A simple form for nucleon–nucleon (NN) potential is introduced as an alternative to the popular M3Y form using the relativistic mean field theory (RMFT) with the non-linear terms in 𝜎 -meson for the first time. In contrast to theM3Y form, the new interaction becomes exactly zero at a finite distance and the expressions are analogous with the M3Y terms. Further, its applicability is examined by the study of proton and cluster radioactivity by folding it with the RMFT-densities of the cluster and daughter nuclei to obtain the optical potential in the region of proton-rich nuclides just above the double magic core ¹⁰⁰Sn. The results obtained were found comparable with the widely used M3Y $NN$ interactions.