Constraints on both the quadratic and quartic symmetry energy coefficients by 2β− -decay energies

Abstract

In this Rapid Communication, the $2{\ensuremath{\beta}}^{\ensuremath{-}}$-decay energies $Q(2{\ensuremath{\beta}}^{\ensuremath{-}})$ given in the atomic mass evaluation are used to extract not only the quadratic volume symmetry energy coefficient ${c}_{\mathrm{sym}}^{v}$, but also the quartic one ${c}_{\mathrm{sym},4}^{v}$. Based on the modified Bethe-Weizs\"acker nuclear mass formula of the liquid-drop model, the decay energy $Q(2{\ensuremath{\beta}}^{\ensuremath{-}})$ is found to be closely related to both the quadratic and quartic symmetry energy coefficients ${c}_{\mathrm{sym}}^{v}$ and ${c}_{\mathrm{sym},4}^{v}$. There are totally 449 data of decay energies $Q(2{\ensuremath{\beta}}^{\ensuremath{-}})$ used in the present analysis where the candidate nuclei are carefully chosen by fulfilling the following criteria: (1) large neutron-proton number difference $N\ensuremath{-}Z$, (2) large isospin asymmetry $I$, and (3) limited shell effect. The values of ${c}_{\mathrm{sym}}^{v}$ and ${c}_{\mathrm{sym},4}^{v}$ are extracted to be 29.345 and 3.634 MeV, respectively. Moreover, the quadratic surface-volume symmetry energy coefficient ratio is determined to be $\ensuremath{\kappa}={c}_{\mathrm{sym}}^{s}/{c}_{\mathrm{sym}}^{v}=1.356$.