Productions of sd-shell hypernuclei $_{\Lambda}^{19}$F and $_{\Lambda}^{20}$Ne in shell-model calculations

Detailed hypernuclear studies have been mainly focused on structures of $s$- and $p$-shell systems. As the next stage of hypernuclear studies, experiments of $sd$-shell hypernuclei will be carried out at J-PARC. The level structures of $sd$-shell nuclei are richer and more complex than those of $p$-shell nuclei. Even the $\Lambda$ single-particle energies are not well known experimentally, and the theoretical study on the interplay with nuclear core excitations have just started in these medium-mass systems. We anticipate innovated $(K^{-}, \pi^{-})$ reaction experiments to be done at J-PARC, as well as $(e, e^{\prime}K^{+})$ reaction experiments at JLab and Mainz. In this work, we focus on $_{\Lambda}^{19}$F and $_{\Lambda}^{20}$Ne hypernuclei and calculate wave functions by using a multi-configuration shell model and the conventional $\Lambda N$ effective interactions derived from the Nijmegen NSC97f potentials. We estimate production cross sections of $(K^{-}, \pi^{-})$, $(\pi^{+}, K^{+})$ and $(e, e^{\prime}K^{+})$ reactions and analyze differences of characteristics between these reactions.