Sub-barrier fusion of O + Ge systems

RevÚlta Mexicana de Fúica 38, Suplemento
Sub-barrier fusion of O
E.F.
AGUILERA,
J.J.
+
1 (1992) 6."1-66
Ge systems
VEGA
Instituto Nacional de Investigaciones Nucleares
Apartado postal 18-1027, México, D.F. 11800, México
J.J.
KOLATA
AND
R.J.
TIGlIE
Physics Department, University of Notre Dame
Notre Dame, Indiana 46556
Recibido el 16 de agosto de 1991; aceplado el 6 de diciembre de 1991
ABSTRACT.
11casurernents of the fusion cross section of
160
+ 12,73Ge
have been made for energies
ranging from wel! below lo aboye lhe Coulomb barrier. The enhancemenl observed wilh respecl lo
ane-dimensional
barrier penetration calculations in the region below the barrier could be explained
by assuming thal bolh the largel and lhe projeclile are spherical vibralors and by coupling lhe
rclevant collective excitations
to the fusion channel.
RESUMEN.
Se realizaron mediciones de la sección eficaz de fusión de 160 + 72,73Ge para energías
desde muy abajo hasta ligeramente arriba de la barrera coulombiana. La sobreproducción observada
con respecto a cálculos modelo de penetración de barrera unidimensional en la región abajo de
la barrera, pudo ser explicada suponiendo que tanto el blanco como el proyectil son vibradores
esféricos y acoplando las excitaciones colectivas relevantes al canal de fusión.
PACS: 25.70.Jj
1. [NTIWDUCTION
It has been recognized for a long time that lhe process of heavy-ion fusion might be
strongly inflllenced by the internal degrees of freedom of the involved nudei, specially in
the sub-barrier region [1-6]. In a recent paper [7]' we reported our observations that the
sub-barrier fusion excitation functions for 27Al
70.72.73,74.76Ceshow sorne quite interesting efTects. In particular, the struet tlfal change suggested by the data between 72Ce
and 7JCe could be explained by assuming that both isotopes are spherical vibrators and
noticing that the 73Ce nueleus has more low-Iying collective inelastic channe]s that can
be eoup!ed to the ground state with appreciable strength because of its odd-A nature.
A 5tatically-deformed
oblate shape for Al was used in the mode! ca1culations, consistent
with previous spectroscopic information. The method of analysis, which produced excel.
lent '1uantitative agreernent wil h the data, was in later works [8,9) successfully used to
describe the independent systems 37C1 + 58.60.62.64Niand 160 + 148.150.152.154Sm.
A common feature of al! the corresponding model calculations was that a statically
deformed nueleus \\'as always combined with either a spherical or a statically deformed
col!ision partner in oreler to describe the data and simultaneously rnaintain consistency
with the existing spectroscopic information. For the last systems, for example, a spherical
160 nl1del1S was assurned together with pral ate deformed Sm isotopes.
+
64
E.F. AGUILERAET AL.
With the double purpose of tinding independent evidenee for the mentioned struetural
ehange in the Ge isotopes, on one hand, and testing the goodness of the model ealculations
for the case of spherieal collision partners, on the other hand, we decided to investigate
the 160 + 72,73Ge systems. In this paper we present sorne preliminary results of this
investigation. In Section 2 the experimental proeedure and the eorresponding results are
deseribed. Seetion 3 is devoted to discuss the data in terms of model ealculations and,
tinally, the eonclusions of this work are presented in Section 4.
2. EXPERIMENTAL PROCEDURE AND RESULTS
The 160 projectiles were obtained from the FN Tandem Van de Graaff aceelerator at the
Vniversity of Notre Dame, The 72Ge target, 96.23% enriehed, was 565:J: 15 I'g/em2 thiek,
while the thiekness of the 73Ge target (94.50% enriehed) was 115:J: 12 I'g/em2. The evaporation residues were deteeted in a reeoil-velocity speetrometer whose main eomponents
are an eleetrostatie defleetor, to separate the residues out of the beam, and a time-of-flight
arm, whieh allows us to identify their mass. Further details of the speetrometer and the
experimental proeedure can be found in Refs,[7,8j.
The produet of integrated beam eharge times target thickness was determined for eaeh
point by simultaneously measuring the elastie scattering yield with an array of four monitor counters symmetrieally distributed with respeet to the beam axis and at a laboratory
angle of 15°. The performance of this system has been extensively deseribed in Re£. [la].
In this preliminary work the data have been normalized to model ealculations in the
following way: tirst, the barrier para meter for 160+ 72Ge was determined from the semiempirieal formula in Re£. [1] and then the data were normalized to ooe-dimensional
barrier
penetration ealculations using this parameter in the region of eross seetions between 100
and 500 mb. The same normalization factor was then applied to the 160
73Ge data. The
necessary work to determine the experimental absolute normalization is under way. The
results for eaeh system are displayed in Fig. 1, together with model ealculations that will
be diseussed in the following seetion.
+
3. DISCUSSJON
In order to analyze the data, the simplified eoupled ehannel eode CCDEF [111 was used in its
mode of only vibrational excitation (no statie deformation), following a proeedure similar
to the one described in Re£. [71. While the potential depth para meter was fixed by the
normalization procedure deseribed above for 160
72Ge, for the case of the 160
73Ge
system it was determined from the eondition that the Iimit of no inelastie exeitation
(eorresponding to the one-dimensional barrier penetration model (RPM)) should produce
a good description of the data in the regio n where the eross seetion lies between 100 and
500 mb. The eorresponding BPM ealculations for eaeh system are displayed by the dashed
Iines in Fig. 1.
Once the nuclear potential was determined in this way, CCDEF calculations were performed in whieh the values of the dynamic deformation parameters reported in the litera.
+
+
o + GE
SUB-BARRIER FUSION OF
EXC¡TAT¡ON
o
2
,•
,,
z
~
10'
o o
z
o
UJ
1 O'
z
10'
ce
1O"
30
,,
~'
u
,
,,,
,
UJ
'"en
'"o
u
'"
z
,
,,,
1O'
,
,,,
o
,
,,,
,
,, ,
:o
10'
~
,
,, ,
,
,,,
,
,,,
,,
u
'"
FUNCT¡ON
-"
o
o
65
~
110
'"
'"'"o
'u"
EXC¡TAT¡ON
FUNCT¡ON
10'
SYSTEMS
'"ce:o
1O'
30
35
35
40
ECM
E,"
45
(MeV)
FIGURE l. Experimenlal fusion cross seelions for (a) 160 + 72Ge and (b) 160 + 73Ge. The dashed
curve corrcsponds to BPM ealculations, while the coritinuous curve ¡neludes the vibrational excitalions of bolh lhe projeclile and lhe largel.
TABLE I. IncJastic channels included in the couplcd-channel
ealculations and respective coupling
parameters.
J'
E. (MeV)
A
f3A
2+
2+
3-
6.92
11.52
6.13
2
2
3
0.37
0.24
0.70
72Ge
2+
3-
0.83
2.51
2
3
0.25
0.24
73Ge
5/2+
7/2+
7/2+
13/2+
.013
.069
.499
.826
2
2
2
2
0.24
0.32
0.13
0.27
Nucleus
0
16
73
lure were used (see Table [). Nolice that lhe paramelers
used he re for O and 72, Ce have
73
the same values used in our previous works lo describe the Al
72, Ce (ReL [7]) and
16
the
0 ASm (ReL [9]) systems. The corresponding
results are shown by the continuous
curves in Fig. 1.
Since lhese mode! ca1cu!alions
produce a good descriplion
of lhe experimenlal
dala, lhe
presenl resulls supporl our previous conclusions
[7,9]lhal
lhe relevanl degrees of freedom
for fusing O and Ge nuclei are lhe ones lisled in Table I. In addilion,
lhe fact lhal the
+
+
66
E.F.
ACUILERA ET AL.
larger enhancement observecl for the heavier target is well accountecl for by the model,
provides inclependent evidence for the effect oC the aboye mentioned structural change in
the 72.73Ge isotopes.
4.
CONCLUSIONS
Suh-barrier fusion measurements performecl for the i60+72,73Ge systems support pre"ious
conclus;ons that both Ge ¡sotopes can be treated as spherical vibrators and that the
larger enhancement observed for the heavier system can bc explained in terms oC the
corresponding larger number of low-Iying collective states.
The results are also cop.sistent with a previous work using 160 projectiles in the sense
that the same elegrees of freedom usecl in that work for 160 successfully describe the
present data.
ACKNOWLEDGMENTS
This work was partially supported by CONACYT (México) under contIact
and by the us NSF under contract PIIY88-03035.
140105 G102-139
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