Improved density-dependent cluster model in α -decay calculations within anisotropic deformation-dependent surface diffuseness

Abstract

The density-dependent cluster model (DDCM) is one of the successful theoretical models for $\ensuremath{\alpha}$-decay studies. It gives a good description of the experimental $\ensuremath{\alpha}$-decay half-lives for a wide range of $\ensuremath{\alpha}$ emitters. Nuclear surface diffuseness, one important quantity in determining the nucleon density profiles, is extremely sensitive to deformation, Bohr, Mottelson et al. proposed an anisotropic feature of the surface diffuseness for the deformed nuclei. In this work, an improved version of the density-dependent cluster model, abbreviated as $\mathrm{DDCM}+$, is developed to optimize $\ensuremath{\alpha}$-decay calculations on half-lives, by accounting for the anisotropy and polarization effects of surface diffuseness due to nuclear deformation. Within a deformation-dependent diffuseness correction, the response of $\ensuremath{\alpha}$-decay dynamics to the diffuseness anisotropy is first investigated in detail. It demonstrates that such an anisotropic deformation-dependent diffuseness would change the shape of nucleon density profile and effective $\ensuremath{\alpha}$-core interactions, yielding longer calculated $\ensuremath{\alpha}$-decay half-lives, as well as suggesting larger estimated $\ensuremath{\alpha}$-preformation factors. The systematic calculations on $\ensuremath{\alpha}$-decay half-lives are subsequently performed for 157 even-even nuclei with $52\ensuremath{\le}Z\ensuremath{\le}118$, which reproduce the experimental data within an average factor of 1.88, and drastically reduce the root-mean-square deviations between theoretical results and experimental data by about $41.4%$ in contrast to conventional DDCM. Noticeably, the theoretical result of new isotope $^{214}\mathrm{U}$ [Zhang et al., Phys. Rev. Lett. 126, 152502 (2021)] given by $\mathrm{DDCM}+$ also shows good agreement with the latest reported experimental data, demonstrating the high reliability of the improved model. It is expected that this improved model could be useful for future experimental and theoretical studies of $\ensuremath{\alpha}$ decays.