Abundance and systematics of nuclear superdeformed states; relation to the pseudospin and pseudo-SU(3) symmetries

Results of a multidimensional (..beta../sub 2/, ..gamma.., ..beta../sub 4/, ..omega.., Z, and N) search for nuclear superdeformed configurations are presented. Calculations based on a realistic deformed average field give a relatively strong dependence of the ''super'' elongation on the particle number. This dependence is shown to be a cyclic function of the particle number. It originates from the pseudospin and pseudo-SU(3) symmetries which are obeyed approximately in a realistic average field.