Experimental nuclear moments of inertia at high spins along the yrast line have been determined systematically and found to differ from the rigid-body values. The difference is attributed to shell effects and these have been calculated microscopically. The data and quantal calculations are interpreted by means of the semiclassical Periodic Orbit Theory. From this new perspective, features in the moments of inertia as a function of neutron number and spin, as well as their relation to the shell energies can be understood. Gross shell effects persist up to the highest angular momenta observed.

Energies and excitation probabilities of compressional and vortical collective 1states are calculated in the frame of the time-dependent Hartree-Fock theory. The method of Wigner function moments is used to find collective solutions of an equation for a density matrix. Good agreement with experiment is obtained for the low-energy isoscalar dipole resonance in '08Pb. The toroidal excitation is predicted.

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We use a perturbative semiclassical trace formula to calculate the three lowest-order multipole (quadrupole ǫ2, octupole ǫ3, and hexadecapole ǫ4) deformations of simple metal clusters with 90 ≤ N ≤ 550 atoms in their ground states. The self-consistent mean field of the valence electrons is modeled by an axially deformed cavity and the oscillating part of the total energy is calculated semiclassically using the shortest periodic orbits. The average energy is obtained from a liquid-drop model adjusted to the empirical bulk and surface properties of the sodium metal. We obtain good qualitative agreement with the results of quantum-mechanical calculations using Strutinsky's shell-correction method.PACS numbers: 03.65. Sq, 05.30.Fk, 31.15.Ew, 71.10.Ca Free clusters made of simple metal atoms exhibit a pronounced electronic shell structure [1][2][3]. Although the detailed experimental information obtained, e.g., from photo-excitation measurements can only be understood if the ionic structure is taken into account [4], the qualitative features of the electronic shell structure can be well described, for not too small systems, by phenomenological deformed shell-model potentials [5][6][7]. Self-consistent density functional calculations in the framework of a deformed jellium model [8] have revealed that the cluster ground-state shapes can be well characterized in terms of the lowest three multipole orders ǫ 2 (quadrupole), ǫ 3 (octupole), and ǫ 4 (hexadecapole). Since such self-consistent calculations are quite time consuming computationally, it is often more efficient to resort to simpler methods, such as the shell-correction method introduced by Strutinsky in nuclear physics [9], in particular, if more shape degrees of freedom are to be investigated [7].An even more economical approach is the semiclassical periodic orbit theory (POT) (see, e.g., Ref.[10] for a general introduction), in which quantum oscillations in the level density or other observables can be described in terms of the leading shortest periodic orbits of the corresponding classical system through so-called trace formulae [11,12]. This method has been used for quadrupoledeformed clusters in a Nilsson-type model [13] and, more recently, using cavities with axial ǫ 2 , ǫ 3 , and ǫ 4 deformations [14,15]. The approximation of the self-consistent mean field of the valence electrons by a cavity with reflecting walls has received strong support from the quantitative explanation [14] of the experimental magic numbers found in connection with the electronic supershells [16] in terms of the trace formula of the spherical cavity [12]. The validity of the cavity model has also been confirmed by calculations with more realistic Woods-Saxon type potentials [17] and by selfconsistent Kohn-Sham calculations [18] in the spherical jellium model. In Ref.[15], a perturbative trace formula derived by Creagh [19] has been used for axially deformed cavities with small multipole deformations ǫ 2 , ǫ 3 , or ǫ 4 and found to reproduce the quantum-mechanical results very well...

Various fission processes are described in terms of high-dimensional potential energy surface in the frame of the Strutinsky shell correction method for actinide region. The complete deformation space is necessary to study the potential energy minima responsible for the cluster radioactivity, cold fission and cold multi-fragmentation valleys. The nuclear shape families for the different fission configurations are obtained without any specific change of the parameters. The coordinate system based on the Cassini ovaloids makes it possible to increase the number of independent deformation parameters without divergence. The higher orders of the deformation are shown to play an important role in the description of the potential energy surface structure.