[en] A new island of superdeformed nuclei with major-to-minor axis ratio of 2:1 has recently been discovered in the A ∼ 80 medium-mass region, confirming the predictions for the existence of a large SD gap at particle number N,Z ∼ 44. The general properties of more than 20 bands observed so far will be reviewed here, and compared with those of the superdeformed bands in the heavier nuclei

[en] The discovery of the triaxial superdeformed bands provide a new opportunity to understand the axial symmetry breaking even in highly elongated nuclei. A total of 17 triaxial superdeformed nuclei in the mass A∼160 region and 11 in the mass A∼80 region are predicted by the three dimensional total surface calculations. A possible way to identify the triaxiality of triaxial superdeformed nuclei is suggested

[en] A parametrization of hexadecapole deformation is suggested when both quadrupole and hexadecapole deformation are considered and the intrinsic frame is defined in terms of quadrupole deformation

[en] The authors have systematically analysed the dynamic moments of inertia of the experimental superdeformed (SD) bands observed in the A = 190, 150 and 60-80 mass regions as functions of rotational frequency. By combining the different mass regions, the dramatic features of the dynamic moments of inertia were found and explained based on the calculations of the pairing fields of SD nuclei with the anisotropic harmonic oscillator quadrupole pairing Hartree-Fock-Bogoliubov model

[en] Present large scale shell model calculations give a very accurate and comprehensive description of light and medium light nuclei. Full pf-shell calculations have made it possible to describe many collective features in an spherical shell model context. Calculations including two major oscillator shells can cope with superdeformed bands. The underlying symmetries are seen to be variants of Elliott's SU3

[en] New methods to identify the high- and low-spin HD cluster states are suggested. (author)

[en] The possibility that atomic nuclei possess stable, extremely elongated (hyperdeformed) shapes at very high angular momentum is investigated in the light of the most recent experimental results. The crucial role of the Jacobi shape transitions for the population of hyperdeformed states is discussed and emphasized. State-of-the-art mean-field calculations including the most recent parametrization of the liquid-drop energy together with thermal effects and minimization algorithms allowing the spanning of a large deformation space predict the existence of a region of hyperdeformed nuclei in the mass A∼120-130: Te, Cs, Xe, I, and Ba isotopes. In agreement with predictions presented in reviews by J. Dudek, K. Pomorski, N. Schunck, and N. Dubray [Eur. Phys. J. A 20, 15 (2003)] and J. Dudek, N. Schunck, and N. Dubray [Acta Phys Pol. B 36, 975 (2005)], our extended calculations predict that only very short hyperdeformed bands composed of a dozen discrete transitions at the most are to be expected-in contrast to the results known for the superdeformed bands. We stress the importance of the experimental research in terms of multiple-γ correlation analysis that proved to be very efficient for the superdeformation studies and seems very helpful in the even more difficult search for the discrete transitions in hyperdeformed nuclei

[en] Relationship between quantum shell structure and classical periodic orbits is briefly reviewed on the basis of semi-classical trace formula. Using the spheroidal cavity model, it is shown that three-dimensional periodic orbits, which are born out of bifurcation of planar orbits at large prolate deformations, generate the superdeformed shell structure

[en] Deformed Gaussian Ensembles of Random Matrices are used to describe situations intermediate between fully chaotic complex quantum systems and regular ones. Such descriptions encompass the study of discrete symmetry breaking in nuclei, atoms and mesoscopic systems. In this short review we present several of the recent developments in this area. The deformation of Gaussian Ensembles is enforced through the use of the maximum entropy principle with appropriate constraints. The resulting Deformed Gaussian Ensemble (DGE) is applied to study isospin symmetry breaking in nuclei, the metal-insulator transition in condensed matter and in the evolution of level curvature distribution. More recently, this theory is applied to study the dependence of tunneling on the degree of chaoticity in the decay out of superdeformed bands in heavy nuclei. We derive and discuss the average level density of the DGE

No abstract available