Shell structure and orbit bifurcations in finite fermion systems
| Autor: | Alexander G. Magner, Ken-ichiro Arita, I. S. Yatsyshyn, Matthias Brack |
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| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
Physics
Nuclear and High Energy Physics Nuclear Theory Nuclear structure Shell (structure) Semiclassical physics FOS: Physical sciences Fermion Mathematical Physics (math-ph) Atomic and Molecular Physics and Optics Nuclear Theory (nucl-th) Classical mechanics Quantum system Woods–Saxon potential Orbit (control theory) Harmonic oscillator Mathematical Physics |
| Popis: | We first give an overview of the shell-correction method which was developed by V. M. Strutinsky as a practicable and efficient approximation to the general selfconsistent theory of finite fermion systems suggested by A. B. Migdal and collaborators. Then we present in more detail a semiclassical theory of shell effects, also developed by Strutinsky following original ideas of M. Gutzwiller. We emphasize, in particular, the influence of orbit bifurcations on shell structure. We first give a short overview of semiclassical trace formulae, which connect the shell oscillations of a quantum system with a sum over periodic orbits of the corresponding classical system, in what is usually called the "periodic orbit theory". We then present a case study in which the gross features of a typical double-humped nuclear fission barrier, including the effects of mass asymmetry, can be obtained in terms of the shortest periodic orbits of a cavity model with realistic deformations relevant for nuclear fission. Next we investigate shell structures in a spheroidal cavity model which is integrable and allows for far-going analytical computation. We show, in particular, how period-doubling bifurcations are closely connected to the existence of the so-called "superdeformed" energy minimum which corresponds to the fission isomer of actinide nuclei. Finally, we present a general class of radial power-law potentials which approximate well the shape of a Woods-Saxon potential in the bound region, give analytical trace formulae for it and discuss various limits (including the harmonic oscillator and the spherical box potentials). LaTeX, 67 pp., 30 figures; revised version (missing part at end of 3.1 implemented; order of references corrected) |
| Databáze: | OpenAIRE |
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