The effect of self interacting isoscalar-vector meson on finite nuclei and infinite nuclear matter

A detailed study is made for the nucleon-nucleon interaction based on relativistic mean field theory in which the potential is explicitly expressed in terms of mass and the coupling constant of the meson fields. A unified treatment for self-coupling of isoscalar-scalar $\sigma-$, isoscalar-vector $\omega$-mesons and their coupling constant are given with a complete analytic form. The present investigation is focused on the effect of self-interacting higher order $\sigma$ and $\omega$ field on nuclear properties. An attempt is made to explain the collapsing stage of nucleon by higher order $\omega$-field. Both infinite nuclear matter and the finite nuclear properties are included in the present study to observe the behaviour or sensitivity of this self interacting terms.