Density dependence of the symmetry energy constrained by β−-, 2β−-, and 4β−-decay energies

Abstract

In this paper, the β−-, 2β−-, and 4β−-decay energies Q(β−), Q(2β−), and Q(4β−) given in the newly updated atomic mass evaluation (AME2016) are used to systematically constrain not only the quadratic symmetry energy coefficient and the surface-volume symmetry energy coefficient ratio , but also the quartic symmetry energy coefficient . Based on the modified Bethe–Weizsäcker mass formula, the decay energies Q(β−), Q(2β−), and Q(4β−) are all derived to be closely related to the quantities , κ, and , and then their values can be obtained by fitting the decay energies given in the AME2016. Besides, with the extracted values of and κ, by applying the relationship between the quadratic density-dependent symmetry energy S(ρ) and the mass-dependent symmetry energy coefficient of finite nuclei asym(A), the density slopes L(ρ0) for two different forms of S(ρ) at the saturation density ρ0 are constrained and the values are calculated to be L(ρ0) = 42.2 ± 8.0 MeV and L(ρ0) = 42.8 ± 7.6 MeV, respectively.