  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.
