Effect of Wigner energy on the symmetry energy coefficient in nuclei

TL;DR

This study analyzes how Wigner energy influences the nuclear symmetry energy coefficient in finite nuclei, revealing its impact on isospin asymmetry and providing precise parameter values through extensive data fitting.

Contribution

It introduces a detailed extraction of symmetry energy coefficients considering Wigner correction, with new parameter estimates based on a large dataset of nuclear binding energies.

Findings

Symmetry energy coefficient decreases with isospin asymmetry due to Wigner correction.

Optimal parameters for symmetry energy are determined with high precision.

The $a_{ m sym}^{(4)}$ term significantly affects neutron-rich nuclei.

Abstract

The nuclear symmetry energy coefficient (including the coefficient $a_{\rm sym}^{(4)}$ of $I^{4}$ term) of finite nuclei is extracted by using the differences of available experimental binding energies of isobaric nuclei. It is found that the extracted symmetry energy coefficient $a^{*}_{\rm sym}(A,I)$ decreases with increasing of isospin asymmetry $I$, which is mainly caused by Wigner correction, since $e^{*}_{\rm sym}$ is the summation of the traditional symmetry energy $e_{\rm sym}$ and the Wigner energy $e_{\rm W}$. We obtain the optimal values $J=30.25\pm0.10$ MeV, $a_{\rm ss}=56.18\pm1.25$ MeV, $a_{\rm sym}^{(4)}=8.33\pm1.21$ MeV and the Wigner parameter $x=2.38\pm0.12$ through the polynomial fit to 2240 measured binding energies for nuclei with $20 \leq A \leq 261$ with an rms deviation of 23.42 keV. We also find that the volume symmetry coefficient $J\simeq 30$ MeV is insensitive to the value $x$, whereas the surface symmetry coefficient $a_{\rm ss}$ and the coefficient $a_{\rm sym}^{(4)}$ are very sensitive to the value of $x$ in the range $1\leq x\leq 4$. The contribution of $a_{\rm sym}^{(4)}$ term increases rapidly with increasing of isospin asymmetry $I$. For very neutron-rich nuclei, the contribution of $a_{\rm sym}^{(4)}$ term will play an important role.