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

By using point-coupling versions of finite range nuclear relativistic mean field models containing cubic and quartic self interactions in the scalar field $σ$, 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, $\,L\,=\,3J\,+f(m^{*},ρ_{o},B_{o},K_{o})$, where the quantities $m^{*}$, $ρ_{o}$, $B_{o}$ and $K_{o}$ are bulk parameters at the nuclear matter saturation density $ρ_{o}$. 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.

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