Evolution of collectivity and neutron-proton interactions

Abstract

In this paper we study the correlation between the evolution of nuclear collective motion and neutron-proton interactions. We construct empirical neutron-proton interactions (denoted by ${V}_{\mathrm{NP}}$) for nuclei in the $(28<Z<50,$ $50<N<82)$, $(50<Z<82,$ $50<N<82$), and $(50<Z<82,$ $82<N<126)$ major shells. The ratios between ${V}_{\mathrm{NP}}$ and ${N}_{\mathrm{n}}{N}_{\mathrm{p}}$ (the product of valence proton number and valence neutron number) are found to be different for particle-particle, particle-hole, and hole-hole regions of the same major shell, suggesting different average strengths of neutron-proton interactions for these regions. Very interestingly, collective observables of even-even nuclei, e.g., ${2}^{+}$ and ${4}^{+}$ state energies, which follow different trajectories in the ${N}_{\mathrm{n}}{N}_{\mathrm{p}}$ scheme for particle-particle, particle-hole, and hole-hole regions, are found to form one unified and compact trajectory if those collective observables are plotted in terms of total neutron-proton interactions, ${V}_{\mathrm{NP}}$.