Shell model results for $^{47-58}$Ca isotopes in the $fp$, $fpg_{9/2}$ and $fpg_{9/2}d_{5/2}$ model spaces

We have reported shell-model results for $^{47-58}$Ca isotopes in the $fp$, $fpg_{9/2}$ and $fpg_{9/2}d_{5/2}$ model spaces using realistic $NN$ interaction. We have also performed a systematic shell-model study using interactions derived from in-medium similarity-renormalization group (IM-SRG) targeted for a particular nucleus with chiral $NN$ and $3N$ forces. The results obtained are in a reasonable agreement with the available experimental data in $fp$ model space with $NN$ interaction. It is shown that the $g_{9/2}$ and $d_{5/2}$ orbitals play an important role for heavier neutron-rich $^{54-58}$Ca isotopes, while it is marginal for $^{47-52}$Ca. We have also examined spectroscopic factor strengths using $NN$ and $NN+3N$ interactions for recently available experimental data.