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

Abstract

Energy spectra of $0s$-orbit $\Lambda$ states in $p$-shell $\Lambda$ hypernuclei (${}_{\Lambda }^{A}Z$) and those in ${}_{\Lambda }^{19}\text{F}$ 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 ${}_{\Lambda }^{A}Z$. 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 ${}_{\Lambda }^{A}Z$ and ${}_{\Lambda }^{19}\text{F}$ are predicted with the modified $\Lambda NG$ interactions.

27 pages, 4 figures