ANALYTICAL FORMULATION OF THE ION–ION INTERACTION POTENTIAL INCLUDING SPIN DENSITY TERM IN ENERGY DENSITY FORMALISM

Abstract

The heavy-ion interaction potentials are calculated in sudden approximation, using the Fermi density distribution in the proximity theorem treatment of the Skyrme interaction energy density formalism. The contribution of the spin density term is included and the effects of varying the Skyrme force parameters, Fermi density parameters and the strength of the surface correction to Thomas–Fermi kinetic energy density are studied in detail. The universality of the "universal function" of proximity potential is tested and analytical formulas are obtained for both the proximity potential and spin density dependent potentials. The analytical formula for spin density potential works only for colliding nuclei belonging to the same shell. Adding the Coulomb potential, the interaction barriers and their positions can now be calculated analytically which are required for the calculations of fusion cross-sections. Our calculations are made for both the closed and unclosed shell nuclei consisting of light spherical nuclei from 0d-1s and 0f 7/2 shells. In all, over 100 cases are studied and comparisons with other model calculations are presented.