# 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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- L. R. Gasques, M. Evers, D. J. Hinde, M. Dasgupta, P. R. S. Gomes, R. M. Anjos, M. L. Brown, M. D. Rodríguez, R. G. Thomas, K. Hagino[Show abstract] [Hide abstract]

**ABSTRACT:**High precision quasi-elastic scattering excitation functions have been measured at energies well below the Coulomb barrier for the reactions of 32S with 208Pb, 197Au, 186W, and 170Er. Single-channel and coupled-channels calculations have been performed to extract the diffuseness parameter of the nuclear potential. For the reactions involving near-spherical targets, both theoretical analyses give the same diffuseness parameter. On the other hand, for deformed systems, couplings are important even at deep sub-barrier energies. In general, the effect of couplings is to reduce the diffuseness parameter value extracted from a single-channel potential. Single-channel fits to quasi-elastic scattering data result in a=0.72-0.82 fm, whereas coupled-channels calculations give diffuseness parameters in the range 0.58–0.75 fm.Physical Review C 08/2007; 76(2). · 3.72 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We measured large-angle quasielastic scattering for the spherical {sup 16,17,18}O+²Mo systems at deep sub-barrier energies. This is a process sensitive to the surface region of the nuclear potential which can be used to probe surface diffuseness. The derived diffuseness values are of the order of 0.70 fm for the three systems, larger than predicted by previous works on similar systems.Physical Review C 08/2007; 76(2):027601-027601. · 3.72 Impact Factor - SourceAvailable from: N. V. Antonenko[Show abstract] [Hide abstract]

**ABSTRACT:**The relationship between the threshold energy for a deep sub-barrier fusion hindrance phenomenon and the energy at which the regime of interaction changes (the turning-off of the nuclear forces and friction) in the sub-barrier capture process, is studied within the quantum diffusion approach. The quasielastic barrier distribution is shown to be a useful tool to clarify whether the slope of capture cross section changes at sub-barrier energies.European Physical Journal A 11/2012; 49(2). · 2.04 Impact Factor

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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

Page 2

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

2

Page 3

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

3

Page 4

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.

4

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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

Page 6

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.

6

Page 7

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.

7

Page 8

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

8

Page 9

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

Page 10

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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11

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