Cluster-shell competition and effect of adding hyperons

Abstract

Background: The fundamental question is how the hyperon plays a role in the nuclear structure. It is of particular importance, especially in the light mass region, to verify the structure change when $\mathrm{\ensuremath{\Lambda}}$ particle(s) is added to normal nuclei.Purpose: The ground state of $^{8}\mathrm{Be}$ has been known to have a well-developed $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\alpha}$ cluster structure, whereas $^{12}\mathrm{C}$ has a mixed structure of three $\ensuremath{\alpha}$ clusters and $jj$-coupling shell model, where $\ensuremath{\alpha}$ clusters are partially broken. Adding $\mathrm{\ensuremath{\Lambda}}$ particle(s) could induce the structure change. We compare the Be and C cases.Methods: Using the antisymmetrized quasicluster model (AQCM), the $\ensuremath{\alpha}$-cluster states and $jj$-coupling shell-model states of $^{8}\mathrm{Be}$ and $^{12}\mathrm{C}$ are prepared on the same footing, and we add $\mathrm{\ensuremath{\Lambda}}$ particles. The cluster-shell competition in the ground state can be well described with this model. Using AQCM, we calculate $^{8}\mathrm{Be}, _{\mathrm{\ensuremath{\Lambda}}}^{9}\mathrm{Be}, _{\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}}^{10}\mathrm{Be}, ^{12}\mathrm{C}, _{\mathrm{\ensuremath{\Lambda}}}^{13}\mathrm{C}$, and $_{\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}}^{14}\mathrm{C}$.Results: By adding one or two $\mathrm{\ensuremath{\Lambda}}$ particle(s), the ground state of $^{12}\mathrm{C}$ approaches the $jj$-coupling shell model side. On the other hand, in the Be case, although the $\mathrm{\ensuremath{\Lambda}}$ particle(s) shrinks the $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\alpha}$ distance, the breaking effect of the cluster structure is rather limited.Conclusions: The spin-orbit interaction is the driving force of breaking the $\ensuremath{\alpha}$ clusters, and whether the glue-like effect of $\mathrm{\ensuremath{\Lambda}}$ particle(s) attracts the cluster inside the range of this interaction is crucial. In $_{\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}}^{14}\mathrm{C}$, the breaking of $\ensuremath{\alpha}$ clusters in $^{12}\mathrm{C}$ is much enhanced by the addition of the $\mathrm{\ensuremath{\Lambda}}$ particles than the case of free $^{12}\mathrm{C}$. We also found that breaking $\ensuremath{\alpha}$ clusters in the ground state of $_{\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}}^{14}\mathrm{C}$ affects the excited state with the pure cluster structure.