Nuclear matter symmetry energy and the symmetry energy coefficient in the mass formula

TL;DR

This paper demonstrates that the symmetry energy coefficient in the mass formula and the nuclear matter symmetry energy at a specific density can be derived from the symmetry energy and its slope at saturation density, providing constraints on these parameters.

Contribution

It shows a linear relationship between the symmetry energy coefficient and the symmetry energy at a subsaturation density within the Skyrme-Hartree-Fock approach, linking nuclear mass models to nuclear matter properties.

Findings

E_{sym}(ρ_A) is approximately equal to a_{sym}(A).

Constraints on E_{sym}(ρ_0) and L are derived from symmetry energy at ρ_A.

Estimated values: E_{sym}(ρ_0)=30.5±3 MeV, L=52.5±20 MeV.

Abstract

Within the Skyrme-Hartree-Fock (SHF) approach, we show that for a fixed mass number A, both the symmetry energy coefficient a_{sym}(A) in the semi-empirical mass formula and the nuclear matter symmetry energy E_{sym}(\rho_A) at a subsaturation reference density rho_A can be determined essentially by the symmetry energy E_{sym}(rho_0) and its density slope L at saturation density rho_0. Meanwhile, we find the dependence of a_{sym}(A) on E_{sym}(rho_0) or L is approximately linear and is very similar to the corresponding linear dependence displayed by E_{sym}(\rho_A), providing an explanation for the relation E_{sym}(\rho_A) \approx a_{sym}(A). Our results indicate that a value of E_{sym}(\rho_A) leads to a linear correlation between E_{sym}(rho_0) and L and thus can put important constraints on E_{sym}(rho_0) and L. Particularly, the values of E_{sym}(rho_0)= 30.5 +- 3 MeV and L= 52.5 +- 20 MeV are simultaneously obtained by combining the constraints from recently extracted E_{sym}(\rho_A=0.1 fm^{-3}) with those from recent analyses of neutron skin thickness of Sn isotopes in the same SHF approach.