Systematic study of the symmetry energy under the local density approximation

Abstract

The nuclear matter symmetry energy ${C}_{\mathrm{sym}}(\ensuremath{\rho})$ and its slope parameter $L$ are studied using local density approximation. With this method, the symmetry energy of nuclear matter can be deduced from matter density distributions of finite nuclei. By systematically analyzing the extracted $L$ for different isotopes, the variation trends of values of extracted $L$ along isotopic chains can be obtained. The study can explain why the neutron rich nuclei in isotopic chains such as ${}^{208}$Pb can be used to extract $L$ under local density approximation. By studying the regularity of extracted $L$ for different isotopic chains, we finally obtain the value of $L$ and its error bar: $L=66\ifmmode\pm\else\textpm\fi{}7$ MeV. Besides, the density dependence parameter $\ensuremath{\gamma}$ is constrained to be $0.69\ifmmode\pm\else\textpm\fi{}0.07$ for the ansatz of symmetry energy ${C}_{\mathrm{sym}}(\ensuremath{\rho})={C}_{\mathrm{sym}}({\ensuremath{\rho}}_{0}){(\frac{\ensuremath{\rho}}{{\ensuremath{\rho}}_{0}})}^{\ensuremath{\gamma}}$.