Beyond--mean--field effective masses in the nuclear Fermi liquid from axial breathing modes

TL;DR

This paper investigates how the nucleon effective mass in nuclear matter is modified beyond mean-field approximations by analyzing axial breathing modes using the SSRPA model, linking excitation energies to effective mass changes.

Contribution

It introduces a method to estimate the enhancement of the nucleon effective mass beyond mean-field using axial breathing mode energies within the SSRPA framework.

Findings

Effective mass is increased beyond mean-field estimates.

SSRPA self-energy corrections align with effective mass enhancement.

Axial breathing mode energies serve as indicators of effective mass modifications.

Abstract

Axial breathing modes are studied within the nuclear energy--density--functional theory to discuss the modification of the nucleon effective mass produced beyond the mean--field approximation. This analysis is peformed with the subtracted second random--phase--approximation (SSRPA) model applied to two nuclei, $^{48}$Ca and $^{90}$Zr. Analyzing the centroid energies of axial breathing modes obtained with the mean--field--based random--phase approximation and with the beyond--mean--field SSRPA model, we estimate the modification (enhancement) of the effective mass which is induced beyond the mean field. This is done by employing a relation, obtained with the Landau's Fermi liquid theory, between the excitation frequency of axial modes to $\sqrt{m/m^*}$, where $m$ ($m^*$) is the bare (effective) mass. Such an enhancement of the effective mass is discussed in connection with the renormalization of single--particle excitation energies generated by the energy--dependent SSRPA self-energy correction. We find that the effective beyond--mean--field compression of the single--particle spectrum produced by the self--energy correction is coherent with the increase of the effective mass estimated from the analysis of axial breathing modes.