Cluster structures of the 0+ states of CΛ13 with the 3α+Λ four-body orthogonality condition model

Abstract

We study structures of the ${0}^{+}$ states of $_{\mathrm{\ensuremath{\Lambda}}}^{13}\mathrm{C}$ within the framework of the $\ensuremath{\alpha}+\ensuremath{\alpha}+\ensuremath{\alpha}+\mathrm{\ensuremath{\Lambda}}$ four-body orthogonality condition model with the Gaussian expansion method. We obtain five ${0}^{+}$ states of $_{\mathrm{\ensuremath{\Lambda}}}^{13}\mathrm{C}$ and compare them with the low-lying four ${0}^{+}$ states of $^{12}\mathrm{C}$. We find that the ${0}_{1}^{+}$, ${0}_{2}^{+}$, and ${0}_{4}^{+}$ states correspond to the ${0}_{1}^{+}$, ${0}_{2}^{+}$, and ${0}_{4}^{+}$ states of $^{12}\mathrm{C}$, respectively. We also find that both the ${0}_{3}^{+}$ and ${0}_{5}^{+}$ states have analogous nature to the ${0}_{3}^{+}$ state of $^{12}\mathrm{C}$, where the additional $\mathrm{\ensuremath{\Lambda}}$ particle couples with the $^{8}\mathrm{Be}$ cluster and one $\ensuremath{\alpha}$ cluster, in the ${0}_{3}^{+}$ state of $^{12}\mathrm{C}$, respectively. The former is then shown to have an elongated ${}_{\mathrm{\ensuremath{\Lambda}}}^{9}\mathrm{Be}({0}_{1}^{+})+\ensuremath{\alpha}$ cluster structure with a higher nodal behavior for its relative wave function, and the latter has a dilute three-body gas consisting of $2\ensuremath{\alpha}{+}_{\mathrm{\ensuremath{\Lambda}}}^{5}\mathrm{He}$ clusters.