Seniority-two valence-shell building blocks of the octupole phonon

TL;DR

This paper investigates the ordering of $J^-$ levels in multiplets related to octupole phonons using a simplified shell-model with harmonic oscillator wavefunctions and residual interactions.

Contribution

It demonstrates how specific subshell configurations influence the energy ordering of octupole-related states, explaining observed low excitation energies.

Findings

Preference for $ riangle j=3, riangle l=3$ subshells in particle-particle channel

Less pronounced energy gain for $ riangle j=3, riangle l=3$ in particle-hole channel

Explains low excitation energies of 3$^-_1$ states in octupole-soft nuclei

Abstract

The relative ordering of $J^-$ levels of multiplets resulting from two-body excitations, which include a $J^{\pi}=3^-$ state that can contribute to the octupole phonon, are investigated in a simplistic shell-model approach. To calculate the relative level ordering, harmonic oscillator wavefunctions and a residual $\delta$ interaction are used. The simplistic approach confirms for the particle-particle channel, the often stated preference of the $\Delta j=3, \Delta l =3$ subshell combination over the $\Delta j=3, \Delta l =1$ subshell combination through an enhanced energy gain. Furthermore, it is shown that, in the particle-hole channel, the gain is less pronounced for the $\Delta j=3, \Delta l =3$ subshell configuration. In combination with the overall structure of an oscillator shell, these results explain the comparatively low excitation energy for 3$^-_1$ excitations observed for the octupole-soft proton and neutron numbers predicted by various models.