Analytical description of heavy ion potentials for collisions between nuclei of same shell

Abstract

Using Skyrme energy density formalism, we present an analytical formula of ion-ion potential (including spin-density part) in terms of the masses of colliding nuclei. The parametrization of the spinindependent part of the ion-ion potential is based on the proximity theorem whereas the spin-dependent potential is parametrized in terms of "the masses of colliding nuclei and their associated particle strength". The particle strength accounts for the number of valence particles outside the closed core. Adding Coulomb interaction, this parametrization of ion-ion potential introduces a great simplification for the calculation of fusion barriers and cross-sections analytically. Our parametrized potentials are in good agreement with other theoretical potentials and the fusion cross-sections calculated with this potential are in good agreement with experimental data. PACS. I IntroductionIn last several years, lot of work has been done in low energy heavy ion physics. In this energy domain, the Skyrme Energy Density Formalism (SEDF) has proven to be quite successful in explaining the phenomena like interaction barriers, fusion cross-sections, elastic scattering, nucleon transfer processes, etc. [1-9]. The same Skyrme energy density formalism is also used extensively for heavy ion collisions at intermediate and relativistic energies [10−12].One of the important questions at low energy is whether we can understand the nucleus -nucleus potential in terms of some fundamental quantities like masses and charges of colliding nuclei or not. These quantities are always known in any experiment and therefore, such parametrization of the nucleus-nucleus potential can be of great importance for comparing the theoretical predictions directly with experimental results. The present study deals with a parametrization of the ion-ion interaction potential in terms of some fundamental quantities like masses and charges of colliding nuclei at low energy. In the past, several successful attempts have been made to parametrize the spin density-independent ion-ion potentials [2,7,8]. By neglecting the spin-density part of the heavy ion potential, one is reducing the scope of formalism to spin saturated nuclei (like 16 O, 40 Ca etc.) only. On the other hand, we know that the contribution of spin-density part towards fusion cross-section can be as much as 50 mb [5]. Therefore, an apparent need is to obtain a general analytical formula of the potential for both the spin-saturated and spin-unsaturated colliding nuclei.The analyticity of the spin-saturated potential is guided by the proximity concept and hence the parametrization is straight forward. The proximity theorem states that the interaction potential V = 2πRΦ(s), where Φ(s) is an universal function andR is responsible for the geometry of colliding nuclei. One can parametrize the Φ(s) uniquely and hence the spin-saturated nuclear potential. On the contrary, the parametrization of the spin-density dependent part of the ion-ion potential is quite tedious. This is because it involves the angular m...