Investigation of the role of neutron transfer in the fusion of 32,34S with 197Au,208Pb using quasi-elastic scattering

Abstract

Excitation functions for quasi-elastic scattering have been measured at backward angles for the systems 32,34S+197Au and 32,34S+208Pb for energies spanning the Coulomb barrier. Representative distributions, sensitive to the low energy part of the fusion barrier distribution, have been extracted from the data. For the fusion reactions of 32,34S with 197Au couplings related to the nuclear structure of 197Au appear to be dominant in shaping the low energy part of the barrier distibution. For the system 32S+208Pb the barrier distribution is broader and extends further to lower energies, than in the case of 34S+208Pb. This is consistent with the interpretation that the neutron pick-up channels are energetically more favoured in the 32S induced reaction and therefore couple more strongly to the relative motion. It may also be due to the increased collectivity of 32S, when compared with 34S. Comment: 11 pages, 5 figures

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arXiv:nucl-ex/0207012v1 22 Jul 2002
Investigation of the role of neutron transfer in
the fusion of32,34S with197Au,208Pb using
quasi-elastic scattering
T.J. Schucka,b, H. Timmersc, M. Dasguptaa
aDepartment of Nuclear Physics, Australian National University, Canberra, ACT
0200, Australia
bInstitut f¨ ur Kernphysik, Universit¨ at Frankfurt, D-60486 Frankfurt, Germany
cSchool of Physics, University of New South Wales at the Australian Defence
Force Academy, Canberra, ACT 2600, Australia
Abstract
Excitation functions for quasi-elastic scattering have been measured at backward
angles for the systems32,34S +197Au and32,34S +208Pb for energies spanning the
Coulomb barrier. Representative distributions, sensitive to the low energy part of
the fusion barrier distribution, have been extracted from the data. For the fusion
reactions of32,34S with197Au couplings related to the nuclear structure of197Au
appear to be dominant in shaping the low energy part of the barrier distibution.
For the system32S +208Pb the barrier distribution is broader and extends further
to lower energies, than in the case of34S +208Pb. This is consistent with the
interpretation that the neutron pick-up channels are energetically more favoured in
the32S induced reaction and therefore couple more strongly to the relative motion.
It may also be due to the increased collectivity of32S, when compared with34S.
PACS codes heavy-ion nuclear reaction 25.70, heavy ion induced fusion
25.70J, nuclear scattering 25.30
KEYWORDS NUCLEAR REACTIONS197Au,208Pb(32,34S,X), E = 115 −
175MeV; measured quasi-elastic scattering excitation functions; deduced rep-
resentations of fusion barrier distributions; subbarrier fusion, channel-coupling,
neutron transfer.
Preprint submitted to Elsevier Preprint 8 February 2008

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1Introduction
Measured cross sections for heavy ion fusion at energies below the Coulomb
barrier show strong isotopic dependences and exceed theoretical predictions
based on a single barrier penetration model by several orders of magnitude [1,2].
This has been observed for a wide range of systems and is understood to arise
from the coupling of the relative motion of the interacting nuclei to their
rotational and vibrational states or to particle transfer channels. The cou-
pling gives rise to a distribution of fusion barriers D(E) [3]. Experimentally,
a representation Dfus(E) of this distribution can be extracted from precision
measurements of fusion excitation functions σfus(E) using [4]:
Dfus(E) =d2(Eσfus)
dE2
(1)
At energies below the Coulomb barrier quasi-elastic scattering excitation func-
tions dσqel/dσR(E), measured at backward angles, have been found [5] to be
another suitable means to extract representations Dqel(E) of the distribution
D(E) with:
Dqel(E) = −d
dE
?dσqel
dσR(E)
?
(2)
In this technique, which is generally less complex than detailed fusion measure-
ments, quasi-elastic scattering is understood to comprise elastic and inelastic
scattering and also particle transfer channels. Experiments which have em-
ployed this approach have recently been carried out by several other groups
[6–8].
In previous work [5] it has been clearly demonstrated that the quasi-elastic
scattering representation Dqel(E) is not identical to the representation Dfus(E)
extracted from fusion data, although it appears that this has not been appre-
ciated in all studies. In particular, Dqel(E) has been shown to be insensitive to
the high energy part of the barrier distribution D(E). The quasi-elastic scat-
tering representations are therefore most useful for investigating couplings,
which produce signatures in the low energy part of D(E). This is the case
when the relative motion of the two nuclei couples to positive Q-value chan-
nels [2].
Indeed, the comparison of the representations Dfus(E) and Dqel(E) for the
systems40Ca +90,96Zr has shown that the effect of positive Q-value neutron
transfer channels on the fusion dynamics are clearly seen in the representation
Dqel(E) [9]. The low-lying collective states in the two Zr isotopes have very
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32S +197Au
34S +197Au
36S +197Au
1n+0.569
−1.086
−3.768
2n +5.342+2.158
−2.377
32S +208Pb
34S +208Pb
36S +208Pb
1n+1.274
−0.382
−3.064
2n+5.953 +2.769
−1.766
Table 1
The Q-values (in MeV) for the pick-up of one (1n) and two (2n) neutrons from
the target nucleus for the systems studied in this work and the reactions36S +
197Au,208Pb.
similar excitation energies and deformation parameters β2, and the main differ-
ences between these two systems are in their Q-values for neutron transfer. In
the heavier system the calcium nucleus can pick-up as many as eight neutrons
in transfer reactions with positive Q-value, whereas the equivalent channels
in the lighter system all have negative Q-values. This pronounced difference
has been found to be reflected in both types of representations, Dfus(E) and
Dqel(E), measured for these systems [9]. The straight-forward measurement
of quasi-elastic scattering excitation functions thus appears to be a promising
tool to investigate the role of positive Q-value transfer channels in fusion.
The fusion reactions of the sulphur projectiles32,34S with197Au and208Pb
are a suitable test case for this new experimental approach to the dynamics of
fusion. This is apparent from Table 1, which shows the Q-values for the pick-up
of one and two neutrons for these systems. Also shown are the equivalent Q-
values for the reactions36S +197Au,208Pb. It is apparent that with decreasing
projectile mass the Q-values progessively favour the neutron pick-up channels.
The32S and34S projectile nuclei have similar structure, with the lowest 2+
states not being very different in terms of excitation energy and deformation
parameter (see Table 2).
The systems32,34S +197Au,208Pb are intermediate in mass between a large
number of lighter fusion reactions, which have been well-studied using the
coupled-channels framework [2], and the more massive systems employed for
the synthesis of super-heavy elements [10]. Results may thus indicate, if the
representation Dqel(E) is also applicable to this important latter group of
fusion reactions, for which multiple neutron transfer may lead to macroscopic
effects such as neutron-flow or neck-formation.
This paper presents detailed measurements at backward angles of quasi-elastic
scattering excitation functions for the two pairs of reactions32,34S +197Au
and32,34S +208Pb, from which representations Dqel(E) of the fusion barrier
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E2[MeV]
β2
32S2.2300.31
34S 2.1270.25
Table 2
Excitation energies E2and deformation parameters β2for the first 2+states of32S
and34S.
distribution have been extracted.
2 Experimental Method
The experiments were performed with32,34S-beams from the 14UD Pelletron
accelerator at the Australian National University in the energy range Elab=
90.0–180.0MeV. Three different self-supporting Au targets were used, with
thicknesses in the range 140–170µg/cm2. The208PbS target was 140µg/cm2
thick, evaporated onto a ∼ 20µg/cm2carbon backing. The target thickness
was determined by measuring the energy loss of elastically scattered projectiles
in the target at a backward angle.
A schematic diagram of the experimental setup is shown in Figure 1. In the ini-
tial study of the32S +208Pb reaction [11] quasi-elastic scattering was detected
at a scattering angle of θlab= 170◦. An energy loss signal ∆E was measured
with a gas ionisation detector. The gas detector was backed by a silicon sur-
face barrier detector which detected the residual energy Eresof the scattered
nuclei. The ∆E signal allowed the separation of the charged particle trans-
fer contributions to the quasi-elastic scattering yield. Since this separation
was not required for the interpretation of the data, in the other experiments
the (∆E − Eres) detector telescope was replaced with a single silicon surface
barrier detector at θlab= 159◦.
For normalisation purposes, two silicon surface barrier detectors were placed at
scattering angles θlab= ±30◦to measure Rutherford scattering of projectiles.
For some preliminary measurements, instead of these two monitor detectors,
a readily available gas-ionisation detector [12] at θlab= 30.35◦was employed.
Both setups gave consistent results, so that the data have been combined.
Figure 2 shows typical energy spectra from the backward silicon detector for
the system32S +197Au. The spectra for the other three systems are similar. At
low beam energies the spectrum only shows a well-defined peak of elastically
scattered sulphur nuclei. With increasing energy the peak gradually develops
a low energy tail as the yield of non-elastic scattering events rises and elastic
scattering is diminished. At the higher energies fission fragments from quasi-
fission and fission following compound nucleus formation are also detected.
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197Au
208PbS/C
target
silicon detector
α
monitor detector
monitor detector
−θ
+θ
Fig. 1. A schematic diagram of the experimental setup used. The backward silicon
surface barrier detector was at an angle α = 21◦. In the study of32S +208Pb a
∆E−Erestelescope detector at α = 10◦was used instead. The beam was monitored
using two silicon detectors at θ = ±30◦.
counts
Energy [MeV]
0 2040 6080
0
500
1000
1500
(a)
elastic
scattering
E = 143 MeV
lab
counts
Energy [MeV]
020 406080
0
50
100
(b)
fission fragments
quasi-elastic
scattering
E = 171 MeV
lab
Fig. 2. Typical energy spectra from the backward silicon detector at θlab= 159◦for
the system32S +197Au at (a) Elab= 143MeV and (b) Elab= 171MeV (b). At the
low energy all scattering is elastic, in the high energy spectrum fission fragments
and quasi-elastic scattering can be identified. The vertical, dashed lines indicate the
gate which was used to integrate the quasi-elastic scattering yield.
The energy window chosen for the integration of the quasi-elastic scattering
yield is indicated in the figure.
For all experiments the quasi-elastic scattering yield, measured at the back-
ward angle, comprising the sum of elastic, inelastic and transfer events, was
divided by the Rutherford scattering yield detected at forward angles. These
ratios have been normalised to unity at energies well below the Coulomb bar-
rier, where only Rutherford scattering is observed. The normalised ratios thus
5

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Ecm [MeV]
dσqel/dσR
32S + 197Au
32S + 208Pb
34S + 197Au
34S + 208Pb
10
-1
1
120 125 130 135 140 145 150 155
Fig. 3. The measured quasi-elastic scattering excitation functions. Centrifugal ener-
gies and energy loss in the target have been subtracted to allow a direct comparison
of the four measurements. Statistical uncertainties are smaller than the symbol size,
unless indicated otherwise.
represent the quasi-elastic scattering excitation function
indices qel and R indicate quasi-elastic scattering and Rutherford scattering,
respectively.
dσqel
dσR(E), where the
The measured quasi-elastic scattering excitation functions are shown in Figure
3. With the exception of the highest energies, where the quasi-elastic scatter-
ing yield is low, the statistical uncertainty is better than 1%. The energy scale
has been adjusted for energy loss in the target, and the centrifugal energy cor-
responding to the respective detection angle has been subtracted, as described
in [5]. The excitation functions decrease smoothly with energy. The apparent
energy shifts between the four sets of data reflect the expected differences in
Coulomb barrier height.
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3Discussion of the Experimental Data
The barrier distribution representations Dqel(E) have been extracted from the
quasi-elastic scattering excitation functions
respect to energy according to Equation (2). A point-difference formula with
discrete energy steps in the range ∆Elab=3–6MeV was used to evaluate the
differential. The data sets obtained for the different energy steps are con-
sistent, so that they have been combined. The resulting barrier distribution
representations Dqel(E) are shown for all four systems in Figure 4. In order
to facilitate a direct comparison, the energy scales of the barrier distribution
representations have been normalised by dividing by an average barrier B0,
which was chosen as the energy where
mination of the average barriers may seem somewhat arbitrary, the values
obtained are realistic. For example, the average barrier for the system32S +
208Pb has been determined as 144.4MeV by fitting the high energy part of the
fusion excitation function using a single barrier penetration model [13]. This
compares well with the value of B0=144.2MeV used here.
dσqel
dσR(E) by differentiation with
dσqel
dσR(E) = 0.5. Although this deter-
As emphasized in the introduction, above the average barrier energy B0the
representation Dqel(E) is not sensitive to the fusion dynamics. Indeed, at these
high energies Dqel(E) is the same for all four systems. The low energy parts
of the measured representations Dqel(E) are discussed below.
For the system34S +208Pb (open circles in Figure 4 (top)) the slope of Dqel(E)
over the energy range 0.92 < E/B0 < 0.99 is steeper than that for32S +
208Pb (filled circles in Figure 4 (top)). Also, the maximum of Dqel(E) for the
reaction34S +208Pb is 0.08 MeV−1, whereas the maximum for the lighter
system is only about 0.06 MeV−1. Since the integral of D(E) is unity, this
implies that the barrier distribution for34S +208Pb is narrower than that for
32S +208Pb. This is consistent with significant coupling to positive Q-value
neutron transfer channels in the32S +208Pb fusion reaction. Indeed, both
the one neutron (Q = +1.3 MeV) and two neutron transfer (Q = +6.0MeV)
Q-values for this system are positive.
The equivalent data for the197Au target (Figure 4 (bottom)) do not show such
a pronounced difference. It is apparent from Figure 5 (top) that the representa-
tions Dqel(E) for32S +197Au and32S +208Pb agree, which would be consistent
with these systems having similar barrier distribution and thus equivalent cou-
pling interactions. However, the comparison of the representations Dqel(E) in
Figure 5 (bottom) for34S +197Au and34S +208Pb demonstrates that for the
gold systems Dqel(E) is already broad for the heavier sulphur projectile, for
which coupling to neutron transfer is less favoured. This suggests that cou-
pling to states in the197Au nucleus generates barrier strength at low energies,
which is absent for the reactions with208Pb.
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Ecm/B0
Dqel(E)[MeV-1]
32S+208Pb
34S+208Pb
0
0.02
0.04
0.06
0.08
0.850.9 0.9511.05
Ecm/B0
Dqel(E)[MeV-1]
32S+197Au
34S+197Au
0
0.02
0.04
0.06
0.08
0.85 0.90.951 1.05
Fig. 4. Representations of the barrier distributions for32,34S +208Pb (top) and
32,34S +197Au (bottom). The energy scales have been normalised with the respective
average barrier energy B0.
The experimental results for the two lead systems are consistent with those
reported from fusion measurements for the two reactions32,36S +110Pd [14],
where additional barrier strength at low energies was also found for the lighter
projectile32S. While the new data support an important role of positive Q-
value neutron transfer channels in the fusion of32S +208Pb, such an inter-
pretation is only unique, if the properties of the collective states in32S and
34S are identical, or at least can be assumed to be very similar. Recent results
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Ecm/B0
Dqel(E)[MeV-1]
32S+197Au
32S+208Pb
0
0.02
0.04
0.06
0.08
0.850.90.9511.05
Ecm/B0
Dqel(E)[MeV-1]
34S+197Au
34S+208Pb
0
0.02
0.04
0.06
0.08
0.85 0.90.951 1.05
Fig. 5. Representations of the barrier distributions for32S +197Au,208Pb (top)
and34S +197Au,208Pb (bottom). The energy scales have been normalised with the
respective average barrier B0.
for the fusion of the sulphur nuclei32,34S with89Y [15] show that in that case
the different collectivity of their quadrupole excitations (Table 2) results in a
broader fusion barrier distribution for32S than for34S. Thus the differences
observed in this work between the barrier distributions for32S +208Pb and
34S +208Pb may not be solely due to coupling to the positive Q-value neutron
pick-up channels. Measurements for the heavier system36S +208Pb may shed
additional light on the fusion mechanism. In this latter system the Q-values
9

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for both one neutron and two neutron transfer are negative (see Table 1), so
that any effects due to neutron pick-up can be ruled out.
4Conclusions
The experiments reported here have demonstrated that precision measure-
ments of quasi-elastic scattering at backward angles are able to probe the
fusion barrier distribution of heavy systems below the average barrier. Such
measurements are thus in principle sensitive to the effects of positive Q-value
transfer channels. Indeed it was found that neutron transfer may affect the
fusion of32S with208Pb. The results, however, are also consistent with the ob-
served additional barrier strengths at low energies being due to the increased
collectivity of32S, when compared with34S. For the fusion reactions of32,34S
with197Au couplings related to the nuclear structure of197Au appear to be
dominant in shaping the low energy part of the barrier distibution.
Since quasi-elastic scattering experiments are generally not as complex as
fusion measurements, they are well suited to survey a number of reactions
to determine good candidates for detailed studies of the fusion dynamics.
The extracted representations of the barrier distribution can be indicative
of important coupling interactions, however, the conclusive identification of
these couplings may require the measurement and interpretation of the fusion
excitation function.
Acknowledgements
The authors are grateful to the late Prof. Trevor Ophel for his contributions
to these experiments and would like to thank Dr David Hinde for indepth
discussions of the results. The support of Dr Jack Leigh and Dr Clyde Morton
is also acknowledged.
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