Robustness of pair structures for nuclear yrast states*

Abstract

In this work we study robustness of pair structures for nuclear yrast states, i.e., whether the structures of relevant collective pairs as building blocks of different yrast states are the same. We focus on deformed nuclei and transitional nuclei and study yrast states of $^{28}$Si, $^{50}$Cr, and $^{132}$Xe, whose experimental $R_{4/2}$ values are 2.60, 2.40, and 2.16, respectively, using the nucleon-pair approximation (NPA) and shell-model effective interactions. For each yrast state, we consider optimized pair structures to be the ones giving the energy minimum for this state, and to find the minimum, a great number of full NPA calculations with varying pair structures are performed and the numerical optimization recipe of the conjugate gradient method is implemented. Our results suggest that optimized pair structures remain the same for all the states within a rotational band of a deformed nucleus. Our results also suggest that after the backbending, i.e., the change of the intrinsic state, the structure of the $S$ pair which is essential to build up the monopole pairing correlation still remains unchanged approximately, while the structures of the non-$S$ pairs which are essential to build up the quadrupole correlation change significantly.