Constraining the shell correction energies of super-heavy nuclei
Abstract.The existence of super-heavy nuclei can only be explained by the introduction of stabilizing ground state shell effects. The macroscopic-microscopic masses are constructed from the sum of a macroscopic, liquid-drop, energy contribution and a microscopic, shell correction energy. In the present study, shell correction energies are inferred by subtracting the liquid-drop contributions to their corresponding experimental masses. As most super-heavy nuclei masses are not precisely known, they are deduced from measured $ Q_{\alpha}$Qα values. Furthermore, a detailed uncertainty analysis regarding experimental masses and more importantly the liquid-drop masses delivers decisive theoretical constraints on shell correction energies. The current work focuses on two $ \alpha$α decay chains, the first following from a hot fusion reaction leading to the synthesis of 291Lv , and the second following from a cold fusion reaction leading to the synthesis of 277Cn . Contrasting the outcomes obtained for these two decay chains demonstrates that mass measurement precisions of about 50keV are required in order to efficiently constrain the shell correction energies of super-heavy nuclei.