Empirical nucleus-nucleus potential deduced from fusion excitation functions

Abstract

Existing data on near-barrier fusion excitation functions for 48 medium and heavy nucleus-nucleus systems have been analyzed using a simple ``diffused-barrier formula'' derived assuming the Gaussian shape of the barrier height distributions. The obtained mean values of the barrier height have been used then for determination of the parameters of the empirical nucleus-nucleus potential, assumed to have Woods-Saxon shape. The mean barrier heights calculated with this potential are reproduced with an accuracy of about $1\phantom{\rule{0.3em}{0ex}}\text{MeV}$, while other frequently used potentials, i.e., the proximity potential and the Aky\"uz-Winther potential, considerably overpredict the experimental values, especially for heavy systems. In order to predict fusion excitation functions with the diffused-barrier formula, we propose a simple method of theoretical prediction of the second parameter of the barrier distribution, its width. The proposed formula accounts for the quantum effect of sub-barrier tunneling, static quadrupole deformations, and collective surface vibrations of the colliding nuclei. With the theoretical knowledge of the mean height and width of the barrier distributions, one can predict cross sections for overcoming the barrier (``sticking'' or ``capture'') in reactions of very heavy systems used to produce superheavy nuclei.