Semi-microscopic calculations of the fusion barrier distributions for reactions involving deformed target nuclei

Abstract

The double-folding model with an M3Y effective nucleon-nucleon (NN) interaction was applied to obtain the angle-dependent bare nucleus-nucleus potential for heavy-ion fusion reactions involving deformed target nuclei. The angular dependence with a zero-range exchange NN interaction is almost identical to that with a finite-range interaction, allowing quick calculations of the fusion cross sections and corresponding barrier distributions $D({E}_{c.m.})$. Since in the literature the experimental $D({E}_{c.m.})$ have been analyzed usually using a Woods-Saxon shape for the nuclear part of the nucleus-nucleus potential, we fitted the spherical double-folding potentials at the barrier radii with a Woods-Saxon (WS) form. The calculated $D({E}_{c.m.})$ with this fitted WS potential, but now accounting for the deformation of the target nuclei, are significantly different from the $D({E}_{c.m.})$ calculated directly using the double-folding potential. This indicates that the finite size effects are substantial and should not be ignored in the analysis of experimental fusion cross sections and barrier distributions for reactions with statically deformed nuclei.