in physical properties related to the chemical potentials or to their derivatives with respect to the density, such as spinodal regions, as compared with the more common NL3 or TM1 parametrizations.

NL${\omega\rho}$ model
======================

The Lagrangian density that incorporates the extra non-linear $\sigma-\rho$ and $\omega-\rho$ couplings [@hp01; @hp2001; @bunta; @bunta2] reads

$${\cal L}=\bar \psi\left[\gamma_\mu\left(i\partial^{\mu}-g_v V^{\mu}-
\frac{g_{\rho}}{2}  {\boldsymbol {\tau}} \cdot \mathbf {b}^\mu \right. \right.$$ $$\left. \left. -e  \frac{(1+\tau_{i3})}{2} A^\mu \right)
-(M-g_s \phi)\right]\psi$$ $$+\frac{1}{2}(\partial_{\mu}\phi\partial^{\mu}\phi
-m_s^2 \phi^2)
-\frac{1}{3!}\kappa \phi ^{3}
-\frac{1}{4!}\lambda \phi ^{4}
-\frac{1}{4}\Omega_{\mu\nu}\Omega^{\mu\nu}$$ $$+\frac{1}{2}m_v^2 V_{\mu}V^{\mu}
-\frac{1}{4}\mathbf B_{\mu\nu}\cdot\mathbf B^{\mu\nu}+\frac{1}{2}
m_\rho^2 \mathbf b_{\mu}\cdot \mathbf b^{\mu}
-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$$ $$+g_\rho^2\mathbf b_{\mu}\cdot \mathbf b^{\mu}[\Lambda_s
g_s^2\phi^2+\Lambda_v g_v^2 V_\mu V^\mu],
\label{lagacoplada}$$ where $\Omega_{\mu\nu}$, $\mathbf B_{\mu\nu}$ and $F_{\mu\nu}$ are defined after eq.(\[lagtw\]). The parameters of the model are again the masses and the couplings, which are now constants, i.e., $g_s$ replaces $\Gamma_s$, $g_v$ replaces $\Gamma_v$ and $g_\rho$ replaces $\Gamma_\rho$. Non-linear $\sigma$ terms are also included. We have followed the prescription of [@hp01], where the starting point was the NL3 parametrization and the $g_\rho$ coupling was adjusted for each value of the coupling $\Lambda_i$ studied in such a way that for $k_F=1.15$ fm$^{-1}$ (not the saturation point) the symmetry energy is 25.68 MeV. In the present work we set $\Lambda_s=0$ as in 