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

TL;DR

This study explores how the addition of a lambda particle affects the energy levels and size of low-energy states in p-shell hypernuclei, revealing a correlation between energy shifts and nuclear size differences.

Contribution

It provides a systematic analysis of excitation energy shifts in p-shell hypernuclei using microscopic models, highlighting the relationship with nuclear size differences and cluster structure shrinkage.

Findings

Energy change correlates with size difference between states.

Core nuclei show small size reduction for A>10.

Significant cluster shrinkage observed in light hypernuclei.

Abstract

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.