Subtraction method in the second random--phase approximation: first applications with a Skyrme energy functional

TL;DR

This paper introduces a subtraction method in the second random-phase approximation (SRPA) to improve stability and reduce cutoff dependence, enabling more reliable analysis of nuclear excitations with Skyrme functionals.

Contribution

The authors implement a subtraction procedure in SRPA for the first time, ensuring stability and weak cutoff dependence within nuclear density-functional theory.

Findings

The subtraction method guarantees real excitation energies.

Results show reduced downward shift in SRPA spectra.

Method is applicable to medium and heavy nuclei.

Abstract

We make use of a subtraction procedure, introduced to overcome double--counting problems in beyond--mean--field theories, in the second random--phase--approximation (SRPA) for the first time. This procedure guarantees the stability of SRPA (so that all excitation energies are real). We show that the method fits perfectly into nuclear density--functional theory. We illustrate applications to the monopole and quadrupole response and to low--lying $0^+$ and $2^+$ states in the nucleus $^{16}$O. We show that the subtraction procedure leads to: (i) results that are weakly cutoff dependent; (ii) a considerable reduction of the SRPA downwards shift with respect to the random--phase approximation (RPA) spectra (systematically found in all previous applications). This implementation of the SRPA model will allow a reliable analysis of the effects of 2 particle--2 hole configurations ($2p2h$) on the excitation spectra of medium--mass and heavy nuclei.