Coupled-Cluster and Configuration-Interaction Calculations for Odd-$A$ Heavy Nuclei

We compare coupled-cluster (CC) and configuration-interaction (CI) results for ${}^{55}\mathrm{Ni}$ and ${}^{57}\mathrm{Ni}$ obtained in the $pf$-shell basis, focusing on the practical equation-of-motion (EOM) CC approximations that can be applied to systems with dozens of correlated fermions. The weight of the reference state and the strength of correlation effects are controlled by the gap between the $f_{7/2}$ orbit and the $f_{5/2}$, $p_{3/2}$, $p_{1/2}$ orbits. Independent of the gap, the CC methods with up to $2p\mathrm{\text{−}}2h$ components in the cluster operator and $3p\mathrm{\text{−}}2h/3h\mathrm{\text{−}}2p$ components in the EOMCC excitation operator are more accurate than the computationally more demanding CI approach with up to $3p\mathrm{\text{−}}3h$ excitations and almost as accurate as the even more demanding CI approach truncated at $4p\mathrm{\text{−}}4h$ excitations.