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.

We searched for the shell closure proton and neutron numbers in the superheavy region beyond 𝑍 = 82 and 𝑁 = 126 within the framework of non-relativistic Skryme–Hartree–Fock (SHF) with FITZ, SIII, SkMP and SLy4 interactions. We have calculated the average proton pairing gap $\Delta_p$, average neutron pairing gap $\Delta_n$, two-nucleon separation energy $S_{2q}$ and shell correction energy $E_{\text{shell}}$ for the isotopic chain of 𝑍 = 112–126. Based on these observables, 𝑍 = 120 with 𝑁 = 182 is suggested to be the magic numbers in the present approach.