Correlations between the nuclear breathing mode energy and properties of asymmetric nuclear matter

TL;DR

This study uses microscopic calculations to explore how the nuclear breathing mode energy relates to properties of asymmetric nuclear matter, revealing moderate correlations with symmetry energy slope and effective mass, and implications for extracting nuclear matter parameters.

Contribution

It introduces a new analysis method to quantify correlations between nuclear breathing mode energy and asymmetric nuclear matter properties, including the symmetry energy slope and effective mass.

Findings

$E_{ISGMR}$ of $^{208}$Pb correlates with $L$, $m_{s,0}^{ ext{*}}$, and $K_0$.

Uncertainty of about $ extpm 16$ MeV in $K_0$ extraction.

$E_{ISGMR}$ difference between $^{100}$Sn and $^{132}$Sn correlates with $L$.

Abstract

Based on microscopic Hartree-Fock + random phase approximation calculations with Skyrme interactions, we study the correlations between the nuclear breathing mode energy $E_{ISGMR}$ and properties of asymmetric nuclear matter with a recently developed analysis method. Our results indicate that the $E_{ISGMR}$ of $^{208}$Pb exhibits moderate correlations with the density slope $L$ of the symmetry energy and the isoscalar nucleon effective mass $m_{s,0}^{\ast}$ besides a strong dependence on the incompressibility $K_{0}$ of symmetric nuclear matter. Using the present empirical values of $L=60\pm 30$ MeV and $m_{s,0}^{\ast}=(0.8\pm 0.1)m$, we obtain a theoretical uncertainty of about $\pm 16$ MeV for the extraction of $K_{0}$ from the $E_{ISGMR}$ of $^{208}$Pb. Furthermore, we find the $E_{ISGMR}$ difference between $^{100}$Sn and $^{132}$Sn strongly correlates with $L$ and thus provides a potentially useful probe of the symmetry energy.