Simple phenomenology for the ground-state bands of even-even nuclei.

Abstract

It is observed that the even-even nuclei having identical ${\mathit{N}}_{\mathit{p}}$${\mathit{N}}_{\mathit{n}}$/\ensuremath{\Delta} values exhibit identical excitation energies and/or energy ratios (${\mathit{E}}_{\mathit{J}}$/${\mathit{E}}_{2}$,${\mathit{E}}_{\mathit{J}}$/${\mathit{E}}_{4}$) in their ground-state bands (g.s.b.). ${\mathit{N}}_{\mathit{p}}$ (${\mathit{N}}_{\mathit{n}}$) is the valence proton (neutron) number and \ensuremath{\Delta} is the average pairing gap, (${\mathrm{\ensuremath{\Delta}}}_{\mathit{p}}$+${\mathrm{\ensuremath{\Delta}}}_{\mathit{n}}$)/2. It is shown that this correlation is a manifestation of a very simple but uniform dependence of the excitation energies of the g.s.b. of even-even nuclei, spanning a wide mass region (70\ensuremath{\le}A\ensuremath{\le}244), on the ratio of their pairing and n-p interaction energies. An explicit form of this dependence is phenomenologically deduced and subsequently used to study the development of collectivity, existence of subshell closures and some other nuclear systematics.