Global properties of the Skyrme-force-induced nuclear symmetry energy

Abstract

A novel concept for the nuclear symmetry energy (NSE) is corroborated by large scale calculations. The paper firmly demonstrates that within the local density approximation, the value of the NSE coefficient, ${a}_{\mathrm{sym}}(A)$, depends on two basic ingredients: the mean-level spacing, $\ensuremath{\varepsilon}(A)$, and the effective strength of the isovector mean-potential, $\ensuremath{\kappa}(A)$. Surprisingly, our results reveal that these two basic ingredients of ${a}_{\mathrm{sym}}$ are almost equal after rescaling them linearly by the isoscalar and the isovector effective masses, respectively. This result points towards a hidden and hitherto unresolved fundamental property of the effective nuclear interaction. In addition, our analysis yields naturally the ratio of the surface-to-volume contributions to ${a}_{\mathrm{sym}}$ with a value of \ensuremath{\sim}1.6, consistent with hydrodynamical estimates for the static dipole polarizability as well as the neutron-skin. Although the present study is restricted to energy density functionals obtained from Skyrme forces the method is general and can easily be applied to more general local energy density functionals and nonnuclear bifermionic systems.