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

The relative ordering of J⁻ levels of multiplets resulting from two-body excitations, which include a J^π = 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 δ interaction are used. The simplistic approach confirms for the particle-particle channel, the often stated preference of the Δj = 3, Δl = 3 subshell combination over the Δj = 3, Δl = 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 Δj = 3, Δl = 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.