Effect of density and nucleon-nucleon potential on the fusion cross section within the relativistic mean field formalism
M. Bhuyan, Raj Kumar, Shilpa Rana, Deepak Jain, S. K. Patra, B. V. Carlson
Abstract
We have studied the effect of density and the nucleus-nucleus interaction potential on the fusion reaction cross section for the synthesis of heavy and superheavy nuclei within the relativistic mean field formalism. The double-folding procedure is used to obtain the nuclear interaction potential for the well-known M3Y and recently developed R3Y nucleon-nucleon potential for relativistic mean field densities. The $\mathrm{NL}{3}^{*}$ parameter set is used to calculate the density distributions for targets and projectiles and is further used to obtain the nuclear potential. The $\ensuremath{\ell}$-summed Wong formula is used to provide a transparent and analytic way to formulate the fusion cross sections for even-even $^{48}\mathrm{Ca}+^{154}\mathrm{Sm}$, $^{48}\mathrm{Ca}+^{238}\mathrm{U}$, $^{48}\mathrm{Ca}+^{248}\mathrm{Cm}$, $^{64}\mathrm{Ni}+^{238}\mathrm{U}$, $^{26}\mathrm{Mg}+^{248}\mathrm{Cm}$; even-odd $^{46}\mathrm{K}+^{181}\mathrm{Ta}$; and odd-odd $^{31}\mathrm{Al}+^{197}\mathrm{Au}$ and $^{39}\mathrm{K}+^{181}\mathrm{Ta}$ systems. The structural effects are also correlated with the fusion cross section through the equivalent diffuseness parameter using the densities of interacting nuclei for all nuclei (projects and targets) involved in the reactions just listed.