Effect of isospin asymmetry in nuclear system

The effect of $\delta-$ and $\omega-\rho-$meson cross couplings on asymmetry nuclear systems are analyzed in the frame-work of an effective Field theory motivated relativistic mean field formalism. The calculations are done on top of the G2 parameter set, where these contributions are absent. We calculate the root mean square radius, binding energy, single particle energy (for the $1^{st}$ and last occupied orbits), density and spin-orbit interaction potential for some selected nuclei and evaluate the $L_{sym}-$ and $E_{sym}-$ coefficients for nuclear matter as function of $\delta-$ and $\omega-\rho-$meson coupling strengths. As expected, the influence of these effects are negligible for symmetry nuclear system and these effects are very important for systems with large isospin asymmetry.