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By using point-coupling versions of finite range nuclear relativistic meanfield models containing cubic and quartic self interactions in the scalar field$\sigma$, a nonrelativistic limit is achieved. This approach allows ananalytical 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 bulkparameters at the nuclear matter saturation density $\rho_{o}$. This resultestablishes a linear correlation between $L$ and $J$ which is reinforced byexact relativistic calculations. An analogous analytical correlation is alsofound for $J$, $L$ and the symmetry energy curvature ($K_{sym}$). Based onthese results, we propose graphic constraints in $L\times J$ and $K_{sym}\timesL$ planes which finite range models must satisfy.

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