- th / 0 00 80 19 v 1 1 0 A ug 2 00 0 1 Semiempirical Shell Model Masses with Magic Number Z = 126 for Translead Elements with N ≤ 126

A semiempirical shell model mass equation based on magic number Z = 126 and applicable to translead elements with N ≤ 126 is presented. For α-decay energies the equation is shown to have a high predictive power and an rms deviation from the data of about 100 keV. The rms deviations for masses and other mass differences are between about 200 and 300 keV. Recent progress in superheavy elements (SHE) research reaching to 293 118 and its α-decay products [1] makes it necessary to find an appropriate substitute for the semiempiri-cal shell-model mass equation (SSME) [2] (see also ref. [3]) for nuclei in the neighbourhood of Z = 114 and beyond [4]. The α energies of the decaying chain vary smoothly from 293 118 to 269 Sg (Z = 106), with no indication of magicity at Z = 114 in these nuclei [1], whereas the SSME assumes that Z = 114 is the next spherical proton magic number after lead and it stops there. Furthermore, the SSME becomes unsuitable for extrapolation already earlier, beyond Hs (Z = 108), as shown by its increasing deviations from the data when Z increases. (Like in fig. 4 of ref. [1].) 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 dif-fuseness [7]. Recent self-consistent and relativistic mean-field calculations [8–12] variously predict proton magicities for Z = 114, 120, 124 and 126. During the early stages of the SSME [13], 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 postlead proton magic number (see, e.g., ref. [14]), 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 the prevailing view in the mid nineteen-seventies led to the choice of Z = 114 for the SSME mass table [2]. In a recent communication [4] we showed that the early Z = 126 results have a high …