Woods-Saxon-Gaussian Potential and Alpha-Cluster Structures of Alpha+Closed Shell Nuclei

The Woods-Saxon-Gaussian (WSG) potential is proposed as a new phenomenological potential to describe systematically the level scheme, electromagnetic transitions, and alpha-decay half-lives of the alpha-cluster structures in various alpha+closed shell nuclei. It modifies the original Woods-Saxon (WS) potential with a shifted Gaussian factor centered at the nuclear surface. We determine the free parameters in the WSG potential by reproducing the correct level scheme of $^{212}\text{Po}={}^{208}\text{Pb}+\alpha$. It is found that the resulting WSG potential matches with the M3Y double-folding potential at the surface region and makes corrections to the inner part of the cluster-core potential. We also find that the WSG potential with the almost same parameters determined for $^{212}$Po (except for a rescaled radius) could also be used to describe alpha-cluster structures in $^{20}\text{Ne}={}^{16}\text{O}+\alpha$ and $^{44}\text{Ti}={}^{40}\text{Ca}+\alpha$. In all three cases, the calculated values of the level schemes, electromagnetic transitions, and alpha-decay half-lives agree with the experimental data, which shows that the WSG potential could indeed grasp many important features of the alpha-cluster structures in alpha+closed shell nuclei. The study here is a useful complement to the existing cluster-core potentials in literature. The Gaussian form factor centered at the nuclear surface might also help deepen our understanding on the alpha-cluster formation taking place around the same place.