Effect of Wigner energy on the symmetry energy coefficient in nuclei

Abstract

The nuclear symmetry energy coefficient (including the coefficient $a_{\mathrm{sym}}^{(4)}$ 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 $a_{\mathrm{sym}}^{\ast }(A,I)$ decreases with increasing of isospin asymmetry $I$, which is mainly caused by Wigner correction, since $e_{\mathrm{sym}}^{\ast }$ is the summation of the traditional symmetry energy $e_{\mathrm{sym}}$ and the Wigner energy $e_{\mathrm{W}}$. We obtain the optimal values $J=30.25\pm 0.10$ MeV, $a_{\mathrm{ss}}=56.18\pm 1.25$ MeV, $a_{\mathrm{sym}}^{(4)}=8.33\pm 1.21$ MeV and the Wigner parameter $x=2.38\pm 0.12$ through the polynomial fit to 2240 measured binding energies for nuclei with $20\le A\le 261$ 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 $a_{\mathrm{ss}}$ and the coefficient $a_{\mathrm{sym}}^{(4)}$ are very sensitive to the value of $x$ in the range $1\le x\le 4$. The contribution of $a_{\mathrm{sym}}^{(4)}$ term increases rapidly with increasing of isospin asymmetry $I$. For very neutron-rich nuclei, the contribution of $a_{\mathrm{sym}}^{(4)}$ term will play an important role.

Comments: 14 pages, 5 figures, Submitted to Chinese Physics C