Nuclear symmetry energy at subnormal densities from measured nuclear masses

The symmetry energy coefficients for nuclei with mass number $A=20$–$250$ are extracted from more than $2000$ measured nuclear masses. With the semiempirical connection between the symmetry energy coefficients of finite nuclei and the nuclear symmetry energy at reference densities, we investigate the density dependence of the symmetry energy of nuclear matter at subnormal densities. The obtained results are compared with those extracted from other methods.

Figure 1

(a) Value of $e_m$ as a function of isospin asymmetry for selected series of isobaric nuclei. The solid circles and the solid curves denote the experimental data and the results by fitting the experimental data, respectively. (b) Symmetry energy coefficients of nuclei as a function of mass number. The solid circles denote the extracted results from the measured nuclear masses. The shading denotes the results of Danielewicz et al. [9]. The vertical short dashes denote the results when the shell corrections of nuclei from Ref. [10] are removed from the measured energy per particle. The (red) curves denote the results by fitting the circles.

Figure 2

Reference density ${\rho }_A$ as a function of mass number. The solid and dashed curves denote the results in this work and those from Ref. [5], respectively.

Figure 3

Density dependence of the nuclear symmetry energy with different methods. The two vertical dashed lines give the corresponding density region of nuclei with $A=20$–250. The gray shading denotes the region with $S_0=31.1\pm 1.7$ MeV and $\gamma =0.7\pm 0.1$, using the form $e_{\mathrm{sym}}(\rho )=S_0(\rho /{\rho }_0){}^{\gamma }$.

Figure 4

(a) Range of slope parameter $L$ determined by $S_0=31.1\pm 1.7$ MeV and $\gamma =0.7\pm 0.1$ in this work. (b) Range of slope parameter $L$ determined from different observables. The results are taken from Ref. [21] with PDR, from Ref. [22] with neutron skin thickness, and from Ref. [2] with isospin diffusion.