Effects ofδmesons in relativistic mean field theory

Abstract

The effect of $\ensuremath{\delta}$- and $\ensuremath{\omega}\text{\ensuremath{-}}\ensuremath{\rho}$-meson cross couplings on asymmetry nuclear systems are analyzed in the framework 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. To show the effect of $\ensuremath{\delta}$ meson on the nuclear system, we split the isospin coupling into two parts: (i) ${g}_{\ensuremath{\rho}}$ due to $\ensuremath{\rho}$ meson and (ii) ${g}_{\ensuremath{\delta}}$ for $\ensuremath{\delta}$ meson. Thus, our investigation is based on varying the coupling strengths of the $\ensuremath{\delta}$ and $\ensuremath{\rho}$ mesons to reproduce the binding energies of the nuclei $^{48}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$. We calculate the root mean square radius, binding energy, single particle energy, density, and spin-orbit interaction potential for some selected nuclei and evaluate the ${L}_{\mathrm{sym}}$ and ${E}_{\mathrm{sym}}$ coefficients for nuclear matter as function of $\ensuremath{\delta}$- and $\ensuremath{\omega}\text{\ensuremath{-}}\ensuremath{\rho}$-meson coupling strengths. As expected, the influence of these effects are negligible for the symmetric nuclear system, but substantial for the contribution with large isospin asymmetry.