Shell-correction energies determine the stability and the fission barriers of Super-Heavy Nuclei (SHN), the latter being a main factor responsible for their production yield. Although recent experiments performed at FLNR in Dubna (see review articles [1,2]) have confirmed the existence of an island of SHN, the site and strength of highest stability is still uncertain. Predicted Q values as shown in Fig. 1a reveal the ambiguity. The macroscopic-micro-scopic (MM) models [3,4] predict a closed proton shell at Z = 114 and thus increasing Q values beyond. The chiral mean-field model (CMF) [5] and the semi-empirical model (SE) [6] predict subshells or shells at 120 and 126, respectively, resulting in less steep or even decreasing Q values. Experimental data, also shown in Fig. 1a and known up to Z = 116 do not give preference to a specific model. However, decisive information could be obtained from the -decay properties of elements 118 and 120. The following discussion supports our search experiment for element 120. The study also reveals an important uncertainty related to the prediction of cross-sections of the synthesis of SHN.
Shell-correction energiesModel dependent experimental shell-correction energies can be deduced from measured nuclear masses by subtraction of theoretically determined liquid-drop masses. In our case, however, absolute experimental nuclear masses are not known, but relative values can be determined for nuclei within an -decay chain using the experimental Q values. Normalizing these relative masses to the theoretical ones at the end of the decay chain, which is closer to the region of known masses, where relatively good agreement was established [7], results in a reliable approximation of masses up to the heaviest nuclei of the -decay chain. In one case, where a relatively long decay chain starting at 291 Lv and ending at 267 Rf is known, we have performed such an estimate of shell-correction energies. Interestingly, this is the decay chain which would be populated in a 3n channel of the reaction 54 Cr + 248 Cm. In Figs. 1b and 1c, Rf to 279 Ds were normalized by a least squares fit to the theoretical masses. In order to distinguish between the so determined masses, shell-correction energies and fission barriers from the theoretical ones, we denote those 'experimental data' in the following.