model does not include self-interaction terms for the meson fields (i.e. $\kappa =0$, $\lambda =0$ and $\xi=0$ ) as in NL3 or TM1 parametrizations for the NLWM.

The field equations of motion follow from the Euler-Lagrange equations. When they are obtained, some care has to be taken since the coupling operators depend on the baryon fields $\bar
\psi$ and $\psi$ through the density. When the partial derivatives of $\cal{L}$ are performed relatively to the fields $\bar \psi$ and $\psi$, they yield extra terms due to the functional dependence of the coupling operators. The new terms are absent in the usual Quantum Hadrodynamic (QHD, NLWM) models [@sw; @nl3; @tm1]. The equations of motion for the fields read:

$$\begin{aligned}
(\partial_\mu\partial^{\mu} + m_{\phi}^2)\phi &=&
 \Gamma_s \bar \psi \psi , \label{PHI} \\
\partial_{\nu} \Omega^{\mu\nu} + m_v^2 V^{\mu} &=&
 \Gamma_v \bar \psi \gamma^{\mu} \psi, \label{OME}\\
\partial_{\nu} {\mathbf {B}}^{~\mu\nu} + m_\rho^2
{\mathbf b}^\mu &=&
\frac{\Gamma_\rho} {2} \bar \psi \boldsymbol {\tau} \gamma^{\mu}
\psi, \label{RHO}\\
\partial_{\nu} F^{\mu\nu} &=& \frac{e}{2}\bar \psi
(1+\tau_3 )\gamma^{\mu} \psi, \label{EM}\\
\left[ \gamma_{\mu}(i\partial^\mu -\Sigma^{\mu}) -M^{\ast}
\right] \psi&=&0 ~, \label{DIRAC}\end{aligned}$$

where $M^{\ast}=M-\Gamma_s \phi$. Notice that in the equation of motion for the baryon field $\psi$ the vector self-energy consists of two terms, $\Sigma_{\mu}$ = $\Sigma^{(0)}_\mu$ + 