Abstract
Single-particle levels of unknown superheavy and extremely superheavy nuclei are studied using a modified Woods–Saxon potential, which are smooth functions of the number of nucleons. This extrapolation gives that neutron shell closure remains for \(N=308\), and a proton shell has a gap at \(Z=164\), which is weaker than that of a neutron shell. Seven unknown doubly magic spherical nuclei beyond 208Pb are found: 256U164, 298Fl184, 310[126]184, 342Fl228, 366[138]228, 462[154]308, and 472[164]308. Of these, the 298Fl184 and 472[164]308 are beta-stable nuclei. The nucleus 472[164]308 seems to be the heaviest nuclei based on the analysis of neutron and proton drip lines and the fissility line.
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