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

## TL;DR

This study uses shell-model calculations with realistic interactions to analyze calcium isotopes, highlighting the importance of specific orbitals in neutron-rich isotopes and comparing results with experimental data.

## Contribution

It introduces systematic shell-model results for $^{47-58}$Ca isotopes using various model spaces and interactions, including IM-SRG derived forces, providing new insights into orbital roles.

## Key findings

- Good agreement with experimental data in the $fp$ space
- $g_{9/2}$ and $d_{5/2}$ orbitals are crucial for heavier isotopes
- Spectroscopic factors align with recent experiments

## Abstract

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.