Semiempirical Shell Model Masses with Magic Number Z = 126 for Superheavy Elements

A semiempirical shell model mass equation applicable to superheavy elements up to Z = 126 is presented and shown to have a high predictive power. The equation is applied to the recently discovered superheavy nuclei 293 118 and 289 114 and their decay products. 269 Sg has been observed. The α-decay energies vary rather smoothly along the chain. If the above assignments are confirmed, and the decaying nuclei are formed in or near their ground states (g.s.) [2], then the smooth variation seems to preclude the traditional macroscopic-microscopic [3,4] Z = 114 as a magic proton number in these nuclei. Recent phenomenological studies of BE(2) systematics [5] and of the persistence of the Wigner term in masses of heavy nuclei [6] indicate Z = 126 as the next spherical proton magic number after lead, and this is consistent with considerations based on nuclear diffuseness [7]. Recent self-consistent and relativistic mean field calculations [8–11] variously predict proton magicities for Z = 114, 120, 124 and 126. These new developments are contrary to the assumption made in the semiempirical shell-model mass equation (SSME) [12] (see also ref. [13]) that Z = 114 is the next proton magic number beyond lead. The equation stops at Z = 114, and it is unsuitable for extrapolation already earlier, beyond Hs (Z = 108), as shown by its increasing deviations from the data beyond that (like in fig. 4 of ref. [1]). One has to find an appropriate substitute for the equation in the neighbourhood of Z = 114 and beyond. During the early stages of the SSME [14], when it was adjusted separately in individual shell regions in the N − Z plane, both Z = 114 and Z = 126, which were at the time considered possible candidates for the post-lead proton magic number, were tried as a shell region boundary in each of the two heaviest regions with Z ≥ 82 and respective N boundaries 82 ≤ N ≤ 126 (called here region A) and 126 ≤ N ≤184 (called region B). The agreement with the data was about the same for both choices, and considering the prevailing view in