Empirical p-n interactions, the synchronized filling of Nilsson orbitals, and emergent collectivity

Abstract

The onset of collectivity and deformation, changes to the single particle energies and magic numbers and so on are strongly influenced by, for example, proton (p) and neutron (n) interactions inside atomic nuclei. Experimentally, using binding energies (or masses), one can extract an average p-n interaction between the last two protons and the last two neutrons, called delta V-pn. We have studied delta V-pn values using calculations of spatial overlaps between p and n Nilsson orbitals, considering different deformations, for the Z= 50-82, N= 82-126 shells, and comparison of these theoretical results with experimental delta V-pn values. Our results show that enhanced valence p-n interactions are closely correlated with the development of collectivity, shape changes, and the saturation of deformation in nuclei. We note that the difference of the Nilsson quantum numbers of the last filled Nilsson p and n orbitals, has a special relation, 0[110], in which they differ by only a single quantum in the z-direction, for those nuclei where delta V-pn is largest for each Z in medium mass and heavy nuclei. The synchronised filling of such orbital pairs correlates with the emergence of collectivity.