RPA calculations with Gaussian expansion method

TL;DR

This paper demonstrates that the Gaussian expansion method (GEM) effectively computes RPA properties, accurately describing collective states and transition properties in calcium isotopes, including self-consistent calculations with Gogny D1S interaction.

Contribution

The study introduces the application of GEM to RPA calculations, confirming its precision and effectiveness in both test and self-consistent nuclear models.

Findings

GEM accurately reproduces energies and transition strengths of collective states.

GEM effectively separates spurious center-of-mass motion in RPA.

Sum rules for isoscalar transitions are well satisfied.

Abstract

The Gaussian expansion method (GEM) is extensively applied to the calculations in the random-phase approximation (RPA). We adopt the mass-independent basis-set that has been tested in the mean-field calculations. By comparing the RPA results with those obtained by several other available methods for Ca isotopes, using a density-dependent contact interaction and the Woods-Saxon single-particle states, we confirm that energies, transition strengths and widths of their distribution are described by the GEM bases to good precision, for the $1^-$, $2^+$ and $3^-$ collective states. The GEM is then applied to the self-consistent RPA calculations with the finite-range Gogny D1S interaction. The spurious center-of-mass motion is well separated from the physical states in the $E1$ response, and the energy-weighted sum rules for the isoscalar transitions are fulfilled reasonably well. Properties of low-energy transitions in $^{60}$Ca are argued in some detail.