Physics of Atomic Nuclei

, 74:1445 | Cite as

Shell structure and orbit bifurcations in finite fermion systems

  • A. G. Magner
  • I. S. Yatsyshyn
  • K. Arita
  • M. Brack
Nuclei Theory

Abstract

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 self-consistent 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.C. 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).

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • A. G. Magner
    • 1
  • I. S. Yatsyshyn
    • 1
  • K. Arita
    • 2
  • M. Brack
    • 3
  1. 1.Institute for Nuclear ResearchNational Academy of Sciences of UkraineKyivUkraine
  2. 2.Department of PhysicsNagoya Institute of TechnologyNagoyaJapan
  3. 3.Institute for Theoretical PhysicsUniversity of RegensburgRegensburgGermany

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