Nuclear hyperdeformation and the Jacobi shape transition

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.