Dynamical symmetries, multiclustering, and octupole susceptibility in superdeformed and hyperdeformed nuclei

Spectroscopy of superdeformed nuclear states opens up an exciting possibility to probe new properties of the nuclear mean field. In particular, the unusually deformed atomic nucleus can serve as a microscopic laboratory of quantum-mechanical symmetries of a three-dimensional harmonic oscillator. The quantum numbers and coupling schemes characteristic of weakly deformed systems are expected to be modified in the superdeformed world. New classification schemes can be directly related to certain geometrical properties of the nuclear shape.