In this paper we model low-lying states of atomic nuclei in the nucleon-pair approximation of the shell model, using three approaches to select collective nucleon pairs: the generalized seniority scheme, the conjugate gradient method, and the Hartree-Fock approach. We find the collective pairs obtained from the generalized seniority scheme provide a good description for nearly spherical nuclei, and those from the conjugate gradient method or the Hartree-Fock approach work well for transitional and deformed nuclei. Our NPA calculations using collective pairs with angular momenta 0, 2, and 4 (denoted by $SDG$ pairs) reproduce the nuclear shape evolution in the $N=26$ isotones, ${}^{46}\mathrm{Ca}, {}^{48}\mathrm{Ti}, {}^{50}\mathrm{Cr}$, and ${}^{52}\mathrm{Fe}$, and yield good agreement with full configuration-interaction calculations of low-lying states in medium-heavy transitional and deformed nuclei: ${}^{44-48}\mathrm{Ti}, {}^{48}\mathrm{Cr}, {}^{50}\mathrm{Cr}, {}^{52}\mathrm{Fe}, {}^{60-64}\mathrm{Zn}, {}^{64,66}\mathrm{Ge}, {}^{84}\mathrm{Mo}$, and ${}^{108-112}\mathrm{Xe}$. Finally, using the $SDGI$-pair approximation we describe low-lying states of ${}^{112,114}\mathrm{Ba}$, cases difficult to reach by conventional configuration-interaction methods.

• Received 17 December 2020
• Accepted 1 June 2021

DOI:https://doi.org/10.1103/PhysRevC.104.024312