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

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.