Abstract

The influence of hyperons on localized clusters is studied in deformed nuclei $^{20}\mathrm{Ne}$ and $^{28}\mathrm{Si}$ and the spherical nucleus $^{40}\mathrm{Ca}$ by employing the deformed Skyrme-Hartree-Fock approach and the localization function. It is found that hyperons in the $p$ state initially tend to occupy the orbitals with shapes similar to that of the core nucleus. The nucleus $^{20}\mathrm{Ne}$ exhibits a robust prolate configuration characterized by an $\ensuremath{\alpha}{\ensuremath{-}}^{12}\mathrm{C}\ensuremath{-}\ensuremath{\alpha}$ cluster, while $^{28}\mathrm{Si}$ displays a less pronounced oblate ringlike cluster. A spherical shell-like cluster structure is possessed by the nucleus $^{40}\mathrm{Ca}$, and this spherical shape is also maintained in its hyperisotopes. For ${}_{8\mathrm{\ensuremath{\Lambda}}}^{28}\mathrm{Ne}$, the cluster structure retains sufficient strength to maintain its prolate shape even with an enhanced hyperon-nucleon ($YN$) interaction. In contrast, the cluster structure of $_{8\mathrm{\ensuremath{\Lambda}}}^{36}\mathrm{Si}$ is comparatively weak, and only a slight enhancement of the $YN$ interaction leads to its cluster structure and deformation collapse.