Diffuseness parameters of Woods–Saxon potential for heavy-ion systems through large-angle quasi-elastic scattering

Khalid S. Jassim Fouad A. Mageed and Gufran S. Jassim

1Department of physics, College of Education for pure science,
of Babylon, POBox4, Hilla-Babylon, IRAQ
Khalid_ik74@yahoo.com

2Department of physics, College of Education for pure science,
University University of Babylon, POBox4, Hilla-Babylon, IRAQ


3Department of physics, College of Education for pure science,
University of Babylon, POBox4, Hilla-Babylon, IRAQ

Abstract: In this paper, analyses on the nuclear potential for heavy ion systems, namely 48Ti, 54Cr, and 64Ni + 208Pb systems, have been performed through large-angle quasi-elastic scattering at sub-barrier energies. At energies around the Coulomb barrier height, it has been well known that the effect of channel couplings, that is the coupling between the relative motion of the colliding nuclei and their intrinsic motions as well as transfer processes, plays an important role. Therefore, a coupled-channels procedure must be applied to take account of this effect. A modified version of a computer code ccfull has been employed in order to perform these complex calculations. The nuclear potential is assumed to have a Woods-Saxon form, which is characterized by the surface diffuseness parameter, the potential depth, and the radius parameter. In order to find the best fitted value of the diffuseness parameter in comparison with the experimental data, the chi square method ?2 is used. The best fitted value of the diffuseness parameter for studying systems obtained through a coupled-channel calculation with inert Target and vibrational Projectile. The calculated ratio of the quasi-elastic to the Rutherford cross sections for 48Ti, 54Cr and 64Ni + 208Pb systems give a good agreement using a = 0.44 fm, 0.67 fm and a= 0.67 fm, respectively.

Keywords: Heavy-ion fusion reactions, quasi-elastic scattering, Coupled-channels calculations, sub-barrier energies.

1. Introduction

The knowledge of the potential between two colliding nuclei is of fundamental importance in order to describe nucleus-nucleus collisions. The nucleus-nucleus potential is the sum of a short range attractive nuclear potential VN(r) and a long range repulsive Coulomb potential VC(r). The Coulomb potential is well understood. This has been demonstrated by the accurate description of the Coulomb or Rutherford scattering, the scattering where only the long range Coulomb potential acts.
The nuclear potential can be studied through fusion or quasi-elastic scattering experimental data. Quasi-elastic scattering is the sum of elastic scattering, inelastic scattering and transfer reaction. Thus, quasi-elastic scattering and fusion are complementary to each other due to flux conservation. At zero impact parameter (i.e. head-on collision), quasi-elastic scattering is related to the reflection probability by the potential barrier, while fusion is related to the penetration probability [1,2]. The diffuseness parameter determines the characteristic at the surface region of the nuclear potential. Nuclear potential of the Woods-Saxon form, which is described by the potential depth V0, the radius parameter? r?_0, and the diffuseness parameter a, is widely used in the analyses of nuclear collisions.
In this study, we assume that the nuclear potential has a Woods-Saxon form. A diffuseness parameter of around 0.63 fm is widely accepted [3]. This has been supported by recent studies such as by Gasques et al. [4] and Evers et al. [5], where both studies performed analyses on the diffuseness parameter using the experimental data of large-angle quasi-elastic scattering. However, relatively higher diffuseness parameters are required in order to fit fusion data, as shown by Newton et al. [6] for example. The cause of the discrepancy is still not well understood. The aim of the present work is to analysis diffuseness parameters of Woods–Saxon potential for heavy-ion systems through large-angle quasi-elastic scattering at sub-barrier. The chi square method ?^2 is used to find the best fitted value of the diffuseness parameter in comparison with the experimental data.