This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Bracken, D.S.

Brzychczyk, J.

Kwiatkowski, K.

Morley, K.B.

Renshaw, E.

Viola, V.E.

English

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CALCULATIONS OF ISOTOPIC IMF YIELDS 
IN THE 4He + "69124Sn REACTION 
J. Brzychczyk,* D.S. Bracken, K. Kwiatkowski, K.B. Morley, 
E. Renshaw, and V.E. Viola 
Depar tmen t  of Chemis t r y  and t h e  Ind iana  Universi ty  Cyclo tron  Facility,  
B loomington ,  Ind iana  4 7408 
The effect of target N/Z ratio on the properties of intermediate-mass fragment (IMF) 
ejectiles has been investigated in the reaction of E/Ax50 MeV 4He ions with targets of 
'16Sn and '24Sn. Both equilibrium-like and nonequilibrium sources have been studied by 
performing measurements at extreme backward and forward angles. 
The data demonstrate the influence of target composition on both the charge and 
isotopic distributions of the fragments. Elemental cross sections from the *He + ll6Sn 
system are distinctly enhanced relative to He + '24Sn. For nonequilibrium emission, 
both targets produce similar yields for light IMFs; however, the ratio of the elemental 
cross sections from '16Sn to those from 124Sn becomes increasingly larger as a function of 
increasing fragment charge. 
The backward-angle emission of IMFs can be interpreted in terms of statistical emis- 
sion from a compound nucleus.' In order to examine the influence of neutron binding 
energies and angular momentum on the Sn charge distributions, we have performed 
calculations with the evaporation code BUSC0.2 These results are shown in Fig. 1. Using 
a value of L=19h and the maximum available excitation energy, the cross sections for the 
"%n target are relatively well reproduced. For the '24Sn target the calculation success- 
fully predicts the lower IMF cross sections relative to '16Sn, but is much less successful in 
describing the heaviest fragment yields. In both cases the slope of the calculation is steeper 
than the data. By increasing the input angular momentum to L=22h, a somewhat better 
fit to the 124Sn data is obtained, both in magnitude and slope. A possible explanation 
for this result is that the L-wave distribution for the average emitting system formed in 
the 4He + '16Sn reaction may sample a higher range of angular momentum values than 
in 4He + "%n reactions, a result consistent with the increased decay widths for neutron 
emission from the neutron-excess system. Nonet heless, the BUS CO calculation underpre- 
dicts heavy fragment yields, especially for the neutron-excess targets. This suggests that 
calculations of rn/rIMF in this code may need some modification. 
While the backward angle emission of IMFs can be understood relatively well in 
terms of the decay of a compound nucleus, the mechanism of nonequilibrium production 
is still poorly understood. For these ejectiles the important question of the time scales 
complicates the theoretical interpretation of the data. The accreting source model3 is 
based on the assumption of local statistical emission from an excited subsystem of the 
nucleus created by the fusion of the projectile with some number of target nucleons. This 
source simultaneously emits fragments and cools by accreting nucleons from the remainder 
of the target. In our calculations we have assumed an initial source size of eight nucleons, 
an accretion rate of 2 nucleons/fm/c, and an exit-channel Coulomb barrier of 0.9 times the 
touching-spheres value. The Fermi energy of 24 MeV and normalization coefficients were 
a(180 MeV)  + Sn + IMF 
h I I 1 I 1 I I I I I I 
:?\ 
'. \ 
- 
- '16sn 
...-*-....-. 
------- 
124 Sn 
- 
- 
- 
'. \ 
, -- 
*. ---- 
19fi - 
-- + 
' 
' 
---. 
\ 
---.. 
--.. 
' 
- ' . - '. 
'. 225 
... 
'.. 
I I I I I 1 I I I 
Figure 1. Charge distributions for IMFs emitted at 154O for 180 MeV 4He+116.124~n 
reactions, compared with BUS C02  calculations. Calculations are performed for L= 1 9ti 
for both systems and L=22h for 124Sn . 
fixed by requiring a fit to the charge distributions. 
The isotopic yield results are shown in Fig. 2. We observe general agreement with the 
data, including 7Be. The ratios o('16Sn)/a(124Sn) are also reasonably well reproduced by 
the calculations. Emission temperatures calculated with the model are lower for heavier 
fragments and somewhat higher in the case of the 124Sn target. 
a (200 MeV) + Sn -+ IMF 
Fragment Mass Number 
Figure 2. Isotopic ratios for Li, Be, B and C fragments, for l16Sn (upper) and 124Sn 
(lower) targets. The solid line is the prediction of the accreting source model.3 
Whereas the calculation reproduces the total cross sections well, it fails to reproduce 
the angular distributions. The predicted angular distributions are much flatter than the 
experimental ones. Also, the slopes of the energy spectra for the lighter fragments are too 
steep. For the heavier fragments, the spectral shapes are well-reproduced, although the 
absolute cross sections are too small at forward angles. Somewhat more rapidly decreasing 
angular distributions can be obtained by using a lower value of the accretion rate. The 
charge and isotopic distributions, as well as energy spectra, are relatively insensitive to such 
a change. To obtain flatter energy spectra, however, it is necessary to increase the Fermi 
energy, which in turn causes the charge and isotopic distributions to become flatter. Thus, 
the accreting source model describes many features of these data satisfactorily, although 
complete self-consistency cannot be achieved for all observables. 
* Permanent address: Institute of Physics, Jagellonian University, Reymont a 4, 31-059, 
Krakow, Poland. 
1. V.E. Viola and K. Kwiatkowski, Proc. of Symposium: Towards a Unified Picture of 
Nuclear Dynamics, edited by S.M. Lee and F. Sakata (AIP Conf. Proc. No. 250, New 
York, 1991). 
2. J. Gomez de Campo, Phys. Rev. Lett. 61, 290 (1988). 
3. W.A. Friedman and W.G. Lynch, Phys. Rev. C 28, 16 (1983); ibid., 28, 950 (1983); 
D.J. Fields, W.G. Lynch, C.B. Chitwood, C.K. Gelbke, M.B. Tsang, H. Utsonomiya 
and J. Aichelin, Phys. Rev. C, 30, 1912 (1984). 


Calculations of Isotopic IMF Yields in the 4-He + 116,124-Sn Reaction

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Calculations of Isotopic IMF Yields in the 4-He + 116,124-Sn Reaction

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