Cluster-shell competition and effect of adding hyperons

Abstract: 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 $\Lambda$ particle(s) is added to normal nuclei. The ground state of $^{8}$Be has been know to have a well-developed $\alpha$--$\alpha$ cluster structure, whereasn$^{12}$C has a mixed structure of three $\alpha$ clusters and $jj$-coupling shell model, where $\alpha$ clusters are partially broken. Adding $\Lambda$ particle(s) could induce the structure change. We compare the Be and C cases. Using the antisymmetrized quasi-cluster model (AQCM), the $\alpha$-cluster states and $jj$-coupling shell-model states of $^8$Be and $^{12}$C are prepared on the same footing, and we add $\Lambda$ particles. The cluster-shell competition in the ground state can be well described with this model. Using AQCM, we calculate $^8$Be, $^{9}_{\Lambda}$Be, $^{10}_{\Lambda\Lambda}$Be, $^{12}$C, $^{13}_{\Lambda}$C, and $^{14}_{\Lambda\Lambda}$C. By adding one or two $\Lambda$ particle(s), the ground state of $^{12}$C approaches the $jj$-coupling shell model side. On the other hand, in the Be case, although the $\Lambda$ particle(s) shrinks the $\alpha$--$\alpha$ distance, the breaking effect of the cluster structure is rather limited. The spin-orbit interaction is the driving force of breaking the $\alpha$ clusters, and whether the glue-like effect of $\Lambda$ particle(s) attracts the cluster inside the range of this interaction is crucial. In $^{14}_{\Lambda\Lambda}$C, the breaking of $\alpha$ clusters in $^{12}$C is much enhanced by the addition of the $\Lambda$ particles than the case of free $^{12}$C. We also found that breaking $\alpha$ clusters in the ground state of $^{14}_{\Lambda\Lambda}$C affects the excited state with the pure cluster structure.