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

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 the 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 $^{16}\mathrm{O}$. We show that the subtraction procedure leads to (i) results that are weakly cutoff dependent and (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 two particle-two hole configurations (2p2h) on the excitation spectra of medium-mass and heavy nuclei.