Study of the surface energy coefficient used in nuclear proximity potential of the $ \alpha$-nuclei systems from density-dependent nucleon-nucleon interactions

Abstract

An attempt has been made to study systematically the nuclear surface tension coefficient, $ \gamma$ , of the proximity formalism by using the microscopic double-folding (DF) model with the realistic density-dependent (DD) nucleon-nucleon interaction for the ground-state-to-ground-state $ \alpha$ -decays of 235 parent nuclei with $ Z=61\mbox{--}99$ . In the calculations of DF model, the nucleon-nucleon (NN) interactions are formulated using the effective M3Y force of the CDM3Y6 based on the G -matrix elements of the Paris interaction. We present a new dependence of the surface energy coefficient $ \gamma$ on the asymmetry parameter $ A_s$ of the $ \alpha$ -nuclei systems by fitting all of the calculated values. Using the presently obtained formula of the coefficient $ \gamma$ in the proximity potential we calculate the theoretical values of the alpha-decay half-lives for different nuclei in the framework of the Wentzel-Kramers-Brillouin (WKB) approximation. Results of our calculations are compared to the values of the experimental data and proximity potential 1977. Good agreements are found. The quality of the proximity potential accompanied by the analytical formula of the surface energy coefficient is tested for fusion reactions between $ \alpha$ -particles and heavy nuclei 40 Ca, 48 Ti, 51V , 59Co , 63Cu , 93Nb , 154Sm and 162Dy The evaluated $ \alpha$ -capture cross sections agreed well with the corresponding experimental data. In the present study, the role of the proton and neutron magic numbers of daughter nuclei and also the Geiger-Nuttall plots of $ \log_{10} (T_{1/2})$versus$ Q_{\alpha}^{-1/2}$ for various isotopes of heavy parent nuclei have been studied.