Level density and survival of doubly magic SHN beyond Z=120

The increasing survival probabilities with increasing proton number of superheavy elements from Z=114 to Z=118 seem to indicate enhanced shell effects with increasing Z and therefore a possible proton magic shell may emerge beyond Z≥120. The phenomenological studies of BE(2) systematic and of the persistence of the Wigner term in masses of heavy nuclei indicate Z=126 as the next spherical proton magic number after lead. Self consistent and relativistic mean field calculations predict proton magicities for Z=114, 120, 124 and 126. It is pointed out that the pronounced central depressions in the densities lead to the spherical shell gaps at Z=120 and N=172 as a direct consequence of a large PS splitting, where as a flatter density profile favours the shell occurrence at N=184 and Z=126. But the relativistic Hartree-Fock- Bogoliubav approach could not predict Z=126 as a proton magic number, instead 120 and 138 beyond ²⁰⁸Pb