Energy spectra in $p$-shell $\Lambda$ hypernuclei and $^{19}_{\Lambda}\textrm{F}$ and spin-dependent $\Lambda N$ interactions

TL;DR

This study investigates the energy spectra of $ ext{p}$-shell $ ext{Lambda}$ hypernuclei using microscopic models and effective interactions, tuning the spin-dependent terms to match observed data and predicting unobserved states.

Contribution

It introduces a phenomenological tuning of the spin-dependent $ ext{Lambda}N$ interactions within the microscopic cluster and antisymmetrized molecular dynamics models for hypernuclei.

Findings

Spin-dependent interactions influence spin-doublet splittings.

Modified interactions reproduce observed spectra.

Predictions for unobserved excited states are provided.

Abstract

Energy spectra of $0s$-orbit $\Lambda$ states in $p$-shell $\Lambda$ hypernuclei ($^{A}_\Lambda Z$) and those in $^{19}_{\Lambda}\textrm{F}$ are studied with the microscopic cluster model and antisymmetrized molecular dynamics using the $G$-matrix effective $\Lambda N$ ($\Lambda NG$) interactions. Spin-dependent terms of the ESC08a version of the $\Lambda NG$ interactions are tested and phenomenologically tuned to reproduce observed energy spectra in $p$-shell $^{A}_\Lambda Z$. Spin-dependent contributions of the $\Lambda N$ interactions to spin-doublet splitting and excitation energies are discussed. Energy spectra for unobserved excited states in $p$-shell $^{A}_\Lambda Z$ and $^{19}_{\Lambda}\textrm{F}$ are predicted with the modified $\Lambda NG$ interactions.