Effect of Wigner energy on the symmetry energy coefficient in nuclei

Abstract: The nuclear symmetry energy coefficient (including the coefficient a_sym⁽⁴⁾ of the I⁴ 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_sym^*(A,I) decreases with increasing isospin asymmetry I, which is mainly caused by Wigner correction, since e_sym^* is the summation of the traditional symmetry energy e_sym and the Wigner energy e_W. We obtain the optimal values J=30.25±0.10 MeV, a_ss=56.18±1.25 MeV, a_sym⁽⁴⁾=8.33±1.21 MeV and the Wigner parameter x=2.38±0.12 through a polynomial fit to 2240 measured binding energies for nuclei with 20≤A≤261 with an rms deviation of 23.42 keV. We also find that the volume symmetry coefficient J≈30 MeV is insensitive to the value x, whereas the surface symmetry coefficient a_ss and the coefficient a_sym⁽⁴⁾ are very sensitive to the value of x in the range 1≤x≤4. The contribution of the a_sym⁽⁴⁾ term increases rapidly with increasing isospin asymmetry I. For very neutron-rich nuclei, the contribution of the a_sym⁽⁴⁾ term will play an important role.