Empirical information on nuclear matter fourth-order symmetry energy from an extended nuclear mass formula

Abstract

We establish a relation between the equation of state of nuclear matter and the fourth-order symmetry energy asym,4(A) of finite nuclei in a semi-empirical nuclear mass formula by self-consistently considering the bulk, surface and Coulomb contributions to the nuclear mass. Such a relation allows us to extract information on nuclear matter fourth-order symmetry energy Esym,4(ρ0) at normal nuclear density ρ0 from analyzing nuclear mass data. Based on the recent precise extraction of asym,4(A) via the double difference of the “experimental” symmetry energy extracted from nuclear masses, for the first time, we estimate a value of Esym,4(ρ0)=20.0±4.6 MeV. Such a value of Esym,4(ρ0) is significantly larger than the predictions from mean-field models and thus suggests the importance of considering the effects of beyond the mean-field approximation in nuclear matter calculations.