Excitation energy shift and size difference of low-energy levels in $p$-shell $\Lambda$ hypernuclei

Abstract

We investigated structures of low-lying $0s$-orbit $\Lambda$ states in $p$-shell $\Lambda$ hypernuclei (${}_{\Lambda }^{A}Z$) by applying microscopic cluster models for nuclear structure and a single-channel folding potential model for a $\Lambda$ particle. For $A>10$ systems, the size reduction of core nuclei is small, and the core polarization effect is regarded as a higher-order perturbation in the $\Lambda$ binding. The present calculation qualitatively describes the systematic trend of experimental data for excitation energy change from ${}^{A-1}Z$ to ${}_{\Lambda }^{A}Z$, in $A>10$ systems. The energy change shows a clear correlation with the nuclear size difference between the ground and excited states. In ${}_{\Lambda }^7\text{Li}$ and ${}_{\Lambda }^9\text{Be}$, the significant shrinkage of cluster structures occurs consistently with the prediction of other calculations.

Comments: 18 pages, 5 figures