Low-lying states of heavy nuclei within the nucleon pair approximation

Abstract

In this article we perform systematic calculations on low-lying states of 33 nuclei with $A=202\text{\ensuremath{-}}212$, using the nucleon pair approximation of the shell model. We use a phenomenological shell-model Hamiltonian that includes single-particle energies, monopole and quadrupole pairing interactions, and quadrupole-quadrupole interactions. The building blocks of our model space include one $J=4$ valence neutron pair, and one $J=4,6,8$ valence proton pair, in addition to the usual $S$ and $D$ pairs. We calculate binding energies, excitation energies, electric quadrupole and magnetic dipole moments of low-lying states, and $E2$ transition rates between low-lying states. Our calculated results are reasonably consistent with available experimental data. The calculated quadrupole moments and magnetic moments, many of which have not yet been measured for these nuclei, are useful for future experimental measurements.