Mean-field theory of nuclear stability and exotic point-group symmetries

International audienceWe formulate the principles of the mean-field theory of nuclear stability employing the point-group, and group-representation theories. The related pointgroup hierarchy of importance in the context of nuclear stability is constructed and discussed. We introduce the notion of the magic-number chains associated with each symmetry- in analogy to the spherical-symmetry nuclear magic-numbers. To prepare the criteria for the experimental search of introduced symmetries we examine the simplified collective rotation-vibration model whose Hamiltonian is invariant under the symmetries in question. We illustrate the construction of the solutions that form at the same time irreducible-representations of the pointgroups in question- in view of formulating the experimental symmetry-criteria through the application of the branching-ratio techniques. Since the criteria may involve very weak transitions whose experimental research may be at the limit of the present-day experiments, the desires may arise, as it was the case in the past, to replace the difficult experiments by an inadequate modelling. In this context we present an alert: The use of oversimplified quantum mechanics exercises in place of experiments and/or microscopic theories is likely to produce meaningless results