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 (EOS) of nuclear matter and the fourth-order symmetry energy $a_{\mathrm{sym},4}(A)$ 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 $E_{\mathrm{sym},4}(\ddot{I}{}_0)$ at normal nuclear density $\ddot{I}{}_0$ from analyzing nuclear mass data. Based on the recent precise extraction of $a_{\mathrm{sym},4}(A)$ via the double difference of the "experimental" symmetry energy extracted from nuclear masses, for the first time, we estimate a value of $E_{\mathrm{sym},4}(\ddot{I}{}_0)=20.0\pm 4.6$ MeV. Such a value of $E_{\mathrm{sym},4}(\ddot{I}{}_0)$ 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.

7 pages, 1 figure. Presentation improved and discussions added. Accepted version to appear in PLB