Shell structure and orbit bifurcations in finite fermion systems
- National Academy of Sciences of Ukraine, Institute for Nuclear Research (Ukraine)
- Nagoya Institute of Technology, Department of Physics (Japan)
- University of Regensburg, Institute for Theoretical Physics (Germany)
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).
- OSTI ID:
- 22043847
- Journal Information:
- Physics of Atomic Nuclei, Vol. 74, Issue 10; Other Information: Copyright (c) 2011 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7788
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ACTINIDE NUCLEI
CORRECTIONS
FERMIONS
FISSION
FISSION BARRIER
FISSION ISOMERS
HARMONIC OSCILLATORS
INTEGRAL CALCULUS
NUCLEAR DEFORMATION
NUCLEAR STRUCTURE
OSCILLATIONS
PERIODICITY
SEMICLASSICAL APPROXIMATION
SHELL MODELS
SUPERDEFORMED NUCLEI
WOODS-SAXON POTENTIAL