Collective properties of nucleons in the abnormal-parity states

Abstract

In the first part of this work, we study the quadrupole collective properties of ${N}_{a}=2,$ 4, 6, and 8 nucleons occupying the abnormal-parity intruder single-particle states with high angular momenta ${j}_{a}=\frac{9}{2},$ $\frac{11}{2}, \frac{13}{2},$ and $\frac{15}{2}.$ This study is essential for a detailed understanding of the contribution made by these nucleons to the quadrupole collectivity of the yrast states of deformed nuclei. The properties studied include (i) the distribution of the angular momenta J contained in the intrinsic state of ${N}_{a}$ particles in the $|{j}_{a}{k}_{a}〉$ states, (ii) the relationship between the quadrupole moment ${Q}_{0}{(j}_{a}{,N}_{a})$ of such an intrinsic state and the maximum angular momentum ${J}_{\mathrm{max}}$ contained in it, (iii) the complete set of reduced quadrupole matrix elements ${(J}^{\ensuremath{'}}||Q||J)$ for transitions between all the states $|J〉$ and $|{J}^{\ensuremath{'}}〉$ projected from the intrinsic state, (iv) the $B(E2:\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}2)$ values, (v) the transition moments ${Q}_{t}(J),$ and (vi) the spectroscopic quadrupole moment $Q(J).$ We compare these properties with similar properties of an intrinsic state having SU(3) symmetry which contains the same set of angular momenta as contained in the intrinsic state of a particular number of nucleons in a specific ${j}_{a}$ configuration. In the second part, we use the input from the first part to study the collective properties of the coupled system of protons and neutrons in abnormal-parity states. We show that the SU(3)-like features observed for the individual groups of abnormal-parity nucleons become stronger for the coupled system. Finally, in the third part, we consider the yrast bands of well-deformed nuclei projected from their Nilsson intrinsic states of valence nucleons in a major shell. We specify the structure of the wave function of each projected yrast state $|J〉$ in terms of the nucleons in both normal- and abnormal-parity states. These wave functions can be used to determine the individual contributions of the nucleons in normal- and abnormal-parity states to any specific property of the yrast state. In particular, we calculate the transition moments ${Q}_{t}(J)$ of the entire yrast band of even-even ${}^{160\ensuremath{-}166}\mathrm{Yb},$ ${}^{156,158}\mathrm{Dy},$ ${}^{232}\mathrm{Th},$ ${}^{234}\mathrm{U},$ and ${}^{236}\mathrm{U}$ projected from their respective Nilsson intrinsic states.