Shell structure and orbit bifurcations in finite fermion systems View Full Text


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Article Info

DATE

2011-10-12

AUTHORS

A. G. Magner, I. S. Yatsyshyn, K. Arita, M. Brack

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). More... »

PAGES

1445

References to SciGraph publications

  • 1997-03-01. On the role of classical orbits in mesoscopic electronic systems in ZEITSCHRIFT FÜR PHYSIK D ATOMS,MOLECULES AND CLUSTERS
  • 1995-06. Triaxial shapes of sodium clusters in ZEITSCHRIFT FÜR PHYSIK D ATOMS,MOLECULES AND CLUSTERS
  • 1970-01. Stationary-phase method for Feynman's continual integral in THEORETICAL AND MATHEMATICAL PHYSICS
  • 1989-07. Shell structure in deformed nuclei and nuclear fission in PRAMANA
  • 1977-09. Semiclassical interpretation of the gross-shell structure in deformed nuclei in ZEITSCHRIFT FÜR PHYSIK A HADRONS AND NUCLEI
  • 1979-12. Energy- andN-averagings in the shell correction method in ZEITSCHRIFT FÜR PHYSIK A HADRONS AND NUCLEI
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1134/s1063778811100061

    DOI

    http://dx.doi.org/10.1134/s1063778811100061

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