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

## TL;DR

This paper links nuclear mass data to the fourth-order symmetry energy of nuclear matter, estimating its value at normal density and highlighting its larger-than-expected magnitude compared to mean-field models.

## Contribution

It introduces a novel relation between nuclear mass formulas and the fourth-order symmetry energy, enabling the first empirical estimate of its value at nuclear saturation density.

## Key findings

- Estimated $E_{sym,4}(\rho_0)$ as 20.0 ± 4.6 MeV
- Found $E_{sym,4}(\rho_0)$ larger than mean-field predictions
- Highlighted the significance of beyond mean-field effects

## Abstract

We establish a relation between the equation of state (EOS) of nuclear matter and the fourth-order symmetry energy $a_{\rm{sym,4}}(A)$ 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 $E_{\rm{sym,4}}(\rho_0)$ at normal nuclear density $\rho_0$ from analyzing nuclear mass data. Based on the recent precise extraction of $a_{\rm{sym,4}}(A)$ via the double difference of the "experimental" symmetry energy extracted from nuclear masses, for the first time, we estimate a value of $E_{\rm{sym,4}}(\rho_0) = 20.0\pm4.6$ MeV. Such a value of $E_{\rm{sym,4}}(\rho_0)$ 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.