Shell model study of typical sd-shell hypernuclei

Theoretical and experimental studies of $s$- and $p$-shell hypernuclei have been performed and, in the future, experiments of $\mathit{sd}$-shell hypernuclei will be carried out at \mbox{J-PARC}. The level structures of $\mathit{sd}$-shell nuclei are richer and more complex than those of $p$-shell nuclei. For example, the states of ${}_{}^{19}\mathrm{F}$ have the following structures; (i) the energy difference between the $1/2_{}^{+}$ ground state and the $1/2_{}^{-}$ first-excited state is only $0.110$ $\mathrm{MeV}$ and (ii) a rotational band is seen in the energy spectrum. Thus we are interested in effects of the $\Lambda N$ interaction on the parity doublet and the rotational band in the $\mathit{sd}$-shell hypernuclei. Also, an effects of a positive pairing correlation in the $\Lambda N$ interaction may reveal in the structures of the $\mathit{sd}$-shell hypernuclei because of the $0d_{5/2}^{}$ orbit with the higher spin. In this presentation, we will discuss the structures of ${}_{\;\Lambda}^{19}\mathrm{F}$ and ${}_{\;\Lambda}^{20}\mathrm{F}$ obtained by shell-model calculations with $0 \hbar \omega$ and $1 \hbar \omega$ model spaces.