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