A NEW APPROACH FOR THE SCATTERING OF DEFORMED LIGHT
HEAVY-IONS: A CHALLENGE TO THE STANDARD APPROACH
I. B O ZTO SU N
Nuclear Physics Department, University o f Oxford, Keble Road 0X1 3RH Oxford-UK Permanent address: Department o f Physics, Erciyes University, 38039 Kay seri-Turkey
E-mail: i. boztosunl (dphvsics. ox. ac. nk
A B STR A C T
A new approach in the analyses o f deformed light heavy-ion reactions has been introduced to explain the experimental data. This new coupled-channels based approach involves replacing the usual first derivative coupling potential by a new, second-derivative coupling potential. This paper first shows and discusses the limitation o f the standard coupled-channels theory in the case where one o f the nuclei in the reaction is strongly deformed. Then, this new approach is shown to improve consistently the agreement with the experimental data: the elastic and inelastic scattering as well as their 90" and 180" elastic and inelastic excitation functions.
IN T R O D U C T IO N
The elastic and inelastic scattering o f light heavy-ions have stimulated a great deal o f interest over the last 40 years. There has been extensive experimental effort to measure the elastic and inelastic scattering data as well as their 90" and 180" excitation functions. A large body o f experimental data for these systems is available (see [1,2,3] and references therein). Although most o f the theoretical models proposed so far provide reasonably good fits, no unique model has been proposed that explains consistently the elastic and inelastic scattering data over a wide energy range without applying any ad hoc approaches. Consequently, the following problems continue to exist for light heavy-ion reactions: (1) explanation o f anomalous large angle scattering data, 'A L A S'; (2) reproduction o f the oscillatory structure near the Coulomb barrier; (3) the lack o f the correct oscillatory structure between theoretical predictions and experimental data; (4) simultaneous fits o f the individual angular distributions, resonances and excitation functions (for the 12C+12C system in particular); (5) the magnitude o f the mutual-2+ excited state data in the 12C+12C system is unaccounted for; (6) the deformation parameters (□ values): previous calculations require □ values that are at variance with the empirical values and are physically unjustifiable.
Therefore, in this paper, we are concerned with the measured experimental data for 12C+12C, 160 + 28Si and 12C+24Mg in an attempt to find a global model, which simultaneously fits the elastic and inelastic scattering data for the ground and excited states in a consistent way over a wide energy range.
The Standard Coupled-Channels (CC) Model
Although three different reactions are analyzed, we are only going to show some o f the results for the 12C+12C reaction. The details o f the models and a complete set o f the results for all the reactions will be published in [4,5,6,7]. We describe the interaction between 16O and 28Si nuclei with a deformed optical potential. The real potential has the square o f a W oods-Saxon (WS) shape i.e.
V N r) = -V0 / (1+exp(r-R)/a)2
with V 0=706.5 MeV, R=r0(Ap1/3+At1/3) with r0=0.749 fm and a=1.4 fm. The parameters o f the real potential were fixed as a function o f energy and were not changed in the present calculations. The Coulomb potential with radius 5.56 fm was also added.
The imaginary part o f the potential was as the sum o f a W S volume and surface potentials i.e. W (r)=-W v f(r,Ry,ay)+4WSaS df(r,Rg,aS)/dr
f(r,R,a) = 1/(1+exp((r-R)/a)) with WV=59.9 MeV, aV=0.127 fm and WS=25.0 MeV, aS=0.257 fm. These parameters were also fixed in the calculations and only their radii increased linearly with energy according to the following formulae.
RV = 0.06084Ecm-0.442 and R S = 0.2406ECM-2.191
Since the target nucleus 28Si is strongly deformed, it is essential to treat its collective excitation explicitly in the framework o f the CC formalism. It is assumed that the target nucleus has a static quadrupole deformation, and that its rotation is described in the framework o f the collective model. It is therefore taken into account by deforming the real optical potential in the following way
R (0,9)= r0At1/3[1+p2Y20(0,9)]
where p2=-0.64 is the deformation parameter o f the target nucleus, 28Si. In the present calculations, the first two excited states o f the target nucleus 28Si: 2+ (1.78 MeV) and 4+ (4.62 MeV) were included and the 0+-2+-4+ coupling scheme was employed. The reorientation effects for 2+ and 4+ excited states were also included. The calculations were performed with a modified version o f the code CHUCK [8].
Using the standard coupled-channels theory, we found, as other authors had found, that it was impossible to describe consistently the elastic and inelastic scattering o f this and other reactions we considered.
New Coupling Potential
The limitations o f the standard coupled-channels theory in the analyses o f these reactions compelled us to look for another solution. Therefore, a second-derivative coupling potential, as shown in figure 1, has been used in the place o f the usual first-derivative coupling potential.
F ig u re 1: For 16O+28Si, the comparison o f the standard coupling potential which is the first derivative o f the central potential and our new coupling potential, parameterized as the 2nd derivative o f W S shape and has V=155.0 MeV, R=4.16 fm and a=0.81 fm.
The interpretation o f this new coupling potential will be given in the forthcoming paper [4]. Here we employed the same method with small changes in the potential parameters. The empirical deformation parameter (p2) is used in these calculations.
R ESU LTS 16O+28Si
The first system we consider is 16O + 28Si, which shows anomalous large angle scattering (ALAS). In the present work, we consider an extensive simultaneous investigation o f the elastic and the inelastic scattering o f this system at numerous energies from ELab=29.0 MeV to 142.5 MeV over the whole angular range up to 1800. In this energy range, the excitation functions for the ground and 2+ states are also analyzed [5,6,7]. Excellent agreement with the data was obtained.
12C+24M g
The second example we have considered is 12C+24Mg. Fifteen complete angular distributions o f the elastic scattering o f 12C+24Mg system were measured at energies around the Coulomb barrier and were published recently [2]. We have studied these fifteen complete elastic scattering angular distributions. Excellent agreement with the experimental data was obtained by using this new coupling potential.
12C+12C
The final system we have considered is that o f 12C+12C, which has been studied extensively over the last 40 years. There has been so far no model, which fits consistently the elastic, inelastic
scattering data and mutual excited state data as well as the resonances and excitation functions. Another problem is the predicted magnitude o f the excited state cross-sections, in particular for the mutual-2+ channel. The conventional coupled-channels model underestimates its magnitude by a factor o f at least two and often much more [10,11,12]. We have also observed this in our conventional coupled-channels calculations as shown in figure 2 with dashed lines. There are also resonances observed at low energies, which have never been fitted by a potential, which also fits either the angular distributions or the excitation functions.
Using our new coupling potential, we have been able to fit the energy average o f all the available ground, single-2+, mutual-2+ and the backgrounds in the integrated cross-sections of Cormier [9] as well as the main gross features o f the 900 excitation function [3] simultaneously.
F ig u re 2: The 12C+12C system: The results o f the single and mutual-2+ states. The solid lines are the results o f the new coupling potential, while the dashed lines are the results o f standard coupled-channels model, shown only for the mutual case.
In sum, while these three systems show quite different properties and problems, a unique solution has come from a new coupling potential. The approach outlined here is universal and applicable to all the systems. Studies using this new coupling potential may lead to new insights into the formalism and a new interpretation o f these systems.
A C K N O W L E D G M E N T S
Special thanks to B. Buck, A. Merchant, Y. Nedjadi, B. Fulton, G. R. Satchler, D. Brink and N. A. Odman for valuable discussions and providing some data. I. Boztosun also would like to thank the Turkish Council o f Higher Education (YÖK), Oxford and Erciyes Universities, Turkey, for their financial support.
R E FE R E N C E S
1. P. Braun-M unzinger and J. Barrette, Phys. Reports 87 (1982) 209. 2. W. Sciani et al, Nucl. Phys. A620 (1997) 91.
3. R. G. Stokstad et al, Phys. Rev. C20 (1979) 655.
4. I. Boztosun and W .D.M. Rae, to appear on Nucl. Phys. A
5. I. Boztosun and W .D.M. Rae, Proceedings o f the 7th International Conference on Clustering Aspects o f Nuclear Structure and Dynamics, Edited by M. Korolija, Z. Basrak and R. Caplar, W orld-Scientific-2000 (143).
6. I. Boztosun and W .D.M. Rae, to be submitted to Nucl. Phys. A. 7. I. Boztosun, to appear on Izvestia Run (Physics Series).
8. P. D. Kunz, CHUCK, An optical model search code, unpublished. 9. T. M. Cormier et al, Phys. Rev. Lett. 40 (1978) 924.
10. R. W olf et al, Z. Phys. A305 (1982) 179.
11. Y. Sakuragi et al, Proceedings o f the 7th International Conference on Clustering Aspects o f Nuclear Structure and Dynamics, Edited by M. Korolija, Z. Basrak and R. Caplar, W orld-Scientific-2000 (138).
