Mass and isospin dependence of symmetry energy coefficients of finite nuclei

The mass and isospin dependence of symmetry energy coefficients $a_{\mathrm{sym}}$ of finite nuclei are investigated with the measured nuclear masses incorporating the liquid drop mass formula. The enhanced $a_{\mathrm{sym}}$ for nearly symmetric nuclei are observed. To describe the mass and isospin dependence of $a_{\mathrm{sym}}$, a modified formula based on the conventional surface-symmetry term is proposed and the corresponding rms deviation of nuclear masses is checked.

Figure 1

Symmetry-energy coefficients of nuclei as a function of (a) nuclear mass number and (b) of isospin asymmetry. The shades denote the results of Danielewicz et al. [3]. The crosses and the short dashes denote the extracted $a_{\mathrm{sym}}^{(0)}$ and $a_{\mathrm{sym}}^{(1)}$ terms of the symmetry energy coefficients from the measured nuclear masses, respectively.

Figure 2

Wigner energies of nuclei calculated with different models. The open circles and the straight line denote the results in Ref. [10] and those of Satula et al. [11], respectively. The crosses denote results of this work, with $c_{\mathrm{sym}}=29.3$ MeV determined by fitting the 2149 measured nuclear masses.

Figure 3

The same as Fig. 1, but with the results of Eq. (9) (open circles) for comparison.