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

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 spin-independent 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