A Y z,'
Figure 1. Principie of transmission method [7].
^2 = Hil - II —
A A zi,
by considering A=2Z then
l
Figure 2. Backscatter method [7].
The nuclear density gauge operates on the principie that
gamma ray is absorbed as a function of density expressed
mathematically (without buildup factor consideration) as [1, 4,
8]:
It =
=1
(3)
Pi
It means that mass absorption coefficient ‘p’ is constant for a
given process material. Therefore, the resultant radiation, ‘It’
is only a function ofprocess density ‘p’.
By transforming equation (1) to the (2)
logarithmic form, we can write the equation (l)in terms of p:
Ln (It ) = Ln (Ioppx
(4)
Ln(I.)-Ln(Io)
p=
- --- LY
(5)
px
(1)
Ln (' px
Where It transmitted radiation intensity, Io intensity measured
when no material is present, p total mass absorption coefficient
of material, p density of material, x
px
Due to constant consideration of p, equation (6) means that
there is a linear relationship between p and Ln (It) and therefore
the equation (7) will be written:
p = Cx Ln (It) + C2
(7)
that Ci and C2 are constants.
3 The Method
All relations above are for density gauge with both source and
detector collimated. In this configuration the buildup will be
reduced by both source and detector shielding that we consider
this as externai buildup reduction.
Table 1. Material characteristics.
Atomic
Atomic element symbol
Oxygen
O
Silicon
Si
Aluminum
Al
Iron
Fe
Atomic
No(Z)
8
14
13
26
Mass
No(A)
16.00
28.09
26.98
55.85
Z/A
0.500
0.4984
0.4818
0.4655
02004-p.2
TESNAT 2015
Detector numberl would receive transmission intensity plus
buildup and the detector number 2 could receivejust buildup
resulting from gamma interactions with matter. Buildup factor
is described as [3,8]:
B = total
()
1
I
8
unscattered
So the transmission equation considering buildup would be:
It =BI0 e
(9)
similar to equation (1) we transformed equation (9) to
logarithmic form and then we get:
Ln (It)-Ln (B ) = Ln (Io)-ppx
(10)
B in above equation is a function of p, so there is no linear
relationship between Ln (It) and p. Therefore we estimate B
from backscattered radiation by adding another detector to the
source side (detector No. 2). If we consider to Fig. 6 again, it
is clear that, this configuration is combination of backscatter
and transmission methods for measuring the density.
Thereupon, the buildup factor formula would change to:
B =———
(11)
I
Dl ~ ID2
where IDI transmitted radiation intensity to the detector number
1 and ID2 backscattered radiation to the detector number 2. In
the equation (10) B was one of variables. So we can put
equation (11) instead ofB in equation (10):
Ln (IDl - ID^ ) = Ln (Io)- ppx
(12)
above equation can be arranged on the basis of p:
1
,
, Ln (A) z ,
p=— Ln (IDl - ID2 )------------- (13)
px
pL
Now equation (13) is a linear relationship between p and Ln (ID1
Figure 5. Simulated density gauge without internai buildup
reduction.
“
But in our research we used new configuration for buildup
reduction that is coincidence method buildup reduction. We
mentioned this method as an online internai buildup reduction.
As shown in Fig. 6 we used 2 detectors that could work in
coincidence mode for online simultaneous
I
D2 ) •
4 MCNP4C simulation
There are two main procedures of calculating density of the
matter with known density materiais. First method is point
calibration that uses one, two or more calibration points.
Second method is curve fit that calculates calibration equation
for calibration points. In this study we used point calibration
and MCNP4C code for simulation of counting system for three
arbitrary testing materiais. The materiais are gasoline, gas oil
and pure water with the known density of 0.71 gr/cm 3, 0.83
gr/cm3 and 1 gr/cm3, respectively. The radioactive point source
is 137Cs and the emitted beam to the detector is narrow [5, 6].
The detectors are 2 inch NaI detector that could receive both
scattered and transmitted radiations. The source to detector
number 2 distance is 10 cm and the simulated iron pipe has 14
cm inner diameter and 14.5 cm outer diameter. We calculated
linear regression for both combined method and transmission
method, and then made a comparison at these 2 methods.
Figure 6. Simulated density gauge with internai buildup
reduction.
02004-p.3
EPJ Web of Conferences
5 Conclusions
In some special industries those their productions have close density ranges, it is very important to calculate density in reliable
manner. For example in oil industry the density of gasoline ranges from 0.71-0.77 g/cm3. It is important to note that in transmission
method without buildup reduction that simulated by MCNP4C tool, we supposed that the radiation beam is in optimistic condition
(directed beam), so in fact, the regression in Fig. 5 is not reachable and the regression without buildup correction wo uldbe worse
than 0.9736 inreal configuration. With the simulation of combined backscatter and transmission density meter, linear regressi on
of the density of three testing materiais has improved by 2.4%.
Figure 7. Diagram between density and logarithmic intensity (without internai reduction).
Figure 8. Influence of internai buildup correction.
Acknowledgment
We appreciate and acknowledge support for work on this article by Pars Isotope Co.
References
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3.
4.
5.
6.
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A. Vidal, G. Viesti, F. Pino, H. Barros, L. Sajo- Bohus. EPJ Web of Conferences. 66 (2014)
Y. Haiuma. Radiat. Phys. Chem. 41 (1993) 631
B.D. Sowerby, C.A. Rogers. Appl. Radiat. Isotopes
63 (2005) 789
E.R Christensen. Nucl. Eng. Des. 24 (1973) 431
D. Sardari, S. Saudi, M. Tajik. Ann. Nucl. Energy 38 (2011)628
IAEA-TECDOC-1459. (2005) ISBN 92-0-107805-6
G.F. Knoll. Radiation Detection and Measurement 3rd ed. (1989) ISBN 0-471-07338-5. Wiley, NewYork
02004-p.4
EPJ Web of Conferences 100, 02002 (2015)
DOI: 10.1051/epjconf/ 201510002002
© Owned by the authors, published by EDP Sciences, 2015
Geant4 calculations forspace radiation shielding material AI2O3
Veli Capali1'a, Tolga AcarYesil2, Gokhan Kaya2, Abdullah Kaplan1, Mustafa Yavuz2 and Tahir Tilki2
1
Süleyman Demirel University, Faculty of Arts and Sciences, Department of Physics, 32260 Isparta, Turkey 2Süleyman Demirel
University, Faculty of Arts and Sciences, Department of Chemistry, 32260 Isparta, Turkey
Abstract. Aluminium Oxide, AI2O3 is the most widely used material in the engineering applications. It is signií icant aluminium
metal, because of its hardness and as a refractory material owing to its high melting point. This material has several engineering
applications in diverse fields such as, ballistic armour Systems, wear components, electrical and electronic substrates, automotive
parts, components for electric industry and aero-engine. As well, it is used as a dosimeter for radiation protection and therapy
applications for its optically stimulated luminescence properties. In this study, stopping powers and penetrating distances have
been calculated for the alpha, proton, electron and gamma particles in space radiation shielding material AI2O3 for inc ident
energies 1 keV - 1 GeV using GEANT4 calculation code.
1 Introduction
Aluminium Oxide, AI2O3 is the most widely used material in
the engineering applications. It is signifícant aluminium metal,
because of its hardness and as a refractory material owing to
its high melting point. It is one of the most important materiais
due to its interesting characteristics such as easy availability,
low cost, low environmental impact, ease of synthesis, good
optical transparency, high refractive index, high melting point,
hydrophobicity, mechanical strength, dielectric behaviour,
electrical insulating property, thermal, and Chemical stability
[1].
NASA has always had a major emphasis on developing
technologies that can be used for manned space flight, space
station and satellite. Clearly, any sort of manned space requires
extraordinary design considerations and extremely effective
technology, because there are innumerable hazards associated
with manned space flight [2]. Among these, radiation damage
and heat and cold thermal effrcient are very major concem.
Currently, NASA uses aluminium for radiation shielding [3].
This material is marginally effective at radiation shielding,
since it has a low electron density. Therefore, researchers have
been looking for other materiais, which have higher hydrogen
content than aluminium, to use as radiation shielding material.
It would then re-enter the atmosphere of the Earth and glide
back down to the ground. In order to withstand the high
temperatures associated with re-entry, NASA created the
Space Shuttle Orbiter Thermal Protection System (TPS) [4].
However the energy gained by the orbiting electron is often
more than the binding energy of the atom and is therefore
removed from the atom. The interacting atom is said to be
ionized due to this a-particle electron collision. The physical
quantity that describes the slowing down of charged particles
in mater is the stopping power dE/dx where dE is the energy
lost in the distance dx. The Bohr relation for stopping power
of heavy particle is given by
4,
zz2 k2 e4 1 ( 2mv2
mv2
I
n = number of electrons per unit volume,
m = electron rest mass,
v = velocity of the particle,
Z= charge of the particle,
e = electron charge
dE
ko = l/4n£o,
(1)
dx
I = mean excitation
energy of the médium [6].
This was modified by taking into account the quantum
effects by Bethe, and the relativistic effects by Bloch, and
frnally the well-known Bethe-Bloch expression for the
stopping power was given as [7]:
, ( 2mv2 ]
( v2 ] v 2
ln I -----I - In I 1 —- I —-
l I I l c2 I c2
2 Methods
GEANT4 is a free simulation and calculation code that can be
used to investigation of high-energy physics, medicai physics,
space, and radiation physics. GEANT4 is an abundant set of
physics models to handle the interactions of particles with
matter across a large energy range. Data and expertise have
been drawn from many sources around the world and in this
respect, GEANT4 acts as a repository that incorporates a large
part of all that is known about particle interactions [5].
Energy lost by a-particle in a single collision is very small.
a
dE 4~z 2k2e4 dx
mv2
Corresponding author: [email protected]
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510002002
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use,
(2)
EPJ Web of Conferences
The stopping power given in the above equation takes into
account only collisions with electrons. Events with nuclei are
not considered in this formula. There is one important
drawback of this formula. It was derived using the perturbation
theory and the fírst Bom approximation [8].
and alpha particles in the incident energy range of 1 keV - 1 GeV for
AI2O3.
In the incident gamma energy range of 1 keV - 0,9 MeV,
required stopping thickness of AI2O3 could be approximately
1,7 cm.
3 Results
The penetrating distance and stopping power calculations of
alpha, electron, proton and gamma particles for AI2O3
shielding material have been given in Figs. 1 and 2. The
calculated stopping power values of alpha, proton and electron
projectile particles in AI2O3 target for incident energies of 1
keV - 1 GeV have been exhibited in Fig. 1. Based on an
approximate theory i.e. the Thomas Fermi model of atom,
Bohr suggested that for high energies above 100 keV region,
the stopping power decreases as the particle velocity
approaches the velocity of light. When the velocity of the
particle is comparable with speed of light, the normal spherical
field becomes distorted in the direction of motion of the
particle expanding laterally and in the perpendicular direction
shrinking. Bethe Bloch suggested that for high energies above
approximately 1 MeV region, the stopping power decreases as
the incident particle’s energy.
Figure 3. The penetrating distance calculations of gamma in the
incident energy range of 1 keV - 100 keV for AI2O3.
All calculated stopping power and penetrating distance
results used by GEANT4 have been given in Tables 1, 2 and
3.
Table 1. The Geant4 penetrating calculations results ofproton,
electron and alpha particles for AI2O3.
Incident Energy (MeV)
Figure 1. The stopping power calculations of proton, electron and
alpha particles in the incident energy range of 1 keV - 1 GeV for AI2O3.
The penetrating distance calculations of alpha, electron,
proton and gamma particles for AI2O3 shielding material have
been given in Figs. 2 and 3. According to calculated
penetrating results, the penetrating distance of alpha particles
are the poorest. So this particles cannot be managed to enter
into AI2O3. On the contrary alpha particles, gamma has the
most penetrating in the AI2O3 target.
Figure 2. The penetrating distance calculations of proton, electron
02002-p.2
Electron
Penetrating
Distance (cm)
Energy
(MeV)
Alpha
Penetrating
Distance (cm)
Proton
Penetrating
Distance (cm)
0.001
1.76E-05
2.29E-05
6.85E-05
0.01
2.30E-04
4.98E-04
2.17E-04
0.1
4.30E-04
0.00453
7.84E-04
0.2
0.3
6.80E-04
8.42E-04
0.01409
0.02632
0.00135
0.00201
0.4
9.81E-04
0.04012
0.00277
0.5
0.00111
0.0549
0.00363
0.6
0.00168
0.07033
0.00459
0.7
0.00193
0.08622
0.00565
0.8
0.0021
0.10246
0.0068
0.9
0.00234
0.11895
0.00805
1
0.0024
0.13561
0.00938
10
0.05271
1.68422
0.40925
100
0.20755
16.8012
2.42436
200
0.71304
33.4877
8.0816
300
1.46686
50.159
15.9504
400
2.43978
66.8267
25.4686
500
3.60954
83.4936
36.2854
600
4.95783
100.16
48.1289
700
6.46885
116.27
60.7857
800
8.12877
133.494
74.0742
900
1000
9.92531
11.8485
150.16
166.827
87.8831
102.132
TESNAT 2015
thickness of AI2O3 could be approximately 12, 167, 103 cm.
respectively. The obtained AI2O3 stopping power results for the
projectile charged particles can be used in several applications
such as space engineering, radiation therapy and protection.
Table 2. The Geant4 stopping power calculations results of próton,
electron and alpha particles for AI2O3.
Energy
(MeV)
Alpha Stopping
Power
(MeV*cm2/g)
Electron
Stopping
Power
(MeV*cm2/g)
Proton Stopping
Power
(MeV*cm2/g)
0.001
91.7138
80.3267
73.51
References
0.01
260.744
17.3191
232.5
1.
0.1
828.899
3.30542
470
0.2
1083.77
2.26224
412.7
0.3
1222.91
1.91587
345.5
0.4
1306.44
1.7528
310.6
0.5
1355.2
1.66384
276.5
0.6
1379.95
1.60608
249.4
0.7
1386.82
1.56534
227.9
0.8
1382.69
1.53815
210.2
0.9
1
1371.6
1353.52
1.519
1.50706
195.7
183.2
10
394.568
1.47181
35.309
100
68.2801
1.507
5.895
200
39.6243
1.51054
3.659
300
400
29.0284
23.4376
1.51115
1.5113
2.877
2.464
500
19.9658
1.51133
2.214
600
17.5955
1.51133
2.051
700
800
15.8731
14.565
1.51133
1.51133
1.938
1.855
900
13.5382
1.51133
1.793
1000
12.7116
1.51133
1.745
R.K. Sharma, P. Jeevanandam, Ceramics International,
39,3337 (2013)
2. J.W. Wilson, J. Miller, A. Konradi, F.A. Cucinotta, NASA
Conference Publication vii, 3360 (1997)
3. http://www.nasa.gov/vision/space/travelinginspace/ra
diation_shielding.html.
4. http://www.nasa.gov/centers/ames/research/humanin
space/humansinspace-thermalprotectionsystem.html
5. S. Agostinelli, et al., Nucl. Instrum. Methods Phys.
Res. A. 506, 250 (2003)
6. M. Inokuti, Rev. Mod. Phys. 43, 297 (1971)
7. H.Bethe,Ann.Phys. 5, 325 (1930)
8. A. Getachew, “Stopping power and range of Protons of
various energies in Different materiais”, Depart. of Physics,
Addis Ababa University (2007)
Table 3. The Geant4 stopping power calculations results of gamma
particles for AI2O3.
Energy
(MeV)
Gamma Penetrating Distance (cm)
0.001
8.92E-04
0.01
0.00158
0.1
0.12273
0.2
0.36485
0.3
0.67607
0.4
0.96181
0.5
1.18423
0.6
1.34936
0.7
1.4734
0.8
0.9
1.57004
1.64883
Composite materiais that contain the highest hydrogen and
oxygen are very good shielding materiais whereas aluminium
and same materiais are not a good shielding material due to its
low electron density [5]. Therefore, AI2O3 is better than
aluminium for radiation shielding. In the incident alpha, electron
and proton energy range of 1 keV-1 GeV, required stopping
02002-p.3
EPJ Web of Conferences 100, 02001 (2015)
DOI: 10.1051/epjconf/ 201510002001
© Owned by the authors, published by EDP Sciences, 2015
Comparison of RPL GD-301 and TLD-100 detectors responses by Monte
Cario simulation
A-H. Benali1'2, G. Medkour Ishak-Boushaki2, A. Nourreddine 3, M. Allab 2
1
2
3
Faculty of Science of Nature and Life, Univ. Echahid Hamma Lakhdar, El-oued Algeria.
Laboratory SNIRM-Faculty of Phys., Univ. of Sciences and Technology Houari Boumediène, Algiers Algeria.
Institut Pluridisciplinaire Hubert Curien de Strasbourg, France.
Abstract: (LiF:Mg,Ti) Thermo Luminescent Detectors are widely used for monitoring patient dose in radiotherapy treatments
whereas Radio-Photoluminescent Dosimeters (RPL) are increasingly devoted to radiological protection purposes. A study, aiming
at extending the use of RPL glasses to clinicai applications, is conducted by comparing the dosimetric characteristics of a RPL glass
dosimeter, commercially known as GD-301 to those of a TLD -100 detector. In this paper, preliminary Monte Cario simulation
results describing these dosimeters responses in terms of absorbed dose, source- detector distance and characteristics of the incident
gamma field are presented.
1 Introduction
A radiation dosimeter is a detector used to measure or
evaluate, either directly or indirectly, quantities required for
radiation protection purposes as the exposition rate, kerma,
absorbed dose or equivalent dose.
For radiation protection applications, two kinds of
dosimeters are used: active or operational dosimeter and
passive one. The fírst device measures absorbed dose in real
time. The second gives integrated absorbed dose over a period
of time [1].
Some materiais, known as luminescent detectors, when
irradiated emit a quantity of light proportional to the absorbed
ionizing radiation. Three groups of luminescence detectors are
applied in personal dosimetry: thermoluminescence detectors
(TLDs), detectors based on optically stimulated luminescence
(OSLDs) and radiophotoluminescence (RPL) glasses [2, 3].
Thermoluminescent dosimeters (TLDs) are frequently
used for monitoring ambient and personnel doses. The readout
process of these devices needs a heat treatment. The great
disadvantage of these dosimeters is the fact that their readout
cannot be repeated: luminescents centers, created by ionizing
radiation, disappear after heating [4].
Radiophotoluminescent glass dosimeters (RPLGDs) have
the advantage to be read repeatedly, because the readout
process does not eliminate the luminescent centers [5].
Actually, RPLGD are increasingly used for monitoring
ambient dose and personnel dose but are not yet regularized
for monitoring patients dose in radiotherapy treatments.
In view to evaluate the use of RPLGD in vivo dosimetry
[6], we have undertaken a comparative study, by Monte Cario
simulation, between the dosimetric characteristics of a RPL
glass dosimeter, commercially known as GD-301 and those of
a TLD -100 detector. We give here the preliminary results.
of the glass dosimeter was as follows: 31.55% P, 51.16% O,
6.12% Al, 11.00% Na, and 0.17% Ag. Effective atomic
number and density of the glass dosimeter were 12.039 and
2.61 g/cm3, respectively [6].
The TLD-100 dosimeter is made of lithium fluoride (LiF)
crystals in the form of chips (3x3*lmm3 in dimensions) with
density of 2.635 g/cm3. Because its effective atomic number
of 8.3 close to that of water or tissue, LiF-TLD is used
routinely for dose measurements in radiotherapy. The used
TLD-100 contains 26.7% Lithium, 73.2% Fluorine, 200 ppm
Magnesium, and approximately 10 ppm of Titanium. This
type of TLD- 100 is denoted as TLD-A [4, 7].
The dosimeters are irradiated in a depth of 10 cm of a solid
water phantom. The phantom is a parallelepiped with
dimensions of 30x30x30 cm3 and weight composition as
follows: 8.09% H, 67.17% C, 2.42% N, 19.87% O, 0.13% Cl,
2.32% Ca and 0.17% Ag. Effective atomic number and density
of the solid water phantom were 3.57 and 1.015 g/cm3,
respectively [4].
3 Monte Cario simulation
Monte Cario N-Particle Transport Code System [8] was
2 Dosimetry system
For our study, a model GD-301 glass dosimeter (AGC Techno
Glass Corp., Shizuoka, Japan) is used. The model GD-301 is
1.5 mm in diameter and 8.5 mm in length. Weight composition
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used to calculate the absorbed radiation dose in each
luminescent detector.
The experimental set up modeled by MCNP5 code
consists in a punctual photon point source collimated in a cone
of rectangular extremity surface equal to the X ray fíeld sizes
used in radiotherapy treatments. The photon cone irradiates a
luminescent dosimeter placed in a depth of 10 cm from the
surface of the solid water phantom. Figure 1 gives the modeled
experimental set-up used for Monte Cario simulation.
The “F6 tally” for photons was used to record the energy
deposition in each studied dosimeter. For ensure all statistical
checks recommended by MCNP5 code, a total of 700 millions
starting photons were considered per simulation run.
0,9-
*
0,8 -|---- 1 ----- 1 --- 1 -----1 ---- 1----- 1 --- 1 -----1 --- 1 ----- 1 --- 1 -----1 ---- 1----- 1 ---1 ------1
80
85
90
95
100
105
110
115
120
SSD (cm)
Figure 2. SSD dependence for glass and TLD dosimeters.
4.2 Field size dependence
For the same geometry of Fig. 1, the absorbed energy in each
investigated dosimeter, irradiated by a 15 MV X- ray beams at
a distance of 100cm, evaluated by Monte Cario simulation and
carried out for different fíeld sizes varying from 5x5cm 2 to
20x20 cm2 are reported in Fig.
3. The calculated absorbed energies values are normalized
to the value estimated for a reference fíeld size of 10x10 cm2.
A negligible discrepancy between the results of the RPL GD301 and TLD-100 dosimeter is noticed.
Figure 1. Experimental set-up modeled
4 Dosimetric characteristics
Field size (em)
Aiming to use RPL detectors in vivo dosimetry, Monte Cario
simulation of some dosimetric characteristics, for both TLD100 and RPL GD 301 detectors, have been carried out. We
give here preliminary simulation results.
4.1 SSD dependence
The effect of the distance source-detector (SSD) on dose
measurements was investigated by considering the
experimental set-up of Fig. 1. For Monte Cario simulation, we
have considered a punctual source emitting photons of 3.6
MeV energy (corresponding to the mean energy of 15 MV Xray beams) in a cone of 10x10 cm2 area at the solid water
phantom superfícies (corresponding to a fíxed fíeld size of
10x10 cm2). The dose absorbed, at 10 cm depth in the solid
water phantom, was calculated when increasing the SSD from
85 to 115 cm. The results of simulation, for both dosimeters
RPL GD-301 and TLD-100 are reported in Fig. 2. The
calculated doses are normalized to the dose value evaluated at
SSD of 100 cm. A good agreement is achieved between the
two dosimeters responses except at 115 cm where a
discrepancy of about 1% is noticed.
Figure 3. Field size dependence of the absorbed energy in
RPLGD-301 and TLD-100 dosimeter.
5 Conclusion
This paper is a preliminary comparative study, by Monte Cario
simulation using MCNP5 code, of dosimetry characteristics
between a Radio photoluminescent and a thermoluminescent
dosimeter.
The aim of this work is to evaluate the use of an RPL
dosimeter known commercially as RPLGD-301, instead of a
TLD-100 dosimeter, to monitor patient’s doses in
radiotherapy treatments.
The fírst Monte Cario simulation results show a very
similar behavior of the variation of the absorbed dose in
02001-p.2
TESNAT 2015
either RPL or TLD dosimeter versus the source detector distance and the irradiated fíeld size. This work is in progress.
References
1.
2.
3.
4.
5.
6.
7.
8.
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Aspects. In: E.B. Podgorsak, Radiation oncology physics'.
A Handbook for teachers and students, Vienna, Áustria:
IAEA 2005, 71-100. ISBN 92-0107304-6.
Pawe Olko, Radiation Measurements 45 (2010) 506511.
Z. Knezevi, et al., Radiation Measurements 57 (2013) 918.
D Baltas, L Sakelliou, N Zamboglou, The Physics of
Modern Brachytherapy for Oncology, New York, USA:
Taylor & Francis Group, 2007.
S.-M. Hsu, et al., Radiation Measurements 43 (2008) 538 -541.
J.-E. Rah, U.-J. Hwang, H. Jeong, S.Y. Park, Radiation Measurements 2011; 46: 40-45.
H. Asni, et al., Journal of Engineering Thermophysics, 2011; Vol. 20, No. 3: 329-333.
MCNP-A General Monte Cario N-Particle Transport Code, Version 5 Los Alamos National Laboratory 2003.
02001-p.3
EPJ Web of Conferences 100, 0100 9 (2015)
DOI: 10.1051/epjconf/ 20151000100 9
© Owned by the authors, published by EDP Sciences, 2015
Calculation of pre-equilibrium effects in neutron-induced cross section
on 32-34S isotopes using the EMPIRE 3.2 code
Leila Yettoua, Mohamed Belgaid
University of Bab Ezzouar, Faculty of Physics, Laboratory SNIRM, Algiers, Algeria
Abstract. In this study, a new version EMPIRE 3.2 code was used in the cross section calculations of (n,p) reactions and in the
calculation of proton emission spectra produced by (n,xp) reactions. Exciton model predictions combined with the Kalbach
angular distribution systematics were used and some parameters such as those of mean free path, cluster emission in terms of
Iwamoto-Harada model, optical model potentials of Morillon for nêutrons and protons in the energy range up to 20 MeV, levei
density for spherical nuclei of Gilbert-Cameron model and width fluctuation correction in terms of compound nucleus have been
investigated our calculations. The excitation functions and the proton emission spectra for 32>34S nuclei were calculated, discussed
and found in good agreement with available experimental data.
1 Introduction
Nêutron induced reactions on 32>34S isotopes and double
differential cross sections calculations for proton emission are
important not only for many materiais as requested by the
accelerator driven systems (ADS) and waste transmutation
problems but also for applications of radioactivity in both
diagnostics and therapy [1,2]. According to Gupta et al., [3],
pre-equilibrium processes play an important role in nuclear
reactions induced of few MeV (< 50 MeV) where their
iníluences at 14.8 MeV have been studied. Experimental
nêutrons induced cross section data accessed by the EXFOR
database [4] are necessary to develop the theoretical models.
These models are frequently needed when the experimental
data are not obtained because of the experimental diffículties.
The main purpose of this work is to investigate the sensitivity
to input parameters in neutron-induced reactions in the energy
range up to 20 MeVby using the EMPIRE 3.2 code [5].
(2)
x XWb (E,n,eb )r(n) n
where crrab (Einc) is the cross section of the reaction (a,b) , Wb
-
(E,n,eb) is the probability of emission of a particle of type b (or
gamma ray) with energy eb from a State with n excitons and
excitation energy E of the CN, and D (E ) is the depletion
ab
inc
factor. The PCROSS code uses the Williams formula [10],
with Kalbach's method [11].
The module PCROSS included in the EMPIRE 3.2 code [5]
describes the classical exciton model [6] which includes
nucleon, cluster and gamma emissions. This model is based on
the solution of the master equation [7] in the form proposed by
Cline [8, 9] as:
-qt=o (n) = A- (E,n + 2)T(n + 2)
(1)
(E,n) + T_ (E,n) + L(E,nn) where qt(n) is
a
inc
d
where the Pauli correction A (P,h ) is calculated in accordance
2 Exciton model formulae
+À_(E,n - 2)r{n-2)
the initial occupation probability of the
composite nucleus in the State with the
exciton number n, A+(E,n) and Z.(E, n)
are the transition rates for decay to
neighboring States, and L(E,n) is the total
emission rate integrated over emission
energy for particles (protons n, nêutrons v
and clusters) and y -rays. The preequilibrium spectra can be calculated as:
dd ab
^ (f, ) = ar.(E }D AE- ) b
a,b
inc
a,b
( g ( E - D)-A (p,h))P'
p !h!( p + h-1)!
®(P,h,E )=g
(3)
Using the parameterization of transition
rate proposed by Blann and Mignerey [12] and the particlehole State densities from the Williams formula, we obtain the
expressions for the internai transition rates found by Machner
[13].
Corresponding author: [email protected]
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution,
and reproduction in any medium, provided the original work is properly cited.
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510001009
EPJ Web of Conferences
1
?
À+( E,n )= ------ 1.4xl021 E' -----— 6xWls E
’ Kmp L
n +1
16-S-32(N,X),DAE EÍ1.41E+7
An21
(4)
A
where Kmfp is the mean free path parameter which set to a value
of 1.5 (by default) in our calculations. Kalbach's method
[7,8,13] was implemented for the calculation of the nucleon
emission rate. The probability of emission Wb (E, n, eb) of a
nucleon b with spin sb, reduced mass pb and energy eb from a
State with n excitons is given by,
16-S-32(N,X),DAE
An40
EÍ1.41E+7
Wb ( E,n,eb)
(5)
ESSU
Qb (P’h)
where E(U) is the excitation energy of the CN (residual
nucleus), p,h,U) istheparticle-holestatedensity,and CT“V is the
inverse channel reaction cross section. The factor Qb (p.h)
takes into account the fraction of b nucleons in the n-th stage
of the reaction and is calculated as discussed by Gupta [14]. In
the framework of statistical model (compound nucleus model),
the Hauser-Feshbach model was used.
The decay probability (Eq.6) is defined in terms of
transmission coefficients associated to the reaction channels
which might be particles emission, photon emission or fission.
Pb (E,Jn) =
T (Ex, Jx)
Z T (Ex, Jx)
(6)
1.40E-008 -
7.00E-009 -
O.OOE+
0
OOO
5
10
Energy
(MeV)
16-S-32(N,X),DAE
An59
Energy
(MeV)
16-S-32(N,X),DAE
An79
In the EMPIRE 3.2 code [5], the levei densities are described
by several models with the corresponding parameterizations.
The phenomenological Gilbert- Cameron Model [15], which
is included in RIPL-3 library [16] is used in this work and the
spin cut-off factor a (Ex) is given by:
a2( Ex ) = 0.146 A™4ãU
(7)
16-S-32(N,X),DAE EÍ1.41E+7
Arn7
01009-p.2
EÍ1.41E+7
Energy
(MeV)
EÍ1.41E+7
15
TESNAT 2015
16-S-32(N,X),DAE EÍ1.41E+7 Anl20
4 Conclusion
Energy (MeV)
Fig. 1 Calculated double differential cross sections at various angles
for 32S(n, x)32P reactions at 14.1 MeV incident nêutron energy using
Morillon and Romain potential [19,20] (continuous lines) compared
to the Koning-Delaroche potential standard [21] (dashed lines) and to
the experimental data (open squares) [1],
3 Results and discussions
In this work, the theoretical calculations have been made in the
framework of exciton model [6] combined with Kalbach
angular distributions systematics [17]. Probability of cluster
emission is calculated in terms of the Iwamoto- Harada model
[18]. The mean free path parameter of the nucleon in the
nuclear matter [12] set to 1.5 (by default) in PCROSS module.
Hauser-Feshbach
calculations
require
transmission
coefficients for particle emission, for energies spanning from
zero to the maximum emission energy. The sulíur dispersive
global spherical optical model potential of Morillon [19, 20]
was used both for nêutrons and protons. The dispersive
potentials with different geometry of the imaginary and real
parts are used with the ECIS module of the EMPIRE 3.2 code
[5]. The Gilbert-Cameron model [15] nuclear levei densities
were used which include the levei density a-parameter of
Arthur systematics [22] in order to perform the calculations.
Theoretical predictions based on the exciton model combined
with the Kalbach angular distribution systematics [17] are
shown as continuous lines for all the figures. The calculated
double differential emission spectra at various angles for
32
S(n,x)32P reactions at 14.1 MeV incident nêutron energy
using the Morillon and Romain potential [19, 20] (continuous
lines) compared to the Koning-Delaroche potential standard
[21] (dashed lines) and to the experimental data [1] (open
squares) are shown in Fig. 1. The different free parameters
used by default in PCROSS module of the EMPIRE 3.2 code
[5] and the dispersive global spherical optical model potential
of Morillon for both nêutrons [19] and protons [20] and the
Gilbert-Cameron model [15] nuclear levei densities were
sufficient to fit the proton emission at 14 MeV incident energy
in Figs.l and 2 respectively. Also, the Morillon and Romain
potential for nêutrons [19] and protons [20] give the lower
value of when compared to the Koning- Delaroche potential
standard for nêutrons and protons [21] and when compared to
the experimental data [1] at all emission angles. The calculated
excitation functions and the experimental data [24-33] for
32
S(n,p)32P and 34S(n,p)34P reactions are shown in Figs. 3 and
4 respectively as a function of nêutron induced energy in the
range of 12-20 MeV. The sensitivities of the levei density aparameter of Arthur systematics [22] of Gilbert- Cameron [15]
and the dispersive global spherical optical model potential of
Morillon and Romain [20] for both nêutrons and protons give
a good agreement between the calculations and the
experimental data.
In this study, the results of the calculated double differential
cross sections for 32S(n,x)32P at 14 MeV incident energy agree
well with the experimental data [1, 23] by using the Morillon
and Romain potential of the EMPIRE 3.2 code [5]. Also, the
excitation curves for 32S(n,p)32P and 34S(n,p)34P reactions
exhibit better agreement with the levei density a-parameter
according to Arthur systematics [22] of Gilbert-Cameron [15].
Finally, our calculations using both classical exciton model [6]
and Hauser-Feshbach theory describe the experimental data
well. The reasons can be that the light nucleus of sulfur and/or
the energy range up to 20 MeV are sufficient to fit the curves.
We hope others data above 20 MeV from the EXFOR database
[4] in order to show the pre-equilibrium effect of exciton model
[6] in neutron-induced cross section on 32,34S isotopes using the
EMPIRE 3.2 code [5].
Fig.2 The comparison of the calculated proton emission cross section
(continuous lines) with the Morillon and Romain potential [19, 20]
(continuous lines), the Koning-Delaroche potential standard [21]
(dashed lines) and the experimental data at 14.1 MeV and 14.6 MeV
nêutron incident energies for 32S(n, x)32P reaction. The experimental
data (open square and open lozenge) are taken from the references [1]
and [23],
Fig.3 The comparison of the excitation function for 32S(n, p)32P
reaction using Morillon and Romain potential [20] (continuous lines)
compared to the Koning-Delaroche potential standard [21] (dashed
lines) and to the experimental data [24-27].
Incident Energy (MeV)
Fig.4 The comparison of the excitation function for 34S(n, p)34P
reaction using Morillon and Romain potential [20] (continuous lines)
compared to the Koning-Delaroche potential standard [21] (dashed
01009-p.3
EPJ Web of Conferences
lines) and to the experimental data [28], [3], [29-33],
Acknowledgments
We thank the organizers of the workshop (IAEA) 2-6 dec2013
for this opportunity to offer us view of the EMPIRE 3.2 code.
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(Database Version of March 16, 2015).
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MeV nêutrons. Joum.: Nuovo Cimento 22, 4, 853855,(1961).
24. J.C. Robertson, B. Audric and P. Kolkowski, Some
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sections of some reactions of Al, S, Mn, Fe, Ni, In and I
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26. D.C. Santry, J.P. Butler, The S32 (n.p) P32 reaction as a
fast-neutron flux monitor, revue canadienne de chimie,
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the 34S(n, a)31Si Reactions. Phys. Rev. 107, 1363, (1957).
28. Y. Kasugai, et al., Measurement of (n, p) Reaction Cross
Sections for Short-lived products (TI/2= 0.6 -13.8 s) by 14
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29. P.N. Ngoc, et al., Investigations of (n,p), (n,a) and (n,2n)
reactions around 14 MeV, Thesis abstract, prelim. results
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Univ., Budapest, Hungary, (1980).
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Kemphysik, Vienna, Áustria, (1970) (unpublished).
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(1989).
01009-p.4
EPJ Web of Conferences 100, 01010 (2015)
DOI: 10.1051/epjconf/ 201510001010
© Owned by the authors, published by EDP Sciences, 2015
Calculation of cross-sections and astrophysical s-factors for the
63
Cu(a,n) and 63Cu(a,y) reactions
Ercan Yildiz1’a, Abdullah Aydin1, Ismail Hakki Sarpun2, Eyyup Tel3
1
Kirikkale University, Department of Physics, Kirikkale, Turkey
Afyon Kocatepe University, Department of Physics, Afyonkarahisar, Turkey
3Osmaniye Korkut Ata University, Department of Physics, Osmaniye, Turkey
2
Abstract: The cross sections and astrophysical S-factors of the 63Cu(a,y) and 63Cu(a,n) reactions have been calculated. The
radiative alpha capture reaction cross sections was calculated in the incident energy range of 3 to 10 MeV and the (a,n) reaction
cross sections was calculated in the incident energy range of 7 and 16 MeV. In these theoretical calculations, the TALYS 1.6 and
NON-SMOKER codes were used. Also for these reactions, it was calculated the astrophysical S-factors which describe the
possibility of reaction in low energies. Obtained results were compared to the experimental data taken from EXFOR database.
1 Introduction
In light charged particle induced reactions, the total reaction
cross sections drop swiftly (using of an exponential scale) at
low energy region where Coulomb barrier is more effective,
and measurement of the relevant cross-sections becomes more
diffícult [1]. But the nuclear astrophysical S-factors change
slowly with energy. Therefore extrapolation of the
experimental cross section measurements in the energy range
of the low energy of the s-factor is not possible, it is much more
convenient. Cross-section measurements and calculations for
light charged particle capture sections reactions on heavy
nuclei are important for nucleosynthesis applications [2] and
for statistical model tests.
The temperatures exceed 109K at inner part of the
supemovae. This inner region have proton and a-particle
sections on médium and may be important in determining the
mix of elements and isotopes which have been released from
such stellar explosions. Investigation of the capture crosssections for different mass regions is very important in testing
of theoretical models.
In this study we calculated the cross sections and
astrophysical S-factors of the 63Cu(a,y) and 63Cu(a,n) reactions.
Obtained results were compared to the experimental data taken
from EXFOR database [3].
2 Cross-section, astrophysical s-factor
Nuclear reactions are very important in astrophysics [4] due to
conceiving of evolution, nucleosynthesis, stars, giants and etc.
Depending on some physical parameters, stellar buming may
involve many reactions of various nuclei. The reaction rates
can be calculated using the cross-sections o(E) of reactions, or
related astrophysical S-factor defíned as
o(E)=E-1exp(-2n^)S(E)
S(E) = o(E) E exp(2n^)
a
(1)
(2) where, i] is the
Sommerfeld parameter, (ZiZ2e2)/hv. S(E) is function of
energy with slow variation than exp(-2^q) and o(E) (Fig.l). In
astrophysical applications, S(E) should be known for many
reactions at low energies, E < a few MeV. Experimental
measurements of o(E) at lower energy are mainly not
available (because of the Coulomb barrier exponentially
suppresses low-energy cross sections). Theoretical evaluation
of S(E) is model dependent, so that nuclear physics
uncertainties of evaluated S-factor can be substantial [4].
Figure 1. Dependence on cross-section and S(E) for the
reaction3He(a, y)7Be [5]
3 Calculations and results
In this study, the total reaction cross-sections and by using this
cross-sections astrophysical S-factors of the 63Cu(a,y) and
63
Cu(a,n) reactions were calculated according to Eq. 2. The
radiative alpha capture reaction cross-sections and the (a,n)
reaction cross sections were calculated in the incident energy
range of 3 to 10 MeV and 7 to 16 MeV, respectively. In these
calculations, the TALYS 1.6 [6] and NON-SMOKER [7]
codes were used. Also for these reactions, we calculated the
astrophysical S-factors which describe the possibility of
reaction in low energies. Obtained results were compared to
the available experimental data of EXFOR database in Figs. 2
and 3. One can see that the agreement between the
Corresponding author: [email protected]
This
is anavailable
Open Access
article distributed under the termsorofhttp://dx.doi.org/10.1051/epjconf/201510001010
the Creative Commons Attribution License 4.0, which permits unrestricted use,
Article
at http://www.epj-conferences.org
EPJ Web of Conferences
experimental and evaluated data is reasonable good at the
higher energy but poor at the lower energy for these reactions.
66
Ga and 67Ga produced in these reactions are radioactive
isotopes. Fig. 4 shows schematically the production and decay
of the two produced isotopes. It can be seen from Fig. 4 that
these nuclei decay to stable 66Zn and 67Zn nuclei than heavier
56
Fe.
Figure 3. Comparison of experimental and evaluated crosssections and astrophysical S-factors of 63Cu(a,n)67Ga as a
function a energy.
Figure 4.63Cu(a,y) and 63Cu(a,n) reactions and the decay of the
reaction products.
Figure 2. Comparison of experimental and evaluated crosssections and astrophysical S-factors of 63Cu(a,y)67Ga as a
function a energy.
4 Conclusion
The cross-sections and astrophysical S- factors of the 63Cu(a,y)
and 63Cu(a,n) reactions have been analyzed up to 16 MeV alpha
energy. The reaction products, 66Ga and
01010-p.2
TESNAT 2015
67
Ga, decay to stable 66Zn and 67Zn isotopes than heavier 56Fe.
It appears that the agreement between the experimental and evaluated data is reasonable good at the higher energy but poor at
the lower energy for these reactions. Therefore, theoretical calculations could be repeated with the new nuclear parameters to obtain
the best fit with the experimental data.
Also more low-energy experiments are clearly needed for both alpha induced reactions in the mass range of nuclei above iron.
References
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01010-p.3
EPJ Web of Conferences 100, 01008 (2015)
DOI: 10.1051/epjconf/ 20151000100 8
© Owned by the authors, published by EDP Sciences, 2015
Quantum algorithms for computational nuclear physics
Jakub Visnák1'2'3'a
Dep. of Nuclear Chemistry, FNSPE, Czech Technical University, Brehová 7, 115 19 Prague 1, Czech Rep.
Dep. of Chemical Phys. and Optics, Faculty of Mathematics and Phys., Charles University, Ke Karlovu 3, 121 16 Prague 2, Czech Rep.
3J. Heyrovsky Institute of Physical Chemistry, Dolejskova 2155/3, 182 23 Prague 8, Czech Rep.
1
2
Abstract. While quantum algorithms have been studied as an efficient tool for the stationary State energy determination in the
case of molecular quantum Systems, no similar study for analogical problems in computational nuclear physics (computation of
energy leveis of nuclei from empirical nucleon-nucleon or quark-quark potentials) have been realized yet. Although the difference
between the above mentioned studies might seem negligible, it will be examined. First steps towards a particular simulation (on
classical Computer) of the Iterative Phase Estimation Algorithm for deuterium and tritium nuclei energy levei computation will be
carried out with the aim to prove algorithm feasibility (and extensibility to heavier nuclei) for its possible practical realization on
a real quantum Computer.
1 Introduction
The Quantum Computer as a model of information Processing
device exploiting directly the exclusively quantum resources superpositioning, parallelism, entanglement and destructive
interference [1-3] is a promissive tool for breaking the limits
of asymptotical computational costs derived for classical
algorithms for classical computers. Arguably there could be
quantum algorithms (qA, i.e., algorithm tailored for quantum
Computer) with asymptotic complexity (in practical words the time cost as a function of problem size) scaling
signifícantly slower (most important case is polynomial
scaling vs. exponential scaling) than the best possibly existing
classical algorithm (for the same problem). The latter
prediction is widely believed [1] (for opposing view see [4]),
but still unproven [3]. However, there does exist a class of tasks
which should prefer quantum Computer over the classical one
by their very nature - tasks of modelling quantum systems [5].
The other interesting problems for which are known qAs
outperforming the best currently known classical algorithms
are, e.g. Deutsch-Jozsa [6,7], Grover’s [8] and the famous
Shor’s Algorithm [9] for integer prime- faetorizationa.
This study aims to prepare the fírst step towards the first
simulation of a quantum algorithm for nuclear structure
computation on a classical Computer.
Abrams and Lloyd Algorithm [12-16], its applieation to the H2
dissoeiation curve by Full-CI (Full Configuration Interaetion
method) in minimal basis [17] (ineluding practical realization
on photonie quantum Computer), to slightly larger systems like
LiH, H2O [13] and CH2 [16], generalization for explieitly
relativistie all electron 4- eomponent ealeulations via DiraeCoulomb(-Breit) Hamiltonian for SbH model molecule [18]
(the latter two were just simulations of algorithms on a
classical Computer) or another interesting algorithms, among
them, the Quantum Variational Hamiltonian Estimation [56]
applied on HeH+ molecule electronic energy (for practical
realization of HeH+ energy ealeulation, please see [60]) should
be eited as an example.
The nuclear structure problems, unlike the electronic
structure ones, are complieated not only by computational
complexity of many-body stationary Sehroedinger equation
but by uneertainty in ehoosing the correct Hamiltonian b too.
However, with the phenomenologieal b (in the case of
mechanieal model - the correct deseription of either nucleonnucleon or quark-quark potentials (“quark potential” in this
artiele refers always to the effeetive phenomenologieal
formulae based on the
a
Which, if successfully implemented on a large-scale quantum
Computer would make the current encrypting system RSA
obsolete (on the other hand, quantum teleportation ean provide
us by fundamentally unintereeptable eryptographie method [1,
10, 11]) Simulations of this kind provide us answers on
questions such as - “Which algorithm with which parameters
is best for the class of computational problems in question?
How many qubits will be needed to perform the algorithm?
And how many quantum logieal gates will be needed? (and
therefore for how long will one computation take? Wouldn’t
be computation affeeted by decoherenee after that time?)”. The
inspiration was taken from sueeessful simulation studies done
for the ab initio structure theory computational problems, i.e.
a
Corresponding author:[email protected]
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nucleon-nucleon potentials derived from the scattering
experiments together with three-body (or eventually four- or
more- body forces) carefully fítted to few model nuclei
bonding energies do produce in principie numerically accurate
Hamiltonian for small and médium nuclei and (sooner or later)
the main bottleneck for nuclear structure modeling will tum out
to be the diagonalization of Hamiltonian in Hilbert space of
large dimension (scaling roughly as nA, where n is the oneparticle basis set cardinality and A is number of nucleons,
therefore exponentially in A). Therefore, the same class of qAs
as in the electronic structure may be applied.
Similarly as for the many-body nucleon model above, we
can think about phenomenological mechanical model of nuclei
as bounded State of 3A (constituent, valence) quarks with
given quark-quark effective potentials (the correspondence
with the nucleonic model can be derived through Composite
Particle Representation Theory [19], the feasible example of
quark-quark potentials were derived by Wu [19]).
Diagonalization of second quantized Hamiltonians c nonconserving the number of particles or their generalizations
built from creation and annihilation operators for more then
one kind of particles and containing terms corresponding for
creation of multiple (anti)quarks or composite particles, etc. is
probably completely intractabled on classical Computer.
However, the Abrams-Lloyd algorithm via the direct-mapping
vector space and algebra isomorphism can solve this problem
in time polynomial in n (the exact computational time cost is
of form O(na logb n), where I will discuss the a and b values
for different algorithms below) and the qubit cost is of form
O(n)). Compact mapping [20] and expectation value averaging
quantum algorithms provide similar speed up with respect to
classical Computer algorithm design - the number of quantum
gates required and therefore the computational time scales as
the number of terms in second quantized Hamiltonian or with
overhead at most polynomial in n.
outcomes. The computational model is stochastic and will
produce the correct result with some probability (“the success
probability”, p). In case p > one can always increase the correct
result probability as close to 1 as needed by repeating the
computation enough times and by majority voting on the result.
In the whole article, the ideal digital quantum Computer is
addressed. Real quantum computers suffer from quantum noise
and decoherence. In most cases the resulting negative effects
on quantum computation can be mitigated by quantum error
correcting codes [1, 22, 23].
2 Theoretical background
The qFT may be defíned by unitary transform on n-qubit
register
2.1 Quantum Computer, qubits, gates
2.2 Quantum Fouriertransform (qFT)
(1)
Rz (®) = | 0^0| + é
For the sake of this article, we can think about quantum
Computer (here only the digital quantum Computer will be
presented) as an theoretical device composed of quantum very
simplified model of particles build just from the “constituent”
quarks), however, since the kinetic energies of constituent
particles are much higher than in the electronic case, the
feasibility of any mechanical approach is in question)
c
Through the Dirac picture and second quantized Hamiltonian
(for qA simulation for electronic structure problem please note
[18]) we can arrive into formulation similar to fíeld-theory
(going beyond the no-pair approximation [21]) with second
quantized Hamiltonian consisting of terms creating particleanti-particle pairs.
d
For realistically short computational time. Except for the
smallest possible systems. core from m distinguishable 2-level
quantum systems (qubits), universal sets of gates (acting on the
quantum core State as unitary operators) and measurement
operators (measuring the State of defíned subsets of qubits
(quantum registers)) and classical control unit which realizes
which gate or measurement should be applied according to
program corresponding to particular algorithm. The
computation result is decided upon the measurement
1)(1|). Editedpicturefrom [1],
some authors defíne it with the opposite sign in the exponential
above. Straightforward implementation costs O(n2) Hadamard
gates and controlled phase shifts, effícient O(n log n)
approximations exist [57].
2.3 The phase estimation algorithm (PEA)
The algorithm gives fírst m bits estimation of the phase $ by
parameterizing given 11 x 21 unitary operator U (matrix,
implemented as a quantum logical gate)
Figure 1. Quantum circuit for exact qFT, H e C'2-2' is the Hadamard
gate (Hü = 2‘1/2 (-l)j, ij e {0;l}) and Rp is the zrotation gate with angle
ep=2rc/2p(
01008-p.2
TESNAT 2015
eigenvalue 2 = exp(2 (/)). The algorithm works with m- qubit
phase read-out register „a“ and /-qubit eigenvector (wave
function) register „b“ and requires initialization of the latter
one to the initial guess |i//0^ e C'A(2/) of the corresponding U
eigenvector |
.
In applications for bounded States energy estimation (problem
of fínding Hermitian Hham Hamiltonian eigenvalues) U is then
of the form U = exp (i Aí {Hham - Emin I21)) and then lower
(Emin) and upper (Emax) bounds6 for the Hham eigenvalue E are
also needed as an input for the algorithm (Emin <E< Emax) and
Aí parameter choice of the form Aí = 2n/(Emax - Emin) is used.
Figure 2. PEA quantum circuit. After Hadamard gates are applied, the
equally weighted superposition is created in the register a, the
suhsequent m application of the conditioned U- gate leads to entangled
State (2). Due to the Fourier orthogonality relations it is clear that qFT
will amplify amplitude for States of a corresponding to the closest mhit approximations to (see (3)) Also | (//, ^ would he close to the (U
and) Hham eigenvector (this Information is not accessihle directly hut
can he approximately revealed hy repeated measurements in different
hasis sets) [24, 25, 1],
1
2" -1
\core)^U kX = 2 x=o
1 2 -1
-i=Z x)exp|2v/xH')
m
m
j2m x = o
b
y
where H' = (//_, - Emin) / (Emax - EmiJ is original Hamiltonian (2)
rescaled so that its eigenvalue in question lies witliin^O; 1)
interval and is therefore represented by the phase of the form
0=O.ff2...fm+&2-m, e While the upper bound Emax for the
ground State is easy to compute due to the variational theorem
(in case we use PEA in connection with Full Confíguration
Interaction (FCI) computation, we can use the Hartree-Fock
energy EHF as the upper-bound), the lower bound Emin is less
attainable, the Frobenius Theorem or similar algebraic bounds
may be used, unfortunately this would mean O((2 /)A2) (3)
costly classical precalculation [26, 27]. It would be
interesting to note some works dedicated to lower bounds, e.g.
[28-30]. For lower esíimaíe, the EHF - aíEHF-EMBPi) for some a >
1 (MBPT stands for the Many Body Perturbation Theory)
might be used [61].
is to be|(i//„ |^| > 0.62
2.4 Iterative PEA (IPEA)
Pm *
|(^0 H|2 • Sm
,
(4)
Through the idea of „measurement conditioned operations“
[31] we can „decouple“ individual ^’s bits estimation
measurement and lower the qubit requirements on read-out
register from m qubits to 1 qubit at the cost of repeated
operation of quantum circuit in Fig.? in the next paragraph
where angle (Ok parameterizing z-rotation gate depends on
previous bit measurements (starting from the least signifícant
bit ^m).
Figure 3: Iterative PEA quantum circuit. The algorithm starts for k I.
the angle wk depends on the previously measured bits so Ok = 2K0.0/m-k+2/m-k+3..^fm. In case we maintain the b register for all iterations (|
y/^1^ = | y/^k'^) the term “IPEA A” will be used. Another possibility
(favourable in case the coherence time is too short) is to prepare the
same State at the beginning of each iteration (| y/ok= | l//n b) in this case
the term “IPEA B” will be used. Unlike IPEA A, the IPEA B is not
fully equivalent to original PEA and the success probability formula
(4) doesn’t hold for this case. Instead, lower and upper estimates |(^o
|^| O pm/Sm(â) O |(^01^| can be derived [32], This would lead to
practical uselessness since even for a high overlap, the pm would
decrease with m quickly under 0.5. However, if each iteration in IPEA
B is r-times repeated and bits are decided by the majority vote, for r >
3, the IPEA B pm usually surpass the IPEA A value. IPEA B is likely
to work even when overlap is lower than 0.62 or even 0.5 as long as
the eigenvector | keeps to have highest overlap with the initial
eigenvector guess from the 2z-tuple set of all Hham eigenvectors.
2.5 Abrams-Lloyd algorithm
The idea is to simply exploit the (I)PEA for physical
Hamiltonians. First introduced by Abrams and Lloyd into
quantum chemistry in the second quantized formulation [1216],
Since the U operator is usually exponential of the sum of
non-commuting simple operators, the Trotter-Suzuki
The algorithm is based on quantum circuit above and
(usually very tight) lower bound to the success probability pm
defíned as the sum of probabilities of the two closest
approximations to the correct phase y> equals where Sm(A)
range is ^8 /^2;1^ = { 0.81;^, exact form can be found e.g. in
[3]. Therefore for algorithm to be useful, the sufficient
condition on eigenvector initial guess is that its overlap with
the eigenvector exact within given fmite computational basis
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EPJ Web of Conferences
formulae of various orders [33] are used for its implementation
(the exponentials of the simple operators are easily
decomposed into single qubit gates and CNOTs). The total gate
count for (I)PEA algorithm scales as O(-X.ln(AEòE)/òE).
where X is the asymptotical cost for U operator implementation
(usually in form O(Na logbN), where N is the size of system
studied, or size of the one-particle basis set and a and b are
small and positive), AE = Emax - Emin and SE = 2~™AE is the precision
in energy (should be chosen as slightly higher than expected
magnitude of error due to the fíniteness of basis used).
The particular mapping between algebra of operators
acting on the Hilbert space of physical system we are studying
and Hilbert space of qubits and corresponding mapping of
Hilbert spaces is matter of the next paragraphs.
2.5.1 First quantized formulation
Let us consider a simple fully non-relativistic Hamiltonian of
interacting A-body system (without the center-of-mass (CM)
movement separation, interactions are pair-wise, momentum
and spin independent and local in position basis). The fírst
quantized quantum algorithm was fírst introduced by Weisner
and Zalka [34,35].
.P.
H
+ 2 ;kjk),
V
(5)
Ti 2 mj j
j
The wave íunction of this system is stored „on (cartesian) grid“
in 3A-(b+z)-qubit register, where B = 2b is number of points of
the grid per each cartesian coordinate (chosen as some power
of two) and z corresponds to spin variable and is usually a
small number compared to b (for spin-1/2 fermions z = 1). It
can be shown that when the initial guess wave-function is
properly (anti)symmetrized
with respect to variables of indistinguishable particles of given
statistics (Fermi, Bose), the (anti)symmetry is kept within the
scope of quantum diagonalization algorithm
[36]. The partitioning of H in the exponent in U
for
Trotterization is then
U = exp
(6)
lim
exp
m
acting on wave-function register. It can be shown, that best up
to now known algorithms use at most O(b) one- and two-qubit
gates for its decomposition.
The T and therefore exp(i(At/m) Ê) are diagonal within
momentum basis and are similar to diagonal operators Tj (j
pP
indicates coordinate not particle) and exp(i(At/m) Tj ))
p
respectively via qFT (UQFT j in formula (8) below)
exp f i — fLfí UUQFT j exp íi —Tf ^U^ j,
Q
m j=j Q
m
(8)
The gate costs are O(b) for each exponential and either O(b2)
(for „exact“ qFT) or O(b log b) (for approximate qFT) on the
right side of (8).
Therefore the total gate cost for implementing one timestep of Trotter-Suzuki formula [33] (simple product of the two
exponentials in (6) or three exponentials in (7)) is either O(A2
b) + O(A b2) or O(A2 b) + O(A b log b) depending on our qFT
implementation. The cost of the algorithm also depends on the
scaling of the time-steps number m needed in (6) with A and b
for a constant error in eigenvalue due to Trotter formula error.
Rough examination based on the (15) formula from [37] gives
m = O(A3/2) (at least for a large b, m would not depend on b)
implying the total gate cost of algorithm to scale as O(A3-5 b) +
O(A2-5 b2) or O(A3-5 b) + O(A2-5 b log b) depending on our qFT
implementation. This result shows quantum algorithm to be
effícient when compared to classical FCI exponential scaling
with A. Even for the lowest values of A, the quantum algorithm
poses an advantage over its classical counter-parts due to the
cost scaling with respect to b = log2 B (diagonalization of a
sparse matrix of dimension O(B) has O(B2) time-cost which is
exponentially larger than at most quadratic scaling in log B).
The cartesian grid is assumed here to be equidistant running
from -B-dr/2. to +B-dr/2. in each coordinate axis with
elementary step equal to dr. The eventual non- equidistant grid
computation probably would not need large overhead. First
quantization is also addressed in the works [38] and [39].
The separation of CM movement might be done by
coordinate system choice explicitly (e.g. Jacobi coordinates,
typical for small A) or by subtracting the total kinetic energy of
the system. The subtraction leads to masses mj being replaced
by reduced masses = mj^ - M~l (M = Tj mj) and Vjk now
containing term (- 1/M)( pj ■ pk). The latter should be for the
purpose of Trotter formula [33], however contained in the Ê'
operator (the prime distinguish the operator from the case
where CM movement is not separated) since it commutes with
other momentum-dependent operators. Now
or for second order Trotter-Suzuki [33] formula
U = exp (i At (T +V
lim
m
(7)
| . Al T> I I • Al rf. |
| . At y ||
exp | i----- V | exp | i — T | exp | i ------ V | |
l 2 m ) V m ) l 2m ))
where T stands for the sum of kinetic energy operators and V
for the sum of potential energy operators, the latter being
dependent on position only, the former on momentum only.
The V and therefore exp(i(At/m) V) are diagonal within
position basis and corresponds to 6 b qubit gate
01008-p.4
\ - At ~,)
(.At ~
exp I i — T | = exp I i — T
(m)
(m
TTU r7+ U r7+
. J • At
n QFT,k QFT,j 6XP I i PjPk \ QFT ,jU QFT ,k k j( mM J
U
(9)
TESNAT 2015
meaning O(A2b2) gate cost for this part of Trotter-Suzuki
expansion [33] and also for one Trotter time-step. Rough
estimate for m in Trotter formula gives now m = O(A2)
implying the total gate cost O(A4b2). Similar gate counts would
be expected for Hamiltonian (5) in form of sum of Dirac-like
Hamiltonians (Dirac-Coulomb or Dirac- Coulomb-Breit
Hamiltonian). In case of three-body forces V (r ,rk,rn), or more
generally for the Hamiltonian containing
N-body
forces
V. . , (r, ,r, ,--,r, ) the gate count would be jl j2 JN
JN
increased up to O(ANb) + O(A2b2) for a single Trotter time-step
and m = O(AN), therefore the total cost would be O(A2Nb) +
O(AN+2b2).
However, the nuclear structure theory works with
momentum dependent interaction potential, like HamadaJohnson [40] or Argonne [41]. In this case, since the potential
depends solely on the angular-momentum (but non-linearly)
spherical coordinates are natural and we can think about
discretizing only the radial coordinate, so the single-particle
wave-function has a form
jkn
2
k) =
R
j
^ \ ’ j’ ’ k) ’
j.m1 J.j
j m
(10)
1 S
j,mj ,l,s,T
then the wave-function register would be divided into fewqubits parts storing angular momentum information, isospin
and similar information and b-qubit radial part for R(r) stored
for discrete values of r from dr to 2b dr. While implementation
is straightforward for the two-nucleon problem, in case of
three- and more nucleon problems, íurther formulae would
need to be derived (e.g. multipole expansion of r-dependent
part of potential into radial and angular coordinates of
interacting nucleons).
For this case, the non-relativistic kinetic energy operator
should be written in spherical coordinates as
(11)
where p2 = - r 1 52 r (note: õr is the derivative with respect to r
operator). From [42] we can conclude that similar trick as with
linear momentum could be done with the radial momentum
operator only with quantum discrete sine transformation used
instead of the qFT with the same gate cost of O(b2) for the
quantum sine transform [43].
In [38] rigorous description of different algorithm using
3A.(B+z)-qubit wave-function register with easier
implementation, but with scaling at least O(B log B) with the
respect to grid point number for a single Trotter step is
presented. However, the [38] version allows simple adaptation
of the algorithm to irregular space-sampling (i.e.no rectangular
grid at al).
2.5.2 Second quantized formulation
Let us consider the simplest second quantized Hamiltonian
TT = t hj a+ja +
k
V^jía at , (12)
k
j,k
m
j <k ,l <m
where hjk = hkj* and Vjkim = Vkjmi = Vmijk* are complex numbers
and 0j+ (or aj) are creation (or annihilation) operators for the
single particle basis States fulfilling the (anti-)commutation
relations for bosons (for the bosonic case, they will be marked
as b,') (14) (fermions (13)).
{a*, ak } = 8jk, [a+j, ak^ = {aj, ak }= 0,
[bj, bk ] = djk, [b], b+k~] = [bj, bk ]= 0,
(13)
(14)
The Hamiltonian can be further generalized by adding three((1 / (v) ) V W,^ jta a a am ), or more jklmpq
q p
particle terms and/or by adding another kind of particles with
corresponding different set of creation and annihilation
operators (including the interaction terms between those two
kinds of particles).
2.5.2.I. The direct mapping
For the fermionic case, we can thing about either compact or
direct mapping of the Hilbert space of interacting system
described by (12) onto quantum register and corresponding
mapping of algebras preserving the anticommutation relations
(13). In the case of direct mapping, the Jordan-Wigner
transformation (JWT) [44] where qubits store occupation
numbers for spin-orbitals can be used - in this case, the creation
operator is realized by O(N) sequence of Pauli matrices acting
on the quantum register (15)f.
JWT
a+ p =
-1 Z,Z2...Zp_^+ .
(15)
Later, a more effective, Bravyi-Kitaev transformation (BKT)
(16) was developed [45-46] - in this case qubits store rather
specific partial sums of occupation numbers and creation (and
annihilation) operators are realized by just O(log N) sequence
ofPauli matrices.
BKT
a
p~
X
u(pyr, + ZR(p-)’
(16)
here, U(p) and R(p) are sets with O(log N) elements - for closer
description see [45-46]. For the case of distinguishable
particles, ap+ is represented by OÍ alone. For the bosonic
particles, transformations preserving the commutation
relations (14) (respectively their projection onto Imite
dimensional Fock subspace - note: we can store only States
with maximum Vp bosonic particles in the p-th spin-orbital
when p is finite) have been developed too - Somma et al [47]
presents simple and powerful transformation with gate cost
O(V4N4) for the two-particle term in (12) where V = maxp Vp,
the qubit cost for representingp-th spin-orbital occupation
number is, however Vp+1. Different transformation for bosonic
particles, using only |~log 2 (Vp +1)"| qubits with O(U*Nj gate
cost for the two-particle term in (12) will be presented in article
[48].
Through the Trotter-Suzuki formula [33], the evolution
operator U for (12) Hamiltonian is decomposed into the
products of exponentials of i(At/m) multiples of individual
terms in (12) and each of them is realized by O(log4 N) gates.
This means O(N4 log4 N) gates for applying U in total (I will
address the three-particle force generalization briefly at the end
of the next paragraph). In the case of local basis (and N
denoting size of the system when using always the same ratio
of one-particle basis set dimension to number of
f Zk,Xk, 0k,+ are k-th qubit Pauli
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EPJ Web of Conferences
centers/particles) we can even thing aboutjust O( N log4 N) cost
since only O( N2) terms will be then non-negligible (or even
O(N) in a truly asymptotic region) [49]. Although the scalings
cited in the next paragraph came from electronic structure
theory, they provide probably rather good estimation and worst
scenario bounds [50] for the nuclear structure theory as well.
The trotter number m can be estimated to scale at worst as
m=O(N6) [50], but fortunately realistic simulations done on
electronic structure problems show that the scaling is rather m
= O(N4) [50], Poulin et al [51] presented scaling m = ON1'5'2'5)
for a different, more realistic set of molecules. By simple
multiplication of m with the gate counts for implementing U
gate from previous paragraph, the total gate (and therefore
time) cost of algorithm will range from O(N10 log4 N) through
O(N8 log4 N) [50], O(N5-5-6-5 log4 N) [51] to O(N3-5'4'5 log4 N)
[51, 49]. In the case of q-particle (q > 2) force terms in
Hamiltonian we have to add 2(q-2) (or q-2 with local oneparticle basis set, [49]) to the power of N in the computational
costs.
The most straightforward choice for the one-particle basis
set are the ground State Hartree-Fock spin-orbitals (Mean-field
Solutions), however any orthonormal basis set complete
enough for appropriate precise description could be used. The
Hartree-Fock (HF) many-body wave- íunction solution (Slater
determinant for the ground State) is also the most
straightforward candidate for the initial eigenvector guess | },
in case it will show to have too small overlap for success
probability over 0.5, one can either use some State from
classically carried out post-HF method (usually only few Slater
determinant are necessary) or use quantum algorithms Adiabatic (quantum) State Preparation (ASP) [13, 52] or the
quantum cooling[53]methods forthe p//,^ initialization.
It would be interesting to do similar simulations for nuclear
structure problems in order to evaluate the success probabilities
for HF initial guess and to derive how the Trotter number scales
with the one-particle basis size and number of nucleons of the
system. Work on this matter is in progress (in the collaboration
with P. Vesely from Nuclear Physics Institute of the ASCR).
In case of the nucleon-nucleon mechanical approach one
can either use isospin formalism or to think about nêutrons and
protons as two different kind of particles having their
respective sets of spin-orbitals and corresponding creation and
annihilation operators (let us say aj+’s and aJ+’s, where j and J
are from two non- overlapping sets (so the (12) form holds, just
summation indices change their meaning) and [aj+,aK] =
[aj+,aK+] = 0 - operators on proton and nêutron space commute
with each other).
spin-orbitals, A number of particles (= filled spin- orbitals) and
C(N,A) the combination number) have been developed too and
give rise to U implementation costs of O((N-A)4/3 log log (NA)) in general case [20] and O((N- A)(log(N-A))7/4) using blackbox algorithms [20, 54, 55]. Unfortunately little to no studies
were done for the total one- and two-qubit gate cost for this
case.
2.5.3 Quantum field theory
While in the case of first quantized Abrams-Llyod qA we
would think about the Lattice QCD application, the both lattice
QCD and non-lattice QCD computation within the second
quantized variants are also of possible further interest. Since
the direct mapping, the compact mapping and their eventual
hybrids might be used also for efficient simulation of quantum
field theory Hamiltonians non- conserving number of particles.
2.6 Alternative algorithms
From the plethora of alternative algorithms for Hamiltonian
eigenvalue estimation on quantum computers, the Quantum
expectation estimation (QEE) should be mentioned [56], it is
based on the second quantized Hamiltonian (12) with (JWT) or
(BKT) this results in Hamiltonian represented as a linear
combination of strings of Pauli matrices - each of the strings
are applied to quantum register representing the wave-function
and the register is O(|h|2/p2) measured to obtain contribution to
energy with the precision p. After that, parameters of State
preparation are changed in order to lower energy estimated.
After minimum with respect to the preparation parameters is
achieved, we can conclude we had variationally found ground
State energy [56]. The gate cost for this algorithm is
O(N2q|hmax|2/p2), where q = 2 for Hamiltonian with at most
pair-wise interaction, q = 3 for Hamiltonian with three-body
forces, etc. and \hmaX\ is the largest from j Vjkim parameters
absolute value. The interesting difference with respect to the
(I)PEA is maximal coherence time needed, which here doesn’t
scale linearly with number of gates used, but is O(N) for JWT
or even O(log N) for BKT. The
2.5.2.2. The compact mapping
While the Hamiltonian in the form (12) conservate number of
particles, in direct mapping the quantum register still can
superposition of States from Fock spaces corresponding to
different particle numbers (from the physical vacuum up to
system with all (including the virtual) spin-orbitals filled) - this
seems we are wasting with, at least, the qubit resources
(however the bottleneck for quantum computers and quantum
computation will sooner or later show to be rather the number
of gates and computational time respectively (which should be
always much lesser than the decoherence time)). Fortunately,
algorithms storing only A-particle subspace of the Fock space
onto O(log2 C(N,A)) qubit register (N is the number ofbasis
01008-p.6
TESNAT 2015
drawback is necessity to proceed probably time costly
minimizing procedure.
For finding excited State [56] suggests construction à2H =
(H - E)2 operator (E is estimate of eigenvalue in question),
which increase the computational time to O(N4q|hmax|4/p2).
Similar approach might be used for potential optimization
(with respect to parameter set p) - <H(fi)> is first minimized
with respect to the State preparation and for this States
<P2H(fi)> = <(H(fi) - E)2> is minimized with respect to P The
computational acceleration is due to inutility to store
exponentially large wave-function for each computation and
would be exponential. By this process, nucleon-nucleon
potentials, three- and four- body forces can be fitted to bonding
energies of several nuclei.
3 Deuterium and Tritium simulation
From the scaling derived for second quantized approach it is
obvious that this framework will favourite quantum computers
over the classical ones rather for much higher nucleonic
number A (like A > 10). For the simplest Systems in question,
first quantized formulation is the only option providing
quantum algorithmic speed-up. Unfortunately, only plan of
further simulation will be presented - I would start with Jacobi
coordinates, isospin formalism and in case of deuterium, the
wave function would be written as
1^) = | ) + | ]
S
D
Where (18-22)
(17)
(r = r|s) =
|J = 1, mj = 0, l = 0, s = 1)Lspín (r = r|D)
= 3^1 |j = 1, mj = 0, l = 2, s =
R
S (r) 1)
® Ir = o).
r
isospin
\T =
0 ísospín =
(I
np
-|
P^
(18)
) ’
components.
The wave function register should be initialized into the
sampled wave-function corresponding to the variational
solution of the stationary Schroedinger equation corresponding
to the Hamada-Johnson or Argonne NN-potentials (with the
non-relativistic form of the kinetic energy term p /(2p). where
p is the reduced mass) in the form (23)
R r
r
£
rk
a
a ( ) = P\pl PP -1) “ X cak exp (~^a (r - rc) ‘ )
k=0
where a e {S, D}, l = 0 for a = S and l = 2 for a = D, P
represents size of the basis (P = 0 for the first simulations), aa,
sa > 0 are variational parameters (this part (((r / r0)CT“ -1)s“) of
the radial wave function assures the hard-core behaviour and is
applied only for Hamada- Johnson potential - for r > ro, for r
< ro we put Ra(r) = 0, eventually leading to reinitialization of
the corresponding wave-function register part every p-th
Trotter step for some reasonable positive integer p) as well as
complex numbers ca k e C, and parameters of the exponential
part - rc, rp and cia > 0. For the sake of simplicity cia should
be either 1 or 2. The former would be preferable since it
corresponds to the correct asymptotic behaviour in infinity
(similar to the hydrogen atom, since the dominant part of
potential in this region scales as 1/r). The very general formula
(23) may be, however, simplified for the preliminary
simulations by setting P =0, aa = ua = sa = 1 (or sa =0 and
therefore omitting this term in case of the soft-core Argonne
potential) and r]$=r]D=r] would be the only parameter for
classical precomputation via variational minimization of
energy expectation value.
There is another way of dealing with the hard-core
behaviour of Hamada-Johnson potential or with integral
divergence (when radial part (23) is used), in case of the softcore Agronne potential is introducing different form of the
radial wave-function containing inverse powers of r inside the
exponential, i.e.
(20)
= 1, j = 0, = 0, = 1)L spn
= Y (0,^^= (|T^+|i^)
M = 1, mj = 0, = 2, s = 1)^ =
(0,ç\J
m
l
s
P
® Ir = o)
L,spín
(19)
(21)
l
( Y^ (0, <p) | H) + Y
(0, <p) 144»
(22) for the
both Hamada-Johnson and Argonne NN- potentials, the matrix
elements between angular, spin and isospin parts of the wave
function of the following
2>+1
operators would be of high importance - r, -T2,
a (r) = r
Z a,k ^P(~0 ,-b ~Ha,c ')
C
r
a
r
r
(24)
k = -Q
ísospín
oo
J
R
■ c?2,
S12, LJ2 , (L ■ s) and (L • s'f (please see the Supplementary
Information [59]).
The radial part of the non-relativistic kinetic energy
operator action on is discussed in detail in “First quantized
formulation and its future for Computational Nuclear Physics”
section. The wave-function quantum register would consist of
b qubits (starting with b = 4 and hopefully extended up to 10
or more) for storing radial part (Rs(r) or RD(T~)) of the wave
function and one qubit for distinguishing S (10) and D (11})
where Q is a small positive integer, b, c e {1; 2} (all four
combination possible) and r/a-b, ‘Qa.c > 0. This kind of wavefunction should assure convergence of all integrais over
negative power of r due to the -r]a_ -b rb term in the exponential.
Rough inspection led me to think that all integrais in this case
are also analytical and in the case of b = c =1 could be
expressed in the form of BesselK functions, in the b = 2, c = 1
case in the form of Gamma and HypergeometricPFQ functions
(according to the Mathematica [58] terminology). In case of
Hamada- Johnson potential and wave-function of the form (24)
the hard-core may be replaced by replacing parts of potential
of the ~ ra kind (only for r < r0) into linear combination of two
(or eventually more) functions (A r~b + B r'c) fulfilling equality
of íunction values and first derivatives with respect to r in the
r = r0 point, b and c should be then chosen to be large enough
to emulate the hard-core behaviour. Due to the -pa.-b rb term in
the exponential in (24) this would lead to analytical and finite
expression for all integrais. And for the quantum simulation
this would mean no need for reinitializing of the wave-function
01008-p.7
EPJ Web of Conferences
register in order to assure that its r <ro part remains zero (in
this case it would be just sufficiently small).
I must apologize to the readers that I am stopping here, but
computational details and progress in the work on the
simulation of quantum algorithm for deuterium energy
estimation in the first quantization will be placed on the web
[59].
After the simulation (with m fixed to m = 17 and properly
chosen Emax and Emi„ (preferably based on lower bounds from
[28, 29, 30])) I would like to address this questions:
1. How the correct energy and its m bit estimations scales
with the number of grid points 2b and the dr parameter?g
2. What was the IPEA A and IPEA B success probabilities
pm for several possible initialization of wave-function
register | ij/,^ and values of b and how is this value
correlated with the overlap |^01^|2? For this task, oraclelike application of controlled-U gate would be sufficient.
3. What was the necessary value of the Trotter number and
how it depends on the grid point parameter b? How many
elementary gates would be needed on ideal quantum
Computer for the computation?
Then, similar simulation I plan with tritium ground State
energy calculation.
4 Conclusions
This work aim is to approach the quantum algorithm design to
the Computational Nuclear Physics community, to present gate
count estimations for first quantized formulation of the
Abrams-Lloyd algorithm for nuclear structure problems (in the
“First quantized formulation and its future for Computational
Nuclear Physics" section). The preparative steps for the
simulations of quantum algorithms for bounded State energy
calculation for the smallest two nuclei were presented in the
previous g The maximal largest radial coordinate value in the
computation is then 2b dr, the smallest dr. This question is
rather technical and has not much to do with quantum
algorithms, however, it is important for the eigenvalue problem
in question.
section (Deuterium and Tritium as first systems for the
simulation).
5 Future prospects
Author, in the collaboration with Vesely from Nuclear Physics
Institute of the ASCR plans to proceed simulations of secondquantized Abrams-Lloyd algorithm for 4He, 16O and 40Ca
nuclei and question the success probabilities and Trotter
number scaling.
Acknowledgements
I would like to thank the Department of Nuclear Chemistry for
support, my supervisor at Chemical Physics, Jirí Pittner, for
introduction into Quantum Information Theory, Petr Vesely for
many advices and the Organizing Committee of the TESNAT
2015 workshop for hospitality and the opportunity to present
my work.
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01008-p.9
EPJ Web of Conferences 100, 01006 (2015)
DOI: 10.1051/epjconf/ 20151000100 6
© Owned by the authors, published by EDP Sciences, 2015
Investigation ofthe effects of nuclear levei density parameters on the
cross sections for the 234U(y,f) reaction
Hakan Pekdogan1'a, Abdullah Aydin1 and Ismail Hakki Sarpun2
1
2
Kirikkale University, Faculty of Arts and Science, Department of Physics, Kirikkale, Turkey
Afyon Kocatepe University, Faculty of Arts and Science, Department of Physics, Afyonkarahisar, Turkey
Abstract. In this study, we have investigated the effects of nuclear levei density parameters on the cross sections for the 234U(y,f)
reaction up to 20 MeV. The cross sections on 234U(y,f) reaction were calculated for different levei density models using the
TALYS 1.6 code. First, it was determined the levei density model that was the closest to the experimental data. Secondly, cross
sections obtained for different levei density parameters of this model were compared with experimental data from the EXFOR
database. Thus it was determined the best levei density parameter fít to experimental data.
1 Introduction
The levei density and levei density parameters are very
important quantities for describing the structure properties of
nuclei. Especially, the levei density parameter is an essential
ingredient as input for calculation of reaction cross sections.
The calculated cross sections are important for practical
applications such as the modeling of nuclear astrophysical
processes (e.g. nucleosynthesis in different stellar
environments), medicai research, and reactor technology. Also
knowledge of nuclear físsion cross sections is very important
for understanding of nuclear structure. There are many reliable
Computer program to calculate the físsion cross sections. One
of them is TALYS 1.6 nuclear code [1].
In the literature, there have been many studies on nuclear
data evaluation for físsion cross section and físsion yield using
different model approximation theoretically. For better nuclear
data calculations, Computer codes are used. TALYS, a
software, has been developed to capture all nuclear reaction
model calculation, allowing to provide nuclear reaction
simulation from 1 keV - 1000 MeV energy range more
precisely. Nuclear reaction types that TALYS provided are
nuclear reaction that involved nêutron, proton, deuteron,
photon, triton, 3He and alpha particles as projectile and element
of mass 12 and heavier as target [2].
Calculation result obtained from TALYS are depends on
great input parameter tuning based on experimental value using
curve fítting. At this point, experimental data play important
role in calculation performed by TALYS to achieve better
agreement with it [3,4].
Besides that, to achieve even more accurate result, the
proper selection of parameter adjustment and reaction
mechanism should be implemented. This could be done by
using theoretical prediction about the behavior of specifíc
nuclear reaction. With proper selection of reaction parameter
and mechanism combined with parameter tuning would lead to
better approximated calculation result.
In this study the cross sections on 234U(y,f) reaction were
calculated for different levei density models using the TALYS
a
1.6 code [1]. All the calculations were compared with each other
and with the experimental data obtained from EXFOR library
[5].
2 Levei Densities
Effective levei densities had no explicit dependencies with
nuclear collective effect.
2.1 Constant Temperature Model (CTM)
This model divides energy range into two parts, low energy part
from 0 MeV to the matching energy Em where Constant
Temperature Law applied, and high energy part above Em
where Fermi Gas Model applied [6].
2.2 Back-Shifted Fermi Gas Model (BSFGM)
In this model, Fermi gas expression is used in all energy range.
As a consequence, pairing energy parameter should be
adjustable [7].
Corresponding author: [email protected]
Article
at http://www.epj-conferences.org
This
is anavailable
Open Access
article distributed under the termsorofhttp://dx.doi.org/10.1051/epjconf/201510001006
the Creative Commons Attribution License 4.0, which permits unrestricted use,
EPJ Web of Conferences
2.3 Generalized Superfluid Model (GSM)
This Model takes superconductive pairing correlation into
account based on Bardeen-Cooper-Schrieffer theory [8, 9].
3 The levei density parameter a
A nuclide-specifíc constant value for the levei density
parameter a may be proposition for the form of word described
and in fact the first levei density analyses spanning an entire
range ofnuclides [6, 7, 10] treated a as a parameter independent
of energy. After that, Ignatyuk et al. [11] the correlation in the
middle the parameter a and the shell correction term of the
liquid-drop component of the mass formula was found. These
researchers considered that a more reasonable levei density is
obtained by assuming Fermi gas formula given above is still
valid. However, with energy-dependent expression for a, the
inclusion of energy-dependent shell effects is important for the
effíciency. The existence of shell effects at low energy and their
disappearance at high energy in a phenomenological manner
considered for its appearance [12].
It reads
rc A ' fi , S5«r1-exp[-YU]>l
a = a(Ex) = a I 1 + SW --------^-4—±1-
III
4 Methods
In this study, comparison have been realized between three levei
density models and experimental values taken from the EXFOR
in (y,f) reaction for 234U(y,f) [5]. The TALYS 1.6 code used in
theoretical calculations created by Koning and his colleagues at
NRG Petten, Netherlands and CEA Bruyéres-le-Châtel, France
to provide a complete and accurate simulation of nuclear
reactions involving nêutrons, y rays, protons, deuterons, tritons,
3
He, and alphas in the 1 keV-1 GeV energy range, through an
optimal combination of reliable nuclear models. Nuclear
structure and model parameters are implemented through
Reference Input Parameter Library (RIPL, 1998) [13],
5 Results
In this work (y,f) reaction cross sections of 234U(y,f) were
calculated for three levei density models using TALYS
1.6 code in incident energy range of 4-20 MeV. The calculated
results and available experimental data are presented in Figs. 14.
Table. 1. Levei density parameter values used in CTM model
calculations
234
U(y,f)
default
a-10a%
a+10a%
a-20a%
a+20a%
CTM
15.8128
17.3941
14.2315
18.97540
12.6502
Figure 1. Theoretical calculations of 234U(y,f) reaction cross section
using levei density models in TALYS. The experimental data are
taken from EXFOR.
01006-p.2
EPJ Web of Conferences
Table. 2. Levei density parameter values used in BSFGM model
calculations
300
2M
U(Y,Í) default
a-10a%
a+10a%
a-20a%
a+20a%
a+25a%
BSGFM
14.2466
11.6564
15.5418
10.3612
17.4845
12.9515
200
Table. 3. Levei density parameter values used in GSM model
calculations
100
2M
default
a+10a%
a-10a%
a+20a%
a-20a%
a+35a%
GSM
13.4189
14.7608
12.0770
16.1027
10.7351
18.1155
U(y,f)
12
10
20
Figure. 2. Theoretical calculations of 234U(y,f) reaction cross
section using CTM levei density model. The experimental data are
taken from EXFOR.
01006-p.3
TESNAT 2015
400
2
Conclusion
W
B.L.Bermanat. al,
(1986)[14]
Talys1.6BSFGM
Talys1.6BSFGM(a10a%)
In this study, it has been showed that how the levei density
parameter effects theoretical calculations of reaction cross
sections depend on the levei density models.
CTM model calculations show best compatibility with
experimental results and when the similar results obtained by
changing a parameter in other models, then levei density
parameter of that model approaches the value of CTM model
parameter.
Talys1.6BSFGM(a+10
a%)
300
Talys1.6BSFGM(a20a%)
Talys1.6BSFGM(a+20
a%)
Talys1.6BSFGM(a+25
a%)
200
References
1.
A.J. Koning, S. Hilaire, S. Goriely, TALYS-1.6 (2013)
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100
20
8
12
16
Fig. 3. Theoretical calculations of 234U(y,í) reaction cross section
using BSFGM levei density model. The experimental data are taken
from EXFOR.
2
W)
B.L. Berrnana.al1986
[14]
Taly 1.6 GSM
-------------- Talys1.6ÔSM(a-10a%)
300
200
100
10. H. Baba, Nucl. Phys. A 159 (1970) 625.
11. A.V. Ignatyuk, G.N. Smirenkin, A.S. Tishin, Sov. J. Nucl.
Phys. 21 (3) (1975) 255.
0
8
12
16
20
400
Figure. 4. Theoretical calculations of 234U(y,f) reaction cross section
using GSM levei density model. The experimental data are taken from
EXFOR.
Experimental cross-section values of234U(y,f) reaction have
been compared with theoretically calculated values for three
levei density models with TALYS 1.6 code in Fig.l.
Experimental cross section values are compared with the
theoretically calculated cross section values using CTM,
BSFGM and GSM model of TALYS code in Fig.
1. According to Fig. 1, CTM model calculations have similar
results with experimental cross section values than other models
calculations. Figs. 2-4 have been plotted to show the effects of
the levei density model parameter on the theoretical calculations
for each levei density model. The aim of these graphs is to
obtain best levei density model parameter in each model.
12. A.J. Koning, S. Hilaire, S. Goriely, Nuclear Physics A 810
(2008) 13-76
13. RIPL, 1998. Reference Input Parameter Library for
Theoretical Calculations of Nuclear Reactions
http://www-nds.iaea.org/ripl/.
14. B.L. Berman, J.T. Caldwell, E.J. Dowdy, S.S. Dietrich, P.
Meyer, and R.A. Alvarez, Phys. Rev. C 34, (1986) 2201.
1006-p.3
EPJ Web of Conferences 100, 1007 (2015)
DOI: 10.1051 /epjconf/ 20151000100 7
© Owned by the authors, published by EDP Sciences, 2015
A study on nuclear properties of Zr, Nb, and Ta nuclei used as structural
material in fusion reactor
Halide Sahan1'a, Eyyup Tel1, Muhittin Sahan1, Abdullah Aydin2, Ismail Hakki Sarpun3, Ayhan Kara4 and Mesut Doner1
1
Osmaniye Korkut Ata University, Faculty of Arts and Science, Department of Physics, Osmaniye, Turkey
Kirikkale University, Faculty of Arts and Science, Department of Physics, Kirikkale, Turkey
3Afyon Kocatepe University, Faculty of Arts and Science, Department of Physics, Afyonkarahisar, Turkey
4Sinop University, Faculty of Engineering, Department of Nuclear Energy Engineering, Sinop, Turkey
2
Abstract. Fusion has a practically limitless fuel supply and is attractive as an energy source. The main goal of fusion research is
to construct and operate an energy generating system. Fusion researches also contains fusion structural materiais used fusion
reactors. Material issues are very important for development of fusion reactors. Therefore, a wide range of fusion structural
materiais have been considered for fusion energy applications. Zirconium (Zr), Niobium (Nb) and Tantalum (Ta) containing alloys
are important structural materiais for fusion reactors and many nfhpr fu^lrk \Jatiira11v 7r inz-lnz-ke 7r
7r Í%1 1 T) 7r Í%1 7 H 7r í%17 zT) 7r ROT
90
icntnnpc
OLUCl llClU-S. lNdXULu.Uy HlvlddCS LI1C y/OAl.Aj,
91
92
94
96
[/O^.oU] ISOLOpOS
and 93Nb and 181Ta include the 93Nb (%100) and 181Ta (%99.98), respectively. In this study, the charge, mass, proton and nêutron
densities and the root-mean-square (rms) charge radii, rms nuclear mass radii, rms nuclear proton, and nêutron radii have been
calculated for 87'102Zr , 93Nb,181Ta target nuclei isotopes by using the Hartree-Fock method with an effective Skyrme force with
SKM*. The calculated results have been compared with those of the compiled experimental taken from Atomic Data and Nuclear
Data Tables and theoretical values of other studies.
1 Introduction
There are many advantages of the fusion energy system. One of
the most important advantages is the abundant fusion fuel
availability in the nature, contrary to relatively scarce físsion fuel
resources. Fusion-based nuclear power experiments attempt to
create similar conditions using less dramatic means, although to
date these experiments have failed to maintain conditions needed
for ignition long enough for fusion to be a viable commercial
power source.
The success of fusion power system is dependent on
performance of the fírst wall, blanket or divertor systems [1]. In
design of a fusion reactor, one of the most important parameters
is the selection of the suitable structural material to improve its
neutronic performance. The performance of structural materiais
for fusion power systems and understanding nuclear properties
are important. The Hartree-Fock method with an effective
interaction with Skyrme forces is widely used for studying the
properties of nuclei [2-5]. This method allows possibility to
calculate many aspects of nuclei by means of quantum
mechanical methods in microscopic scale [6,7]. Especially, the
method is successfully used for a wide range of nuclear
characteristics such as binding energy, rms charge radii, nêutron
and proton density, electromagnetic multipole moments, etc. In
this paper, rms charge, mass, nêutron, proton radii, and charge,
mass, nêutron, proton densities were calculated by using the
Hartree-Fock method with an effective interaction with Skyrme
forces for the 87~102Zr, 93Nb,181Ta nuclei. The proton and
nêutron densities, charge densities, mass densities were
calculated by using Skyrme interactions with SI, SIII, SIV, T3,
SKM and SKM* force parameters. The nuclear ground-state
a
properties for the 87~102Zr, 93Nb, 181Ta isotopes are calculated.
Skyrme force parameters can be found from the literature [8-12].
2 Results and Discussions
We have used the Skyrme interaction parameters for calculations
with the program HAFOMN code based on a harmonic oscillator
wave function (HOWF) [13]. In these calculations, the pairing
equations are solved by Newton’s tangential iteration. For
description of the systems consisting of an odd number of
particles, we have used the filling approximation. The HartreeFock and pairing equations are coupled, and they are solved by
simultaneous iteration of the wave íunctions and the occupation
weights [2].
In this study, we have calculated by using the Hartree- Fock
method with an effective interaction with Skyrme forces
parameters for the 87-102Zr, 93Nb and 181Ta isotopes and compared
with experimental data experimental Root- Mean-Square (rms)
charge density radii in Table 1.
Corresponding author: [email protected]
Article
at http://www.epj-conferences.org
This
is anavailable
Open Access
article distributed under the termsorofhttp://dx.doi.org/10.1051/epjconf/201510001007
the Creative Commons Attribution License 4.0, which permits unrestricted use,
EPJ Web of Conferences
Experimental values were taken from Atomic Data and Nuclear
Data Tables [14,15]. The nuclear charge density is a most useful
observable for analyzing nuclear structure and provides
information about the nuclear shape and also can be determined
by clear-cut proceed [16]. It can be seen that the experimentally
measured charge rms density radii little increases from 87Zr
(about 4.2 fm) to 102Zr (about 4.5 fm) except 88Zr (about 4.2 fm),
89
Zr (about 4.2 fm), 90Zr (about 4.2 fm), 91Zr (about 4.2 fm)
isotopes’ charge rms density radii as the mass number increases
in Table 1. The experimentally measured charge rms density
radii for 93Nb and 181Ta are about 4.3 and 5.3 fm respectively as
seen in Table 1. Theoretically the calculated charge rms values
are quite consistent with the theoretical calculations with all the
Skyrme forces parameters. Theoretically calculated charge rms
values are also quite consistent with experimental values.
Especially, theoretical calculations by using the Skyrme forces
parameters with SKM* is closer to experimental values. Also in
Table 1, the nuclear charge rms values calculated by using
Skyrme forces have been compared with the values of radius r o
A1/3 in Liquid-Drop Model in which the number of nucleons per
unit volume is roughly constant. The value of ro has been taken
as 1.25 fm from electron scattering experiments. Similar to the
Hartree-Fock calculations with Skyrme forces, the radius values
in Liquid-Drop Model have been little increased from 5.5 fm (for
87
Zr) to 5.8 fm (for 102Zr) depending on the mass number A. The
values of radius in Liquid-Drop Model for 93Nb and 181Ta are 4.3
and 5.3 fm, respectively. However theoretical calculations by
using the Liquid-Drop Model are very higher than the
experimental values.
We calculated mass rms radius by using the Hartree- Fock
with Skyrme forces parameters for the 87-102Zr, 93Nb and 181Ta
isotopes and we summarized the results in Table
2. For the 87Zr, theoretically calculated mass rms values are
quite consistent with other calculations values. The calculated
neutron and proton rms radius with the Skyrme Hartree-Fock
model for the same isotopes were given in Table 3 and Table 4,
respectively.
The comparison of the calculated values using only the
SKM* parameter charge, proton, neutron and mass densities for
90 94
' Zr, 93Nb, 181Ta isotopes are given in Fig. 1-6. For 90'94Zr
isotopes at the center (r=0), the obtained values of the charge
density with SKM* have approximately been increased from
0.0715 fm'3 (for 90Zr) to 0.0717, 0.0718, 0.0719 fm'3 (91>92’94Zr)
with the increasing of the number of mass. For 90' 94Zr isotopes
at the center (r=0), the obtained values of the proton density with
SKM* have been decreased from 0.0700 fm'3 to 0.0699, 0.0698,
0.0695 fm'3 with the increasing of the number of mass,
respectively. The obtained values of the neutron density with
SKM* for 9°-94Zr isotopes at the center (r=0) have approximately
been increased from 0.0791 fm'3 (for 90Zr) to 0.0814, 0.828,
0.0861 fm'3 (91,92,94Zr) t|le increasing of fhe number of mass,
respectively. The obtained values of the mass density with
SKM* for 9°-94Zr isotopes at the center (r=0) have approximately
been increased from 0.149 fm'3 (for 90Zr) to 0.151, 0.152, 0.155
fm'3 (91>92>94Zr) with the increasing of the number of mass.
Moreover, the obtained values of the charge and proton densities
with SKM* for 93Nb isotope at the center (r=0) were found to be
approximately 0.717 fm'3 and 0.690 fm'3, respectively. The
obtained values of the neutron and mass densities with SKM*
for 93Nb isotope at the center (r=0) were also approximately
0.819 fm'3 and 0.151 fm'3, respectively. The obtained values of
the charge density with SKM* for 181Ta isotope at the center
(r=0) is approximately 0.597 fm'3. The obtained values of the
neutron, proton and mass densities with SKM* for 181Ta isotope
at the center (r=0) are approximately 0.585 fm' 3, 0.898 fm'3,
0.148 fm'3. In Fig. 1-4, the calculated all densities of
90 91 92 94
> > > Zr isotopes are constant from about to 2 fm radius
value than 5-6 fm radius value while they decreases drastically
to zero after 5-6 fm for 9o>9h92>94Zr Target nuclei. The
calculated densities of 93Nb are constant from about to 2 fm
radius value than 5-6 fm radius value while they decreases
drastically to zero after 5-6 fm for 93Nb target nuclei in Fig. 5
and Fig.6. Values approximately to zero value are about in the
vicinity of 7-8 fm. While the calculated densities of target nuclei
90 94
' Zr and 93Nb at the center (at r = 0) appear to give maximum
with the value near to about 2 fm radius value in Fig. 1-5. The
calculated densities of target nuclei 181Ta at the center appear to
give maximum with the value near to about 3 fm radius value in
Fig 6.
3 Conclusion
In this study, the charge, mass, proton, and neutron densities and
the rms charge, mass, proton and neutron radii have been
calculated for i7~102Zr,93Nb,181Ta isotopes by using the HartreeFock method with an effective Skyrme force with SI, SIII, SVI,
T3, SKM, SKM* and compared with experimental data. From
Table 1, since the calculated theoretical charge rms values using
Skyrme forces parameters are quite consistent with experimental
values, we only obtained radii versus densities figures for
SKM*. The radius values in Liquid-Drop Model have been little
increased depending on the mass number A. These results can
be contributed to understanding ground State properties for these
structural íusion materiais.
. ..... ...... .............................................. ..............................
Table 1.fm).
ro=1.25
The calculated rms charge density radius (m fm and
SI
SIII
’Zr
Zr
4.191
4.197
4.308
4.313
4.317
4.322
4.254
4.257
4.264
4.267
4.284
4.286
5.538
5.559
4.282
4.281
89
Zr
Zr
Zr
4.202
4.207
4.217
4.318
4.323
4.333
4.328
4.334
4.344
4.260
4.264
4.272
4.269
4.271
4.280
4.288
4.291
4.299
5.580
5.010
5.622
4.271
4.269
4.284
Zr
Zr
4.225
4.242
4.343
4.361
4.353
4.371
4.278
4.291
4.286
4.299
4.305
4.318
5.642
5.683
4.305
4.331
8
88
90
91
92
94
96
98
Zr
SVI
T3
SKM
SKM*
roA1'3 Exp
[20]
4.260
4.380
4.390
4.305
4.313
4.332
5.723
4.349
/,
Zr
4.269
4.279
4.390
4.399
4.400
4.410
4.314
4.322
4.322
4.331
4.340
4.349
5.743
5.763
4.393
4.418
/,
Zr
Zr
4.288
4.298
4.307
4.409
4.419
4.428
4.420
4.429
4.439
4.331
4.341
4.351
4.340
4.351
4.361
4.358
4.368
4.379
5.782
5.801
5.821
4.434
4.522
4.548
4.317
4.247
5.229
4.438
4.366
5.365
4.449
4.376
5.378
4.361
4.301
5.284
4.372
4.309
5.298
4.389
4.329
5.311
5.840
5.663
7.070
4.569
4.324
5.350
100
101
102
Zr
Ab
181
Ta
01007-p.2
TESNAT 2015
Table 2. The calculated rms mass density radius (in fm)
87
Zr
88
Zr
89
Zr
"Zr
91
Zr
"Zr
94
Zr
96
Zr
"Zr
98
Zr
99Zr
lOOZr
101Zr
102Zr
93Nb
181Ta
SI
4.128
4.139
4.151
4.162
4.180
4.196
4.229
4.262
4.278
4.294
4.310
4.326
4.341
4.358
4.209
5.233
SIII
4.248
4.260
4.273
4.285
4.306
4.324
4.360
4.395
4.412
4.429
4.446
4.463
4.479
4.494
4.337
5.376
SVI
4.251
4.263
4.276
4.288
4.307
4.324
4.357
4.391
4.407
4.424
4.440
4.456
4.472
4.486
4.338
5.379
T3
4.202
4.214
4.226
4.239
4.260
4.276
4.312
4.348
4.367
4.385
4.405
4.424
4.443
4.461
4.288
5.323
SKM
4.209
4.220
4.231
4.242
4.263
4.281
4.316
4.352
4.371
4.391
4.410
4.430
4.449
4.468
4.292
5.334
SKM*
4.228
4.239
4.250
4.261
4.282
4.300
4.334
4.370
4.389
4.408
4.427
4.446
4.465
4.484
4.311
5.347
roA1'3
5.538
5.559
5.580
5.601
5.622
5.642
5.683
5.723
5.743
5.763
5.782
5.801
5.821
5.840
5.663
7.070
Figure 1. The calculated using the SKM* parameter charge, proton,
nêutron, mass densities of 90Zr isotope
Table 3. The calculated rms nêutron density radius (in fm)
87
Zr
88
Zr
89
Zr
"Zr
91
Zr
"Zr
94
Zr
"Zr
97
Zr
98
Zr
99Zr
lOOZr
101Zr
102Zr
93Nb
181Ta
SI
SIII
SVI
T3
SKM
SKM*
4.135
4.151
4.167
4.182
4.207
4.228
4.271
4.311
4.331
4.351
4.370
4.389
4.408
4.427
4.235
5.270
4.258
4.275
4.293
4.309
4.337
4.361
4.407
4.451
4.472
4.493
4.513
4.533
4.552
4.570
4.368
5.420
4.257
4.274
4.291
4.307
4.333
4.355
4.397
4.439
4.459
4.479
4.498
4.517
4.536
4.553
4.363
5.413
4.219
4.238
4.256
4.273
4.303
4.326
4.374
4.422
4.446
4.470
4.494
4.518
4.541
4.563
4.330
5.386
4.223
4.239
4.256
4.272
4.302
4.327
4.375
4.423
4.447
4.471
4.496
4.520
4.543
4.567
4.331
5.395
4.241
4.258
4.274
4.290
4.320
4.344
4.392
4.439
4.443
4.487
4.511
4.535
4.559
4.582
4.349
5.408
roA1'3
5.538
5.559
5.580
5.601
5.622
5.642
5.683
5.723
5.743
5.763
5.782
5.801
5.821
5.840
5.663
7.070
Zr
88
Zr
89
Zr
"Zr
91
Zr
"Zr
94
Zr
"Zr
"Zr
"Zr
99Zr
lOOZr
101Zr
102Zr
93Nb
181Ta
Zr
A
*
.... ...................................... ... *
S o
•í*
....................... •*»... _____________ I _______
12.0
Figure 2. The calculated using the SKM* parameter charge, proton,
nêutron, mass densities of 91Zr isotope
Table 4. The calculated rms proton density radius (in fm)
87
91
• Charge (SKM*)
o Proton (SKM*)
o Nêutron (SKM*)
A Mass(SKM*)
*
SI
SIII
SVI
T3
SKM
SKM*
roA1'3
4.119
4.125
4.131
4.137
4.146
4.155
4.173
4.191
4.200
4.210
4.219
4.229
4.238
4.250
4.175
5.179
4.236
4.242
4.248
4.255
4.266
4.275
4.295
4.315
4.325
4.335
4.345
4.355
4.365
4.373
4.298
5.312
4.243
4.250
4.256
4.263
4.274
4.283
4.303
4.323
4.333
4.343
4.353
4.363
4.374
4.381
4.306
5.328
4.182
4.186
4.190
4.195
4.204
4.211
4.226
4.242
4.251
4.260
4.269
4.279
4.289
4.298
4.233
5.230
4.193
4.196
4.200
4.204
4.214
4.221
4.236
4.252
4.261
4.270
4.280
4.291
4.301
4.311
4.243
5.243
4.213
4.216
4.220
4.224
4.234
4.241
4.256
4.271
4.280
4.289
4.299
4.309
4.319
4.329
4.263
5.256
5.538
5.559
5.580
5.601
5.622
5.642
5.683
5.723
5.743
5.763
5.782
5.801
5.821
5.840
5.663
7.070
Figure 3. The calculated using the SKM* parameter charge, proton,
nêutron, mass densities of 92Zr isotope
01007-p.3
EPJ Web of Conferences
Figure 4. The calculated using the SKM* parameter charge, proton,
nêutron, mass densities of 94Zr isotope
4. T.H.R. Skyrme, Phil. Mag. 1, 1043 (1956); Nucl. Phys. 9,
615 (1959).
5.
E. Tel, et al., Annals of Nuclear Energy, 35 (2), 220 (2007).
6.
H. Aytekin et al., J. Fusion Energy, 30 (1), 21, (2011).
7.
L.G. Qiang, J. Phys. G 17, 1 (1991).
8.
M. Brack, C. Guet, and H. Hakasson, Phys. Rep. 123, 275
(1986).
9.
D. Vauthering and D.M. Brink Phys. Rev. C 5, 626 (1972).
10.
E. Tel, N.N. Akti, §. Okuducu, A. Aydin, M. §ahan, F.A.
Ugur and H. §ahan, Journal of Fusion Energy, 30, 1, (2011).
11.
H. Aytekin, E. Tel, R. Baldik, A. Aydin, Journal of Fusion
Energy, 30, 1, (2011).
12.
http://phys.lsu.edu/graceland/faculty/cjohnson/skhaf o.f
13.
E.G. Nadjakov, K.P. Marinova, Systematics of Nuclear
Charge Rad II, Atomic Data and Nuclear Data Tables, 56, 133
(1994).
14.
I. Angeli, IAEA-NDS-163,. Institute of experimental
Physics, Kossuth University, H-4001 Debrecen, Pf.105 , Hungary
Rev.1, (1999).
15.
B. Dreher et al, Nucl. Phys, A235, 219 (1974).
References
93Nb
1.
2.
3.
• Charge (SKM') o
Proton (SKM') o
Nêutron (SKM*) A
Mass(SKM')
0.1
0.0
2.0
4.0
6.0
8.0
10.0
12.0
Figure 5. The calculated using the SKM* parameter charge, proton,
nêutron, mass densities of 93Nb isotope
Figure 6. The calculated using the SKM* parameter charge, proton,
nêutron, mass densities of 181Ta isotope
01007-p.4
E.E. Bloom, J. Nucl. Mat. 253-268, 7-17 (1998).
D. Vautherin and D.M. Brink, Phys. Rev. C5, 626 (1972).
B.A. Brown, Phys. Rev. C 58, 220 (1998).
EPJ Web of Conferences 100, 1005 (2015)
DOI: 10.1051/epjconf/ 201510001005
© Owned by the authors, published by EDP Sciences, 2015
(n,p), (n,2n), (n,d), and (n,a) cross-section calculations of 16O with 0-40
MeV energy nêutrons
Omer Faruk Ozdemir3, Ali Arasoglu
Yüzüncü Yil University, Science Faculty, Physics Department, 65080, Van, Turkey
Abstract. Oxygen is one of the elements which interacts with emitted nêutrons after fission reactions. Oxygen exists abundantly both
in nuclear fuel (UO2) and moderators (H2O). Nuclear reactions of oxygen with nêutrons are important in terms of stability of nuclear
fuel and nêutron economy. In this study, equilibrium and pre-equilibrium models have been used to calculate (n,p), (n,d), (n,2n) and
(n,a) nuclear reaction cross-sections of 16O. In these calculations, nêutron incident energy has been taken up to 40 MeV. Hybrid and
Standard Weisskopf-Ewing Models in ALICE-2011 program, Weisskopf-Ewing and Full Exciton Models in PCROSS program, and
Cascade Exciton Model in CEM03.01 program have been utilized. The calculated results have been compared with experimental and
theroretical cross-section data which are obtained from libraries of EXFOR and ENDF/B VII.l.
1 Introduction
The most important part of nuclear power reactor is reactor
core. At core, fission reactions take place and thermal energy
was produced. Also at pressurized water reactors, it can reach
to high temperatures. Physical stability of nuclear fuel and
economy of nêutron are effect to security of core region.
Chain fission reactions was constituted by spontaneous
nêutrons emitted during the fission and delayed nêutrons
emitted after the fission. The stability, security and power of
the reactors can be determined by chain fission reactions [1,2].
Generally UO2 is used as a fuel in nuclear power reactor.
In addition to UO2, MOX (UO2+PUO2, Mixed Oxide Fuel)
and DUPIC (Direct Use of Spent PWR Fuel In CANDU
Reactors) can be used as a fuel. Nêutron emitted after fission
in nuclear reactor interact different elements in structural
materiais and one of these elements is oxygen [3-6]. Oxygen
exist both in fuel (UO2 and PUO2) and moderator (H2O). For
stability of nuclear fuel and nêutron economy, reactions
between nêutron and oxygen are very important [7].
In this study, equilibrium and pre-equilibrium models have
been used to calculate (n,p), (n,d), (n,2n) and (n, a) nuclear
reaction cross-sections of 16O. In these calculations, nêutron
incident energy has been taken up to 40 MeV. Hybrid and
Standard Weisskopf-Ewing Models in ALICE-2011 program,
Weisskopf-Ewing and Full Exciton Models in PCROSS
program and Cascade Exciton Model in CEM03.01 program
have been utilized [10-12]. The calculated results have been
compared with experimental and theoretical cross-section data
which are obtained from libraries of EXFOR and ENDF/B
VII.l.
explain this case [8]. In this model, reaction cross section is
given as following;
CT(a, b) = CTa (s)rjb (E)
In this formula, E is the incident energy of particle and <r,(v) is
the cross section for the formation of a compound State.
Particle emitting probability of compound nucleus % is
independent from how the compound nucleus was formed and
given as [9];
(2)
^b
À, b' b'
rb is the emission probability per time for the particle b and
given as:
b
nh
b
rb =
b
u. f d-n (sys0^ (3)
(E)
In equilibrium, the probability of emitting particle is given as
following:
2 Calculations of nuclear reactions
In Weisskopf Ewing Model; projectile particle was absorbed
by target nucleus. Without emitting particles, compound
nucleus reach the equilibrium State. This model can be used to
a
(1)
Corresponding author: [email protected]
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510001005
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use,
EPJ Web of Conferences
b (s) « (2sb +1) u S(7‘bnv (s) ^-t
®i(E)
W
(4)
where sb is spin, fib is reduced mass, e is energy of emitted
particle, tf? is the inverse reaction cross section, rq (U) is the
nuclear levei density of the nucleus, rq (E) is the nuclear levei
density of the nucleus emitting b particle, U is the excitation
energy of residual nucleus and E is the excitation energy of the
emitting nucleus [10].
According to the Griffin Exciton Model, nuclear potential
is consisted by one particle States with evenly- spaces. System
was excited after interaction between nucleus and projected
particle. Therefore, system will be unstable due to given
energy.
One particle one hole (exciton) will occur when projectile
particle enters target nucleus. After interactions between
projectile and system, there will be more excitons. When
system has sufficient excitons, system get stable with pairing
effect. Exciton Model suggests that it is possible to emit
particle during the any steps of excitation process or any steps
of such process that system becomes stable. In this model, preequilibrium and equilibrium emission spectra equation is given
below:
tf) = tf,E)Dab(Einc)tfw(E,n,8b) r„ (5) <tf
Figure 1. Comparison of cross section calculations of
16O(n,p)16N reaction between given nuclear reaction
models, experimental data and evaluated data library
[13,14],
n
where, tfb (Enc) is the cross section of reaction (a,b); Wb (E, n,sb)
is the probability of emission of b particle with energy sb from
a State with n excitons and excitation energy E of the
compound nucleus; Tn the solution of the master equation for a
State with n excitons; Dab (Ejnc) is a coefficient about particle
emission by direct interactions [11].
Another model is named as Cascade Exciton Model. This
model occurs in three steps; Intra Nuclear Cascade (INC), Preequilibrium and Equilibrium stages. In general, these three
steps contribute values obtained as experimentally.
3 Results and discussions
In this study, pre-equilibrium and equilibrium models were
used to calculate (n,p), (n,d), (n,2n) and (n,a) nuclear reaction
cross-sections of 16O with the incident nêutron energies up to
40 MeV. For the pre-equilibrium effects Full Exciton Model
(FEM) and Cascade Exciton Model (CEM), for the equilibrium
effects Weisskopf Ewing Model have been used. Equilibrium
model calculations have been prepared by using PCROSS and
ALICE-2011 Computer codes. FEM and CEM calculations
have been performed by PCROSS and CEM03.01 Computer
codes, respectively. The results of comparisons between cross
section calculations of this study, experimental data and
evaluated ones taken from literature are as following:
In (n,p) reaction calculations (Fig.l); although reaction
models produce smaller results than those of experimental and
evaluated data up to 15 MeV, in 15-20 MeV region results are
in agreement, while in higher energies calculations of ALICE2011 program and CEM03.01 programs are in good agreement
with experimental data and evaluated results.
Figurei.Comparison of cross section calculations oí 16O(n,d)15N
reaction between given nuclear reaction models, experimental data and
evaluated data library [13,14],
As in seen in Fig. 2; Standard WE model is in agreement
with experimental data and evaluated results up to 15 MeV for
(n,d) calculations. Athigh energies, the model calculation
results are in agreement with evaluated data but greater than
experimental data.
Results of calculations of reaction models for (n,2n)
reaction are in agreement with experimental data and evaluated
results.
In (n,a) reaction calculations, results of all models are in
agreement with experimental data and evaluated results up to
20 MeV incident energy. Results gathered from CEM03.01 and
ALICE-2011, which utilizes standard WE model, are in good
agreement with experimental and evaluated data at high
energies.
01005-p.2
TESNAT 2015
Figure 4. Comparison of cross section calculations oí 16O(n,a)13C
reaction between given nuclear reaction models, experimental data and
evaluated data library [13,14],
Projects 2013-FBE-D005. The authors would like to thank Dr.
Murat Aycibin for contributions.
References
1.
Figure3.Comparison of cross section calculations oí 16O(n,2n)15O
reaction between given nuclear reaction models, experimental data and
evaluated data library [13,14],
D.G. Cacuci, Handbook of Nuclear Engineering
(Springer, 2010).
2. Thermophysical properties database of materiais for light
water reactors and heavy water reactors, IAEATECDOC-1496 (2005).
3. https://www.iaea.org/About/Policy/GC/GC51/GC51I
nfDocuments/English/gc51inf-3-att5_en.pdf.
4. S.G. Popov, J.J. Carbajo, V.K. Ivanov and G.L. Yoder,
Thermophysical Properties of MOX and UO 2 Fuels
Including the Effects of Irradiation, ORNL/TM-2000/351.
5. L. Jung-Won, Geun-Il Parkaand Yong Choib, J. Nucl. Sei.
Technol. 49.11, 1092-1096 (2012).
6. J.J. Whitlock, The evolution of CANDU fuel cycles and
their potential contribution to world peace, (2001).
7. J.K. Fink, J. Nucl. Mater., 279.1, 1-18 (2000).
8. V.F. Weisskopf, D.H. Ewing, Phys. Rev. 57, 472485
(1940).
9. J.J. Griffm, Phys. Rev. Lett. 17, 478-481 (1966).
10. S.G. Mashnik, et ah, Monte-Carlo Code System to
Calculate Nuclear Reactions in the Framework of the
Improved Cascade-Exciton Model, LA-UR-05- 7321
(2005).
11. C.H.M. Broeders et ah, ALICE/ASH - Precompound and
Evaporation Model Code System for Calculation of
Excitation Functions, Energy and Angular Distributions
of Emitted Particles in Nuclear Reactiopns at
Intermediate Energies (2006).
12. R. Capote et al., Final report on research contract
5472/RB., INDC (CUB)-004 (1991).
13. EXFOR, http://www.oecdnea.org/janisweb/search /exfor.
14. Evaluated
Data
Library,
http://www.oecdnea.org/janisweb/
Acknowledgments This work has been supported by Yüzüncü Yil University, Office of Scientific Research
01005-p.3
EPJ Web of Conferences 100, 01004 (2015)
DOI: 10.1051/epjconf/ 20151000100 4
© Owned by the authors, published by EDP Sciences, 2015
Nuclear structure of particle-hole odd-odd 130ln nucleus in tin-132 mass
region
Nadjet Laoueta, Fatima Benrachi
The Brothers Mentouri University, Exact Sciences Faculty, Department of physics, 25000, Constantine, Algeria
Abstract. The spectra of odd-odd nuclides near drip lines, that are close to the path of astrophysical r-process flow, involving a single
particle or a single hole in the vicinity of an inert core provide detailed and quantitative information on the N-N interaction. In this
work, we have performed shell model calculation using recent experimental single particle and single hole energies, by means of Oxbash
nuclear structure code, in order to reproduce the nuclear properties of odd-odd 130In nucleus in the 132Sn mass region. The two-body
matrix elements (TBME) of the using effective interaction were deduced from those for 78Ni mass region, using the single hole energies
(SHE) of 132Sn mass region.
1 Particle-hole configuration
l
The spectra of nuclei consisting a single particle or a single
hole in addition to an inert core provide detailed and
quantitative information on the nuclear independent- particle
motion. A closed shell, which contains (2j+l) particles with an
angular momentum j for each particle, must have total angular
momentum J=0 and a positive parity, since each State of total
angular momentum J possesses (2J+1) degenerate substates
[1].
Thus, for a configuration of a single particle, in addition to
closed shells, one expects a number of low- lying States having
angular momentum and parity determined by the quantum
numbers of the orbits available to the single particle.
Confígurations obtained by removing a particle from closed
shells (single-hole confígurations) are expected to have
properties related in a simple manner to those of single-particle
confígurations.
The creation of a hole State with quantum numbers nljm is
equivalent to the annihilation of a particle in the State with
quantum numbers nlj-m (conjugate State). For the operator
creating a single hole [1]
b+(jm^ = a('/m)-(-l) ma(j -m)
(1)
Thus, the single particle State can be obtained using
|j Jtn) = b+(jm)|Ô) = a(jm)|Ô,
(2)
The matrix elements for hole States and those for
the single particle are related by
a
(j2 m2 ^|jl‘mJ =
-(jlml \F\jl ml}
/1m 1, (n2l2 )j2 m2 )
+ ( 0 | |Ô) ^((
1
F
nl
(3)
ll
Here, F is an arbitrary single particle operator.
In this work, we carry out some modifícations on the
jj45apn interaction [2], basing on the consideration of mass
factor effect with the use of the available experimental single
hole energies taken from [3-5].
The calculations of some nuclear properties for 130In are
developed in the framework of the nuclear shell model by
means of Oxbash nuclear structure code, and a new interaction
namedjj45pnh is introduced.
{jlj2
H 2 A) = {( l 2 HÁ) j,- pna * eff
j
j j
4S
maSS
eCt faCtOr
]
(4)
The space model is composed of {0/5/2, lpd/2, lpl/2 and
0gP/2}z'28 orbitais for hole protons and {0g?/2, lds/2,
lds/2, 2si/2, and OAn/2}N'50 orbitais for hole nêutrons.
2 Results and discussion
The structures of odd-odd nuclides provide best opportunities
to examine and develop the properties ofN- N interaction. The
130
In is one of these nuclei, with one proton hole and one
nêutron hole in addition to the tin- 132 core. Their low-lying
States, including the ground State which has J"= 1" with a
mean-life of 0.29 s and decays by [T. are the result of [f decay
of the ground State which has a half-life 162 ms of the rprocess waiting point nucleus 130Cd [6].
The figures Fig.l shows experimental spectrum of 130In.
[email protected]
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510001004
EPJ Web of Conferences
Fig. 1. Experimental spectrum of 130In taken from
nndc.bnl.gov [7].
Fig. 2. Calculated spectrum of 130In in comparison with
experimental anAjj45apn [2] ones.
The microscopic calculations for this nucleus are carried
out by means of Oxbash code [3], mjj45pn space model. The
Fig.2 shows the calculation results in comparison of the
experimental data
For the 130In nucleus, the energetic sequence is reproduced
by the original interaction but the energy of the fírst excited
State, which has an energy of 82 keV, is very far in comparison
with the experimental one with an energy of 388.3 keV.
Indeed, our new interaction gives 3+ as the ground State, and
the 1" State has an energy of 669 keV. The other interaction
(snhole) gives 5 + as the ground State and the energy of the T
State is 233 keV. In these spectra, the energy of 1+ State,
dominated by rn (lg9/2)-1 v (IAH/2)'1 as given by the three
interactions, present an energetic maximum value.
Note that snhole interaction is obtained by using the snet
interaction [2] and taking into account the mass effect.
The reduced electromagnetic transition probabilities can be
calculated by the form:
>:'M : J
Jf) = (2J. +1)-* |{Jf ||MffJ| J|2
(5)
The Tab.1 shows reduced electric transition probabilities
calculated by means of jj45pnh and jj45apn interactions.
Table 1. Electromagnetic reduced transition probabilities of 130In in 132Sn mass region obtained using jj45pn and jj45pnh interactions.
2+
Jí^ Jf
B(E2) e2fm4
B(M1),«2N
1+
3+
1+
3+
2+
4+ -» 2+
4+
3+
5+
3+
5+
4+
6+
4+
jj45pnh
0.050
6.978
4.957
12.110
35.340
26.150
0.076
19.120
jj45apn
1.148
5.931
2.232
15.030
14.880
39.120
3.865
24.600
jj45pnh
0.006
/
2.410
/
0.285
/
0.493
/
jj45apn
0.040
/
1.262
/
0.045
/
1.104
/
Whereas, we calculate the quadrupole electric moment using
ep =1.35e and en = 0.35e effective charges [8]:
The two interaction give different values of B(E2) and
B(M1), using the two interactions. The difference is important
for the mixed transitions. Indeed, these calculations give higher
values for electric reduced transition probabilities in the case
of pure transitions with A.I2,
The lowest negative parity States of 130/n have the
{^lg9/2, xlhini, J} confíguration withj(p) =9/2 andj(n) = 11/2.
The value of the magnetic moment of a State with the spin
j=l±1/2, and tz=±1/2 for a proton or a nêutron is [8]:
j)
J (J +1)
.
Here, Qjp, jn denote respectively single proton/neutron
quadrupole moment
Q (pn) = - (2j ~(r2\ep,n (eff .)
Á-2
The calculated electric quadrupole and dipole moments, by
means oíjj45pnh interaction, are illustrated in Fig.4.
(6)
( h ( P ) _ h ( n ) jp j + 1) ~ jn ( Jn + 0
l jp
(2 j + 2)
(8)
01004-p.2
TESNAT 2015
References
1. Bohr and B. R. Mottelson, Nuclear Structure Volume 1:
Single Particle Motion, World Scientifíc Publishing Co.
Pte. Ltd. (1998).
2. B. A. Brown, A. A. Etchegoyen and W. D. H. Rae NS.
Godwin,
MSU-NSCL
Report
No.
524
(1985).unpublished).
3. H. Grawe et al., Rep. Prog. Phys. 70 (2007)
4. B.A. Brown et al., Phys. Rev. C 71 044317 (2005).
5. L. Corragio et al., Phys. Rev. C 80 061303(R) (2009).
6. I. Dillmann et al., Phys. Rev. Lett 91N° 16 (2003)
7. http://www.nndc.bnl.gov/chart/
8. K. Heyde et al., Hyperfíne Interactions 43 (1988)
Figure 3. Electromagnetic multipole moment of 130In in I32Sn mass
region obtained us\n^jj45pnh wnâjj45apn interactions.
For the electric quadrupole moment, Q the State 1" gives
the lowest value, then the minimum deformation for both
interactions. This State, which represent the experimental
ground State, has also the minimum value of the magnetic
dipole moment p.
Conclusion
This study is based on the nuclear properties calculations, for
odd-odd 130In nucleus, with hole-hole configuration of its
valence space. The calculations are carried out in the
framework of the shell model, by means of OXBASH nuclear
structure code. Using the original interaction of the code, we
carry out some modifícations based on the mass effect to get
jj45pnh interaction. Our new interaction cannot reproduce the
experimental spectra of the studying nuclei. It is the same case
for the original interaction. However, this later reproduce the
energetic sequence of the low laying States. To ameliorate
these results we have to consider other nuclear effects as the
monopole interaction and shell evolution in tin-132 mass
region.
Acknowledgement
The authors of this article thank the organizers of TESNAT
2015 for the organization and the supports providing during
this conference.
Special thanks are owed to B. A. Brown for his help in
providing us the OXBASH code (Windows Version)
01004-p.3
EPJ Web of Conferences 100, 01002 (2015)
DOI: 10.1051/epjconf/ 201510001002
© Owned by the authors, published by EDP Sciences, 2015
Nêutron activation analysis of certified samples by the absolute method
F. Kadema, N. Belouadah and Z. Idiri
Faculté de physique, USTHB BP 32 El-Alia BEZ Alger Algeria
Abstract. The nuclear reactions analysis technique is mainly based on the relative method or the use of activation cross sections.
In order to validate nuclear data for the calculated cross section evaluated from systematic studies, we used the nêutron activation
analysis technique (NAA) to determine the various constituent concentrations of certified samples for animal blood, milk and hay.
In this analysis, the absolute method is used. The nêutron activation technique involves irradiating the sample and subsequently
performing a measurement of the activity of the sample. The fundamental equation of the activation connects several physical
parameters including the cross section that is essential for the quantitative determination of the different elements composing the
sample without resorting to the use of standard sample. Called the absolute method, it allows a measurement as accurate as the
relative method. The results obtained by the absolute method showed that the values are as precise as the relative method requiring
the use of standard sample for each element to be quantified.
1 Introduction
In order to validate our data calculated cross sections, we have
made an application to the data for the quantitative analysis of
certified standard samples using the Nêutron Activation
Analysis (NAA) and the absolute method. Once validated this
method does not require the use of standard samples and just
need to know the cross section for the nuclear reaction induced
by fast nêutrons. This approach is complemented by the use of
data of the cross section quickly calculated by the semiempirical formulas systematic studies. The nêutron activation
analysis of samples certified by the IAEA was carried out
using the absolute method based on using our data calculated
cross sections.
is given is related to the isotopic abundance 0
and the mass m of the element constituting
the sample by:
(2)
mdN n = a
M
where Na is Avogadro's number and M the atomic mass. To
determine the efficiency with gamma ray energy dependence
the following expression is used: £(%) = £a + A exp(Er /Bl) +
J. exp(Er / B1)
The fitting parameters s o, A; and B; were determined by using
the least squares method. The difference between the
experimental points and the calculated points is generally less
than 1%.
2 Treatment data
The photopeak area of an intensity IY and effíciency EY,
corresponding to the activity of a Y radioisotope with decay
constant Á formed in a X (n, b) Y reaction (b = n, 2n, p np,
d,t,a, .. .)is given by:
Net = n^eMl - exp(-@ ))exp(-2trf )(1 - exp(-@))
Á
(1) where G is integrated cross section of the
reaction, O is the incident nêutron flux, n is the number of
target nuclei X, Á is the radioactive decay constant and ti, td
and tc are respectively the time of irradiation , the cooling time
and the time counting [1] . The number n of the target nucleus
a
gamma ray energy (keV)
Figure 1. Efficiency curve via gamma ray energy.
Corresponding author: [email protected]
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution,
and reproduction in any medium, provided the original work is properly cited.
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510001002
EPJ Web of Conferences
present the results of the counting of gamma spectra of samples
of blood, milk and hay.
3 Experimental results
The nêutron activation analysis allows to determine the mass of
samples constituents using the absolute method [4]:
Table 2, Component characteristics of hay sample (V-10),
=
56Fe(n,p)56Mn
24Mg(n,p)24Na
Mg
P
K
Rb
Sr
Ca
3.1 Measurement of nêutron flux
To measure the flux of incident nêutrons we used pure
aluminum sheets. In order to measure the flux to which the
sample is exposed we placed the sample between two aluminum
sheets so that together form a sandwich. The reference reaction
27
A1 (n, a)24Na was used.
The detailed characteristics ofthis reaction are given as
follows: 0=114 mb, Ey = 1369 keV, Iy= 100 %, T1/2 = 53900
s.
The flux, which is exposed, the sample is calculated using
the expression:
x2
/2
= 4- -------- 3(5)
(2x+dy
where d is the thickness of the sample, y are respectively the flux
measured by the aluminum sheets 1 and 2, x is the distance from
the nêutron source and the aluminum foil measuring the flux and
LI is the absorption coeffícient of the nêutrons in the sample. LI
is deduced from the following equation:
reaction
IAEA-V-10
element
Fe
---------------- j
--------------------------- (4)
N. M
N
Oc>úl _ (1 - exp(T t( ))exp(-T td )(1 - exp(Ttc))
A
where N is the net area of the photopeak.
m
31P(n,p)28Al
39K(n,2n)38K
85Rb(n,2n)84mRb
88Sr(n,2n)87mSr
44Ca(n,p)44K
Table 4. AAN results for Animal blood and powdered milk
samples (A-13 & A-ll).
AEA-A- 13
element
Fe
(6)
Table 1. Component characteristics of animal blood sample (A13): __________ ________________ _______ ______________
Fe
Mg
P
K
Rb
“Fe (n,p)56Mn
24
Mg (n,p)24Na
31
P (n,p)28Al
39
K (n,2n)38K
85
Rb(n,2n)84mRb
Tl/2 (s)
9290
53900
117
458
1220
ET (keV)
ly (%)
847
1369
1779
2168
248
98.9
100
100
99.9
59
100
100
99.9
59
81.8
58.2
Within the error bars the measured concentrations in this study
3.3 Experimental results
reaction
1369
1779
2168
248
388
1157
3.4 Discussion
The irradiation time was 20 min for each samples of animal
blood, milk and hay. The components samples have been
identifíed, through the gamma rays characteristic of a
radionuclide produced via a nuclear reaction induced by fast
nêutron on the sample target.
IAEA-A-13
element
53900
117
458
1220
10100
1330
Table 3. Component characteristics of milk powder sample (A111 __________ . ________________ , , , .
reaction
IAEA-A-11
Tl/2 (s)
element
Ey (keV) ly (%)
37
37
Cl
C1 (n,p) S
303 3103
94.1
24Mg (n,p)24Na
Mg
53900 1369
100
31P (n,p)28Al
P
117
1779
100
39K (n,2n)38K
K
458
2168
99.9
reaction
ncai
(mb)
107
Experimental
massic
concentration
(mg/Kg)
2410± 250
Certified massic
concentration
(mg/Kg)
2400
3.2 Analysis of certified samples
,-Ad
Tl/2 (s) Ey (keV) ly (%)
9290
847
98.9
“Fe(n,p
Mg
24
Mg(n,p)
258
55.4 ± 16.1
99
P
31
P(n,p)
160
1310± 230
940
K
39
K(n,2n)
4
1820± 650
2500
Rb
85
Rb(n,2n)
470
40.5 ± 17.3
23
Cl
37Cl(n,p)
IAEA-A-11
36
11.2 ± 1.4
9.08
Mg
24Mg(n,p)
258
0.8 ± 0.2
1.01
P
31P(n,p)
160
11.4 ± 1.6
9.10
K
39K(n,2n)
4
10.6 ± 5.3
17.2
are in agreement with the certified values by the IAEA. A slight
disagreement recorded for some items is mainly due to the low
sensitivity of the activation method probably because of the
small cross section and the inadequacy of the half live
radioisotope irradiation with time so chosen to consider short
and long half live.
The nêutron activation analysis of samples of animal blood,
milk and hay were identifíed qualitatively and quantitatively and
the components of these samples using an absolute method were
carried out. Indeed, this method is based to the fundamental
equation of nêutron activation and using the known cross
section for the nuclear reaction. The experimental results were
compared with data certified by the IAEA. The following tables
01002-p.2
TESNAT 2015
Table 5. AAN results for hay sample (V-10)
AEA-V- 10
reaction
Ocal
Experimental
(mb)
element
massic
concentration
(mg/Kg)
56Fe(n,p)
Fe
107
128 ± 36
Certified massic
concentration
(mg/Kg)
185
Mg
24Mg(n,p)
258
1530 ± 224
1360
P
31P(n,p)
160
2790 ± 427
2300
Ca
44Ca(n,p)
33.7
20500 ± 2130
21600
K
39K(n,2n)
4
25700 ± 2710
21000
Rb
85Rb(n,2n)
474
23.5 ± 11.6
7.6
Sr
88Sr(n,2n)
262
55.7 ± 13.8
40
4 Conclusion
The absolute nêutron activation method is as reliable as the relative method using standards. This approach is complemented by
the use of data of the cross section quickly calculated by the semi-empirical formulas systematic studies.
References
1.
2.
3.
4.
5.
C.M. Lederer, V.S. Shirley, Table of Isotopes, 7th ed., Wiley, New-York (1978)
J.K. Tulli, Nuclear Wallet Cards, NNDC-BNL,Upton, NewYork, 11973, USA (1990)
L. Wielopolski, The Monte Cario calculation of the average solid angle, Nucl. Instr. And Meth., 143, 577 (1977)
M. Belgaid, Thèse de Magister, USTHB, Alger (1991)
F. Kadem, M. Belgaid and A. Amokrane, Nuclear Instruments and Methods in Physics Research B 266 (2008)
01002-p.3
EPJ Web of Conferences 100, 0100 3 (2015)
DOI: 10.1051/epjconf/ 20151000100 3
© Owned by the authors, published by EDP Sciences, 2015
Fission cross section calculations for 209Bi target nucleus based on
fission reaction models in high energy regions
Abdullah Kaplan1'a, Veli Capali1 and Hasan Ozdogan1'2
1
2
Süleyman Demirel University, Faculty of Arts and Sciences, Department of Physics, 32260 Isparta, Turkey
Akdeniz University, Faculty of Medicine, Department of Biophysics, 07058 Antalya, Turkey
Abstract. Implementation of projects of new generation nuclear power plants requires the solving of material Science and
technological issues in developing of reactor materiais. Melts of heavy metais (Pb, Bi and Pb-Bi) due to their nuclear and
thermophysical properties, are the candidate coolants for fast reactors and accelerator-driven Systems (ADS). In this study, a, y,
p, n and 3He induced fission cross section calculations for 209Bi target nucleus at high-energy regions for (a,f), (y,f), (p,f), (n,f)
and (3He,f) reactions have been investigated using different fission reaction models. Mamdouh Table, Sierk, Rotating Liquid Drop
and Fission Path models of theoretical fission barriers of TALYS 1.6 code have been used for the fission cross section calculations.
The calculated results have been compared with the experimental data taken from the EXFOR database. TALYS 1.6 Sierk model
calculations exhibit generally good agreement with the experimental measurements for all reactions used in this study.
1 Introduction
Melts of heavy metais (Pb, Bi and Pb-Bi), due to their nuclear
and thermophysical properties, are candidate coolants for fast
reactors and accelerator-driven systems (ADS) [1]. A design
methodology for the lead-bismuth eutectic spallation target has
been developed and applied for the accelerator-driven test
facility target. This methodology includes the target interface
with the subcritical multiplier of the ADS and the different
engineering aspects of the target design, physics, heattransfer, hydraulics, structural, radiological, and safety
analyses. Several design constrains were defíned and utilized
for the target design process to satisfy different engineering
requirements and to minimize the time and the cost of the
design development. Interface requirements with the
subcritical multiplier were defíned based on target
performance parameters and material damage issues to
enhance the lifetime of the target structure [2].
Nucleon-induced fission cross-section data are important
for the nuclear reactors. Firstly, fission reactions may have a
signifícant effect on spallation target performance. In
particular, fission may contribute notably to the production of
radioactive materiais in the target. On the other hand, the
predictive power of available nuclear reaction models and
codes with respect to the description of the fission process
should be developed.
Fission can be induced not only by nêutrons, but also by
protons, light and heavy ions, photons, electrons, n- mesons
etc. In this study, a, y, p, n and 3He induced fission cross
section calculations for 209Bi target nucleus at high energy
regions for (a,f), (y,f), (p,f), (n,f) and (3He,f) reactions have
a
been investigated using four fission reaction models. TALYS
1.6 Theoretical fission barriers; Mamdouh Table, Sierk,
Rotating Liquid Drop and Fission Path models have been used
for the fission reactions. The calculated results have been
compared with the experimental data taken from the EXFOR
[3] database.
2 Methods
TALYS [4, 5] is a nuclear reaction simulation code for the
estimation and analysis of nuclear reactions that include
protons, nêutrons, photons, tritons, deuterons, 3He and alpha
particles in the energy range of 1 keV-1 GeV. For this, TALYS
integrates the optical model, direct, pre- equilibrium, fission
and statistical nuclear reaction models in one calculation
scheme and thereby gives a prediction for all the open reaction
channels. In TALYS, several options are included for the
choice of different parameters such as y-strength functions,
nuclear levei densities and nuclear model parameters.
The probability that a nucleus físsions can be estimated by
TALYS on both phenomenological and microscopic grounds.
Cross sections for (multi-chance) fission can be calculated. For
this, various nuclear quantities are required. A fission model
has been developed by Schmidt- Jurado [6]. It is based on the
statistical population of States in the fission valleys at the
moment of dynamical freeze- out, which is specifíc to each
collective degree of freedom. Three fission channels are
considered. The separability principie govems the interplay of
macroscopic and microscopic effects.
Corresponding author: [email protected]
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution,
and reproduction in any medium, provided the original work is properly cited.
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/201510001003
EPJ Web of Conferences
In the Sierk físsion barrier model, físsion barrier heights
are estimated in MeV with Sierk’s method using the rotating
fínite range model. It is dependent upon calculations using
exact Coulomb diffuseness corrections, diffuse-matter
moments of inertia, and Yukawa-plus- exponential double
folded nuclear energy [7]. Additional details on the model
parameters and options of TALYS codes can be found in Refs.
[5].
Sierk approximates the partial widths Tj for the emission
of a partielcj (j = n, p, d, t, 3He) and r, for físsion by the
expression
r
/ ■^jj}miLU/f1""(E)p,(Uj -B/ -E)EdE <‘) Pc Uc ) V
1 = 2 L XU ' Pi U - Bj - E) EdE
(2)
7
0V
where pc, pj, and p/iwc the levei densities ofthe compound
nucleus, the residual nucleus produced after the emission of the
j-th particle, and of the físsioning nucleus at the físsion saddle
point, respectively; mj, sj and Bj are the mass, spin and the
binding energy of the j-th particle, respectively, and Bfis the
físsion-barrier height. aim,(E) is the inverse cross section for
absorption of thej-th particle with kinetic energy E by the
residual nucleus. The “thermal” energies Uc are defíned by
Uc = E* - ECR - AJ
Pc \UC )
Uj =E‘ - ER - A j
Figure 1. The comparison of calculated alpha-fission cross sections
of 209Bi(a,f) reaction with the experimental values taken from the
EXFOR.
The 209Bi(y,f) photo-físsion reaction cross section
calculations have been compared with the experimental data in
Fig. 2. The experimental values are higher than the all model
calculations. The TALYS 1.6 Sierk model calculations are in
good agreement with the experimental data in the gamma
energy range of30 - 175 MeV.
(3)
Uf =E* - ERR - AJ
where E* is the total excitation energy of the compound
nucleus. For the físsion cross sections, the approximations
proposed by Sierk [8] are
,-
,-
L Bj
inv
geom j E
aJ (E) = a-111—— I
(4)
where
= KR]; Rj = r f
M
(5)
and
<5. Nin /
\
Of = (W )
f
>l
N.^
where U/ is the total físsion cross section.
(6)
E
Gamma Incident Energy (MeV)
Figure 2. The comparison of calculated photo-fission cross sections
of 209Bi(y,f) reaction with the experimental values taken from the
EXFOR.
3 Results
209
In the present study, físsion reaction cross sections of Bi(a,f),
209
Bi(y,f), 209Bi(3He,f) 209Bi(n,f) and 209Bi(p,f) reactions have
been calculated for the energy range of 1 MeV to 1 GeV
incident energy using different físsion reactions models of
TALYS 1.6 Computer codes. The físsion reaction cross
sections exhibited by (*,f) reactions for 209Bi target nuclei have
been plotted as a function of different incident particle energy
in Figs. 1-5. All the experimental values used in this study have
been taken from the EXFOR library.
The 209Bi(3He,f) reaction calculations have been compared
with the experimental data in Fig. 3. All the calculations show
a similar structure with the experimental values but they are
lower than the experimental results.
The calculated cross sections of 209Bi target nucleus for
(a,f) reaction have been compared with the experimental values
in Fig. 1. All model calculations are harmony with the
experimental data but they are lower than the experimental
values. The TALYS 1.6 Sierk model calculations lower than
the experimental data of Penionzkevich et al. [9].
01003-p.2
TESNAT 2015
In general all figures show the fission models give the same
geometry with the experimental data but they give lower
results than EXFOR data. It can be possible to obtain the better
agreement with experimental cross section data using several
different adjustments of the available parameters. The obtained
209
Bi cross section results for the projectile charged particles
can be used in several applications such as fission reactor
design and cooling.
References
Figure 3. The comparison of calculated helium3-fission cross
sections of 209Bi(3He,í) reaction with the experimental values taken
ífom the EXFOR.
103
1.
Comparative assesstment of thermophysical and
thermohydraulic characteristics of lead, lead-bismuth and
sodium coolants for fast reactors / IAEA- TECDOC1289. Vienna, p. 72 (2002)
2.
Y. Gohar, et al., Argonne National Laboratory Report,
ANL/TD/02-01 (2002)
3.
Brookhaven National Laboratory, National Nuclear
Data Center, EXFOR/CSISRS (Experimental Nuclear
Reaction Data File). Database Version of February 05,
2015
(2015),
(http://www.nndc.bnl.gov/exfor/).
4.
A. Koning, S. Hilaire, S. Goriely, TALYS-1.6 A Nuclear
Reaction Program, User Manual (NRG, The
Netherlands), First Edition: December 23, 2013 (2013)
5.
A.J. Koning, S. Hilaire, M.C. Duijvestijn, TALYS:
Comprehensive Nuclear Reaction Modeling. In: R. C.
Haight, M. B. Chadwick, T. Kawano, P. Talou (eds),
Proceedings ofthe International Conference on Nuclear
Data for Science and Technology-ND 2004, AIP vol 769.
Santa Fe, USA, 1154 (2005)
6.
K.H. Schmidt and B. Jurado, Phys. Rev. C 82 (2011)
7.
A.J. Sierk, Phys. Rev. C 33, 2039 (1986)
8.
A.J. Sierk and S.G. Mashnik, Fourth Workshop on
Simulating Accelerator Radiation Environments,
9812070vl,(1998)
9.
Yu.E., et al., Eur. Phys. J. A 13, 123 (2002)
102i
101
10°-d
E
nr
10’2
10’3
Bi(n,f)
D.Tarrioetal, 2011
A.B.Laptev et al, 2007
P.E.Vcrotnikov et al, 1984
TALYS 1.6 (Theoretical Fission Barriers, Mamdouh Table Model)
104
io-5-! ;
10- i •
Vi
----- TALYS 1.6 (Theoretical Fission Barriers, Sierk Model)
....... TALYS 1.6 (Theoretical Fission Barriers, Rotating Liquid Drop Model)
••— TALYS 1.6 (Fission Path Model)
10' 7--
0
200
400
600
800
1000
Nêutron Incident Energy (MeV)
Figure 4. The comparison of calculated neutron-fission cross
sections of 209Bi(n,f) reaction with the experimental values taken
from the EXFOR.
Figure 5. The comparison of calculated proton-fission cross sections
of 209Bi(p,f) reaction with the experimental values taken from the
EXFOR.
The calculated cross sections of 209Bi target nucleus for
(n,f) and (p,f) reactions in the nêutron incident energy range of
1 MeV to 1 GeV have been compared with the experimental
values in Figs. 5 and 6. All model calculations give similar
geometry with the EXFOR data but they are lower than the
experimental results.
01003-p.3
EPJ Web of Conferences 100, 01001 (2015)
DOI: 10.1051/epjconf/ 201510001001
© Owned by the authors, published by EDP Sciences, 2015
Calculation of photo-nuclear reaction cross sections for 16O
Ali Arasoglua and Omer Faruk Ozdemir
Yüzüncü Yil University, Science Faculty, Physics Department, 65080, Van, Turkey
Abstract. Because of the high thermal expansion coefficient of uranium, the fuel used in nuclear power plants is usually in the form
of UO2 which has ceramic structure and small thermal expansion coefficient. UO2 include one uranium atom and two oxygen atoms.
After fission progress, total energy values of emitted gamma are about 14 MeV. This gamma energy may cause transmutation of 16O
isotopes. Transmutation of 16O isotopes changes physical properties of nuclear fuel. Due to above explanations, it is very important
to calculate photo-nuclear reaction cross sections of 16O. In this study; for (y,p), (y,np), (y,n) and (y,2n) reactions of 16O, photonuclear reaction cross-sections were calculated using different models for pre-equilibrium and equilibrium effects. Taking incident
gamma energy values up to 40 MeV, Hybrid and Cascade Exciton Models were used for pre-equilibrium calculations and WeisskopfEwing (Equilibrium) Model was used for equilibrium model calculations. Calculation results were compared with experimental and
theoretical data. While experimental results were obtained from EXFOR, TENDL- 2013, JENDL/PD-2004 and ENDF/B VII.l data
base were used to get theoretical results.
1 Introduction
2 Calculations of nuclear reactions
Nuclear fuel is basic element of reactor core and source of
energy produced in nuclear reactor. The fuel used in nuclear
reactor has to meet the physical criteria such as linear
coefficient of expansion, thermal inductivity, heat capacity etc.
[1-3]. Due to high linear thermal expansion coefficient of
uranium (a=13.9xl0-6 m/(mK), t=25°C) [4], it can deform fuel
sheath (envelope) at high temperature. So we can't use pure
uranium at fuel rods. In general, UO2 (a=7.69xl0 -6 m/(mK),
t=25°C) [5] having smaller linear thermal expansion
coefficient is used as a fuel in Light Water Reactor (LWR),
Pressurized Water Reactor (PWR), Boiling Water Reactor
(BWR) etc...[6]
Nuclear transmutations and fission in fuel components
change the physical properties of fuel rods. Gamma energies
emitted after fission reaction is approximately 14 MeV. Two
of three atoms of nuclear fuel are oxygen. Transmutations
occur in 16O due to photo-nuclear reactions and it will affect
the physical properties of nuclear reactor fuel. Therefore
calculations of photo-nuclear reaction cross sections of 16O are
very important.
In this study; for (y,p), (y,np), (y,n) and (y,2n) reactions of
16
O, photo-nuclear reaction cross-sections were calculated
using different models for pre- equilibrium and equilibrium
effects. Taking incident gamma energy values up to 40 MeV,
Hybrid and Cascade Exciton Models were used for preequilibrium calculations and Weisskopf-Ewing (Equilibrium)
Model was used for equilibrium model calculations.
Calculation results were compared with experimental and
theoretical data. While experimental results were obtained
from EXFOR, TENDL-2013, JENDL/PD-2004 and ENDF/B
VII.l data base were used to get theoretical results.
Statistical models can be applied to solve excitation functions.
One of these models describes as above: Projectile particle was
absorbed by target nucleus. Without emitting particles,
compound nucleus reaches the equilibrium state. WeisskopfEwing (WE) model can be used to explain this case [7]. In this
model, reaction cross section is given as following;
a
r
b
CT(U, b) = CTa (g) _
b' b'
In this formula, £ is the incident energy of particle and <7a (s)
is the cross section for the formation of a compound state. F b
is the emission probability per time for the particle b and
(i)
given as [8]:
rb = ^-—Ab ídsv™(£)£^^ b V h2 b b
©;(£)
In equilibrium, the probability of emitting particle is given as
following:
W
b(C>« (2sb + OM, sG0^7^7
®i(E)
Corresponding author: [email protected]
This
is anavailable
Open Access
article distributed under the termsorofhttp://dx.doi.org/10.1051/epjconf/201510001001
the Creative Commons Attribution License 4.0, which permits unrestricted use,
Article
at http://www.epj-conferences.org
(2)
(3)
EPJ Web of Conferences
where sb is mspin, pb is reduced mass, s is energy of emitted
particle, a'b ’ is the inverse reaction cross section, ry (U) is
the nuclear levei density of the nucleus,
(E) is the nuclear levei density of the nucleus emitting b
particle, U is the excitation energy of residual nucleus and E is
the excitation energy of the emitting nucleus [9].
One of the other reaction models is Cascade Exciton
Model (CEM) which assumed to occur in three steps:
I. Intra-nuclear Cascade
II. Pre-equilibrium
III. Equilibrium
In INC stage, secondary particles were created by either
incident particle was absorbed by nucleus or projectile particle
consumed its total energy. The next stage is the State where
compound nuclear reaction model is applied. Cascade particles
define in which exciton state compound nucleus has been
emitted. In the last stage, nucleus is in equilibrium and particle
emission will occur through either evaporation or físsion [10].
In general, these three steps contribute values obtained as
experimentally. According to this, particle spectra equation is
following as;
o (p) dp =
{N~ (p) + N™ (p) + V (p )}
Photon Energy (MeV)
Figure 1. Comparison of cross section calculations of 16O(y,p)15N
reaction between given nuclear reaction models, experimental data
and evaluated data library [13,14],
(4)
where _p is the linear momentum and Gln is inelastic cross
sections calculated within cascade model [11].
3 Results and discussions
In this study, to calculate (y,p), (y,np), (y,n) and (y,2n) nuclear
reaction cross-sections of 16O pre-equilibrium and equilibrium
models were used with the incident gamma energies up to 40
MeV. For equilibrium and pre- equilibrium effects, Weisskopf
Ewing Model and Cascade Exciton Model (CEM) have been
used, respectively. Equilibrium model calculations have been
prepared by using PCROSS and ALICE-2011 Computer
codes. CEM calculations have been performed by CEM- 03.01
Computer code. The results of comparisons between cross
section calculations of this study, experimental data and
evaluated ones taken from literature are as following:
In Fig. 1 the results of (y,p) reaction calculations are in
agreement with experimental data and evaluated results up to
20 MeV. At higher energies, results of CEM and WE models
are coherent with ENDF/B VII.l while those of equilibrium
model calculations are in agreement with TENDL-2013 data.
While equilibrium and CEM calculation results are smaller
than experimental and evaluated data in Fig. 2, WE model
calculations are in good agreement for (y,np) reaction crosssection calculations. At higher energies, nuclear model
calculations are coherent with experimental data.
In Fig. 3 for (y,n) reaction cross-section calculations below
25 MeV; all nuclear models are in good agreement with
experimental and evaluated data. In 25-40 MeV energy region;
equilibrium model results are in agreement with TENDL-2013
and JENDL/PD-2004 although experimental data are greater
than them. The other models are in very good agreement with
experimental data.
The calculation results of (y,2n) reactions in Fig. 4 are
below experimental data while they are in agreement with
evaluated results.
Figurei. Comparison of cross section calculations oí 16O(y,np)14N
reaction between given nuclear reaction models, experimental data
and evaluated data library [13,14],
01001-p.2
TESNAT 2015
2.
Thermophysical properties database of materiais for light
water reactors and heavy water reactors, IAEATECDOC-1496 (2005).
3. J.K. Fink, J. Nucl. Mater., 279.1, 1-18 (2000).
4. http://www.engineeringtoolbox.com/linear- expansioncoe_cients-d_95.html
5. R.V. Krishnan, G. Panneerselvam, P. Manikandan M.P.
Antony, K. Nagarajan, J. Nucl. Radiochem. Sei., 10.1, 1926 (2009).
6. https://www.iaea.org/About/Policy/GC/GC51/GC51I
nfDocuments/English/gc51inf-3-att5 en.pdf.
7. M. Blann, Annu. Rev. Nucl. Sei. 25, 123-166 (1975).
8. V.F. Weisskopf, D.H. Ewing, Phys. Rev. 57, 472485
(1940).
9. C.H.M. Broeders et al., ALICE/ASH - Precompound and
Evaporation Model Code System for Calculation of
Excitation Functions, Energy and Angular Distributions
of Emitted Particles in Nuclear Reactions at Intermediate
Energies (2006).
10. S.G. Mashnik, et al., Monte-Carlo Code System to
Figure3.Comparison of cross section calculations of 16O(y,n)15O
Calculate Nuclear Reactions in the Framework of the
reaction between given nuclear reaction models,
Improved Cascade-Exciton Model, LA-UR-05- 7321
experimental data and evaluated data library [13,14].
(2005).
11. S.G. Mashnik et al., User Manual for the Code CEM95
(JINR, Dubna, 1995).
12. R. Capote et al., Final report on research contract
5472/RB., INDC (CUB)-004 (1991).
13. EXFOR, http://www.oecdnea.org/janisweb/search /exfor.
14. Evaluated
Data
Library,
http://www.oecdnea.org/janisweb/
Acknowledgments This work has been supported by Yüzüncü
Yil University, Office of Scientific Research Projects 2013-FBED005. The authors would like to thank Dr. Murat Aycibin for
contributions.
References
1. D.G. Cacuci, Handbook of Nuclear Engineering (Springer,
2010).
Figure4.Comparison of cross section calculations oí 16O(y,2n)14O
reaction between given nuclear reaction models,
experimental data and evaluated data library [13,14].
01001-p.3
International Workshop on
Theoretical and Experimental Studies in Nuclear
Applications and Technology
"TESNAT 2015" aims to discuss and compare all applicable methods as are being applied at present
in nuclear physics. The problems faced in these fields at present are focused in the development of new
methods and in the improving of existing techniques to achieve an understanding of existing experimental
data and in predicting with high reliability new properties and processes. This workshop proposes to bring
together all these related communities with the goal of creating an enriching dialog across the disciplines.
The program composed of a three-days conference. The workshop had given an overview on the theoretical
and experimental challenges in nuclear physics and applications. The main topics of lhe workshops are
computational nuclear physics, medicai physics, Monte Cario applications in Nuclear Physics and other
applications of nuclear physics.
TESNAT 2015 attracted about 170 participants and during the workshop 5 lectures, 38 plenary talks
as well as 70 posters were presented. We would like to thank all the participants as well as the members of
the International Scientific Committee, the Local Organizing Committee, the sponsors: TAEK (Turkish
Atomic Energy Authority), TUBITAK (Scientific and Technological Research Council of Turkey), Private
Osmaniye Bilim School and Private Osmaniye Doga School, and especially the hosting Osmaniye Korkut
Ata University for the extremely warm atmosphere of the workshop. We would also like to thank Prof. Dr.
Arjan KONING, Prof. Dr. A. Günes TANIR, Prof. Dr. ísmail BOZTOSUN and Prof. Dr. Emel ALGIN for
their supports and leaderships.
We would also like to thank Dr. Muhittin Çahan from Osmaniye for his unending supports, Dr.
Bayram Demir, Dr. Ahmet Bülbül and Veli Çapali for their helps in organization and the staff of “European
Physical Journal Web of Conferences” for their help with publishing the proceedings.
Eyyup TEL, Abdullah AYDIN, Abdullah KAPLAN and Ísmail Hakki SARPÜN
Editors