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abstract: |
    Based on microscopic Hartree-Fock + random phase approximation calculations with Skyrme interactions, we study the correlations between the nuclear breathing mode energy $E_{\mathrm{ISGMR}}$ and properties of asymmetric nuclear matter with a recently developed analysis method. Our results indicate that the $E_{\mathrm{ISGMR}}$ 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 $E_{\mathrm{ISGMR}}$ of $^{208}$Pb. Furthermore, we find the $E_{\mathrm{ISGMR}}$ difference between $^{100}$Sn and $^{132}$Sn strongly correlates with $L$ and thus provides a potentially useful probe of the symmetry energy.
author:
- 'Lie-Wen Chen'
- 'Jian-Zhong Gu'
title: Correlations between the nuclear breathing mode energy and properties of asymmetric nuclear matter
---

Introduction
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Determination of the equation of state (EOS) for isospin asymmetric nuclear matter (ANM) is among fundamental questions in both nuclear physics and astrophysics. Knowledge on the nuclear EOS is important for understanding not only the structure of finite nuclei, the 