Eur. Phys. J. Special Topics 229, 2443–2458 (2020)
https://doi.org/10.1140/epjst/e2020-000026-x

Regular Article

A solvable model for octupole phonons

Grand Accélérateur National d’Ions Lourds, CEA/DRF-CNRS/IN2P3 Bvd Henri Becquerel, BP 55027, 14076 Caen, France

^a e-mail: isacker@ganil.fr

Received: 17 February 2020
Accepted: 31 August 2020
Published online: 23 October 2020

Abstract

A solvable model is proposed for the description of octupole phonons in closed-shell nuclei, formulated in terms of shell-model particle–hole excitations. With some simple assumptions concerning single-particle energies and two-body interactions, closed expressions are derived for the energy and wave function of the octupole phonon. In particular, it is shown that the components of the octupole phonon are proportional to Wigner 3j coefficients. This analytic wave function is proven to be exactly valid in light nuclei, which have LS shell closures that coincide with those of the three-dimensional harmonic oscillator, and to be valid to a good approximation in heavier nuclei, which have jj shell closures due to the spin–orbit interaction. The properties of the solvable model are compared with the results of a realistic shell-model calculation for ²⁰⁸Pb.