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

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