Correlations between the nuclear matter symmetry energy, its slope, and curvature from a nonrelativistic solvable approach and beyond

TL;DR

This paper derives analytical correlations between nuclear matter symmetry energy, its slope, and curvature using a nonrelativistic limit of relativistic models, providing constraints for nuclear physics models.

Contribution

It introduces a unified analytical expression linking symmetry energy parameters and establishes linear correlations reinforced by relativistic calculations.

Findings

Derived an analytical formula for symmetry energy as a function of its slope.

Established linear correlations between $J$, $L$, and $K_{sym}$.

Proposed graphical constraints for nuclear matter parameters.

Abstract

By using point-coupling versions of finite range nuclear relativistic mean field models containing cubic and quartic self interactions in the scalar field $\sigma$, a nonrelativistic limit is achieved. This approach allows an analytical expression for the symmetry energy ($J$) as a function of its slope ($L$) in a unified form, namely, $\,L\,=\,3J\,+f(m^{*},\rho_{o},B_{o},K_{o})$, where the quantities $m^{*}$, $\rho_{o}$, $B_{o}$ and $K_{o}$ are bulk parameters at the nuclear matter saturation density $\rho_{o}$. This result establishes a linear correlation between $L$ and $J$ which is reinforced by exact relativistic calculations. An analogous analytical correlation is also found for $J$, $L$ and the symmetry energy curvature ($K_{sym}$). Based on these results, we propose graphic constraints in $L\times J$ and $K_{sym}\times L$ planes which finite range models must satisfy.