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

We investigated structures of low-lying $0s$-orbit $\Lambda$ states in $p$-shell $\Lambda$ hypernuclei ($^A_\Lambda Z$) 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 $^A_\Lambda Z$, in $A>10$ systems. The energy change shows a clear correlation with the nuclear size difference between the ground and excited states. In $^7_\Lambda \textrm{Li}$ and $^9_\Lambda \textrm{Be}$, the significant shrinkage of cluster structures occurs consistently with the prediction of other calculations.