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