Static and energy dependent nucleus-nucleus potential for description of near and sub-barrier fusion data

This article analyzes the validity of static Woods-Saxon potential and the energy-dependent Woods-Saxon potential (EDWSP) to explore the specific features of fusion dynamics of ₆¹²C + ₇₈^194,198Pt and ₃⁶Li + ₈₂²⁰⁸Pb systems. The intrinsic degrees of freedom, such as inelastic surface excitations, play a crucial role in the enhancement of sub-barrier fusion excitation functions over the expectations of the one-dimensional barrier penetration model. Role of dominant intrinsic degrees of freedom of collision partners are entertained within the context of coupled channel calculations. Furthermore, the one-dimensional Wong formula using static Woods-Saxon potential fails miserably to describe the fusion enhancement of ₆¹²C + ₇₈^194,198Pt and ₃⁶Li + ₈₂²⁰⁸Pb systems. However, the Wong formula along with the EDWSP model accurately explains the observed fusion enhancement of ₆¹²C + ₇₈^194,198Pt reactions. In the fusion of ₃⁶Li + ₈₂²⁰⁸Pb reaction, the above-barrier fusion data are suppressed by a factor of 0.66 with reference to the EDWSP model calculations while the below-barrier fusion data are adequately addressed by the EDWSP model and the coupled channel calculations. Therefore, the coupled channel calculations and the EDWSP model calculations reasonably describe the observed fusion mechanism of ₆¹²C + ₇₈^194,198Pt and ₃⁶Li + ₈₂²⁰⁸Pb reactions. This suggests that the energy dependence in the Woods-Saxon potential model introduces similar kinds of barrier modification effects (barrier height, barrier position, and barrier curvature) as reflected from the coupled channel calculations. In the EDWSP model calculations, significantly larger values of diffuseness ranging from a = 0.86 to 0.94 fm, which is much larger than a value extracted from the elastic scattering analysis, are needed to address the sub-barrier fusion data. (author)