Simplified modeling of cluster-shell competition

Abstract

We propose a simple model to describe cluster-shell competition. Introducing only one parameter (\ensuremath{\Lambda}) to the wave function makes it possible to describe the asymptotic transition of two valence neutrons in $^{10}\mathrm{Be}$ ($\ensuremath{\alpha}+\ensuremath{\alpha}+n+n$) from a di-neutron to independent particles when the contribution of the spin-orbit interaction is taken into account. Similarly in $^{12}\mathrm{C}$, a transition from a 3\ensuremath{\alpha} configuration to a $2\ensuremath{\alpha}+4N$ configuration is represented, and we show a strong contribution of the spin-orbit interaction in the ground state. We investigate further this transition from the cluster state ($\ensuremath{\alpha}+^{16}\mathrm{O}$) to the shell-model state ($^{16}\mathrm{O}$ + four nucleons) in $^{20}\mathrm{Ne}$. In these examples, the wave functions for cluster-breaking states are prepared in the same general way.