Pauli blocking effects in α -induced fusion reactions

Abstract

We propose a microscopic calculation of fusion reactions for $\ensuremath{\alpha}+^{197}\mathrm{Au},\phantom{\rule{0.16em}{0ex}}\ensuremath{\alpha}+^{208}\mathrm{Pb},\phantom{\rule{0.16em}{0ex}}\ensuremath{\alpha}+^{209}\mathrm{Bi}$, and $\ensuremath{\alpha}+^{238}\mathrm{U}$ systems. Inspired by recent studies of $\ensuremath{\alpha}$-cluster decay in radioactive nuclei [Phys. Rev. C 95, 061306(R) (2017)], a Pauli blocking term depending on the density overlap of projectile and target nuclei is introduced in addition to the strong and electromagnetic interactions between them. As compared to the $\ensuremath{\alpha}$-core potential obtained from the double-folding potential with standard Michigan-3-Yukawa-Reid effective nucleon-nucleon interaction, the one including the Pauli blocking interaction results in a shallow ``pocket'' in the inner part. On account of highlighting the density dependence of Pauli blocking potential, we make a comparison of fusion cross sections between two extreme neutron density distributions of target nuclei, namely, (i) ``skin type'' with same diffuseness but different half-density radii in density distributions of proton and neutron, and (ii) ``halo type'' with same half-density radii but different diffuseness. The fusion cross sections resulting from the potential considering Pauli blocking effects are also compared with the experimental data in detail.