Density dependence of the symmetry energy probed by beta(-) decay energies of odd-A nuclei

The mass-dependent symmetry energy coefficients a(sym)(A) are extracted with the beta-decay energies Q(beta-) of heavy odd-A nuclei. The dominant position of this approach is that only the Coulomb energy survives in Q(beta-) to determine the unknown a(sym)(A). The obtained a(sym)(A) is employed to analyze the density dependence of the nuclear matter symmetry energy around the saturation density. The estimated a(sym)(A) of Pb-208 is 22.1-22.7 MeV. The slope parameter of the symmetry energy is found to be 50 +/- 15 MeV, with the symmetry energy S-0 = 32.3 +/- 1.3 MeV at saturation density obtained from the analysis of pygmy dipole resonance (PDR) [Carbone et al., Phys. Rev. C 81, 041301(R) (2010)] as input. Furthermore, the corresponding neutron skin thickness in Pb-208 is estimated to be Delta R-np = 0.174 +/- 0.022 fm.