Systematic study of the symmetry energy coefficient in finite nuclei

TL;DR

This study systematically analyzes the symmetry energy coefficients in finite nuclei using covariant density functional theory, addressing shell effects and providing consistent volume and surface coefficients that align with previous non-relativistic models.

Contribution

It introduces a systematic approach to extract symmetry energy coefficients from finite nuclei, accounting for shell effects, and compares covariant DFT results with existing mass tables and models.

Findings

Symmetry energy coefficients decrease smoothly with increasing mass number.

The ratio of surface to volume coefficients is approximately 1.63, consistent with previous models.

Strong linear correlation observed between volume and surface coefficients across different data sets.

Abstract

The symmetry energy coefficients in finite nuclei have been studied systematically with a covariant density functional theory (DFT) and compared with the values calculated using several available mass tables. Due to the contamination of shell effect, the nuclear symmetry energy coefficients extracted from the binding energies have large fluctuations around the nuclei with double magic numbers. The size of this contamination is shown to be smaller for the nuclei with larger isospin value. After subtracting the shell effect with the Strutinsky method, the obtained nuclear symmetry energy coefficients with different isospin values are shown to decrease smoothly with the mass number $A$ and are subsequently fitted to the relation $\dfrac{4a_{\rm sym}}{A}=\dfrac{b_v}{A}-\dfrac{b_s}{A^{4/3}}$. The resultant volume $b_v$ and surface $b_s$ coefficients from axially deformed covariant DFT calculations are $121.73$ and $197.98$ MeV respectively. The ratio $b_s/b_v=1.63$ is in good agreement with the value derived from the previous calculations with the non-relativistic Skyrme energy functionals. The coefficients $b_v$ and $b_s$ corresponding to several available mass tables are also extracted. It is shown that there is a strong linear correlation between the volume $b_v$ and surface $b_s$ coefficients and the ratios $b_s/b_v$ are in between $1.6-2.0$ for all the cases.