▪ Abstract In the first century of nuclear physics, 31 radioactive elements were added to the periodic system of elements. In 1996, at GSI, element 112 was synthesized by fusion of70Zn with208Pb, and its atomic number was established by a decay chain linked to known isotopes. Relativistic mean field calculations of the ground-state stability of nuclei predict the next spherical proton shell not as previously assumed at Z = 114 but at Z = 120 for304184120. Moreover, a region of spherical nuclei with depleted central density is predicted at N = 172 for292172120 by mean field calculations. New elements are established today using recoil separators combined with decay-chain analysis. Three new elements, Z = 110–112, and 18 transactinide isotopes have been discovered since 1985, all assigned by genetical linkage to known isotopes. The production cross sections decrease exponentially going to higher elements and now have reached the 1-pb limit. Fusion aiming at higher and higher atomic numbers is a self-terminated process because of constantly increasing disruptive Coulomb forces. The limitations in the formation and deexcitation stages are presented. The rapid drop to smaller cross sections (“Coulomb falls”) is modified by nuclear structure not only in the ground state of the final product (superheavy element) but also in the collision partners and during the amalgamation process (closed shells and clusters). The prospects to produce higher elements and new isotopes by extrapolating the physics learned from reaching Z = 112 are283114, which might be found in76Ge/208Pb at a level of 0.1 pb and linked to259No. At this level, about 30 transactinide isotopes are still in reach. To explain the stabilization of production cross sections in the pb range claimed in 1999 experiments, new physics delaying the descent in the “Coulomb falls” is to appear. For the FLNR experiments claiming Z = 114, no explanation is offered. For the LBL experiment claiming Z = 118, an explanation from new physics is presented. All experiments need confirmation. Verifying the centrally depleted, spherical nuclei around292172120 would be a victory for nuclear structure physics, much more interesting than the trivial case of another doubly closed shell nucleus.
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