Ground-state properties of rare-earth nuclei in the Nilsson mean-field plus extended-pairing model

Abstract

The Nilsson mean-field plus extended-pairing model for deformed nuclei is applied to describe the ground-state properties of selected rare-earth nuclei. Binding energies, even-odd mass differences, energies of the first pairing excitation states, and moments of inertia for the ground-state band of $^{152\ensuremath{-}164}\mathrm{Er}$, $^{154\ensuremath{-}166}\mathrm{Yb}$, and $^{156\ensuremath{-}168}\mathrm{Hf}$ are calculated systematically in the model employing both proton-proton and neutron-neutron pairing interactions. The pairing interaction strengths are determined as a function of the mass number in the isotopic chains. In comparison with the corresponding experimental data, it is shown that pairing interaction is crucial in elucidating the properties of both the ground state and the first pairing excitation state of these rare-earth nuclei. With model parameters determined by fitting the energies of these states, ground-state occupation probabilities of valence nucleon pairs with angular momentum $J=0,1,\ensuremath{\cdots},12$ for even-even $^{156\ensuremath{-}162}\mathrm{Yb}$ are calculated. It is inferred that the occupation probabilities of valence nucleon pairs with even angular momenta are much higher than those of valence nucleon pairs with odd angular momenta. The results clearly indicate that $S, D$, and $G$ valence nucleon pairs dominate in the ground state of these nuclei.