Fusion cross section of α -induced reactions for heavy target nuclei

Abstract

The fusion reactions induced by $^{4}\mathrm{He}$ projectiles on heavy target nuclei provide the reference to study the reaction dynamics of exotic halo nuclei. The present analysis aims to probe the effects of different nuclear density distributions and the effective nucleon-nucleon ($NN$) interaction potentials on the fusion cross section of $^{4}\mathrm{He}$-induced reactions for heavy target nuclei. The nuclear densities for the heavy nuclei are obtained within the well-known Skyrme-Hartree-Fock model and the relativistic mean-field (RMF) approach for the $\mathrm{NL}{3}^{*}$ parameter set. These densities are integrated with the density-dependent M3Y and the relativistic R3Y nucleon-nucleon ($NN$) potentials to obtain the nuclear interaction potential. The fusion cross section and the astrophysical $S$ factor are obtained for $^{4}\mathrm{He}+^{208}\mathrm{Pb}, ^{4}\mathrm{He}+^{209}\mathrm{Bi}, ^{4}\mathrm{He}+^{235}\mathrm{U}$, and $^{4}\mathrm{He}+^{238}\mathrm{U}$ systems within the $\ensuremath{\ell}$-summed Wong model. The relativistic R3Y $NN$ potential folded with RMF densities are observed to give a better fit to the available experimental data. Furthermore, a comparison is made for the results obtained using Hill-Wheeler and Wentzel-Kramers-Brillouin transmission coefficients for $^{4}\mathrm{He}+^{208}\mathrm{Pb}$ system. We found a reasonable fit in the cross section at around the Coulomb-barrier energies for both the approximations and also similar predictions can be drawn for all considered systems.