Another group of problems relates to recent theoretical predictions of an
existence of new type of isomers whose shapes are not dominated by the
quadrupole elongation.
This prediction originally obtained with the Strutinsky method has recently
been confirmed by using the self-consistent Hartree-Fock plus BCS method.
Although the large elongations, like the super- and hyper-
deformations, are not present there, the possible validation of the
existence of these
states by experiment and deeper theoretical understanding of their quantum
behaviour carries at least the same importance as that of the
superdeformation as argumented below. It would be interesting to perform
here some new estimates on basis of the relativistic mean field theory.
We would like to derive the quantum manifestations of the
symmetry problem introduced above. Each of those symmetries manifest itself
via a set of conserved quantum numbers which differ from symmetry
to symmetry (for instance in the case of the C3-symmetry of the
cranking-field one may expect six families of rotational states in their
spectra while the "traditional" triaxial ellipsoid potential would generate
only 4 (determined essentially by combinations of both parities and
both signatures)).
We intend to apply the formalism based on the theory of irreducible
representations of the point groups and the corresponding relations with
(projections onto) the irreducible representations of the R3-group.
This would allow for the classification and theoretical predictions related
on one hand, to the single-particle spectra (single particle routhians) and
on the other hand to the corresponding many-body solutions.