Shell structure and orbit bifurcations in finite fermion systems

• Published in: Physics of atomic nuclei Vol. 74; no. 10; pp. 1445 - 1477
• Main Authors: Magner, A. G., Yatsyshyn, I. S., Arita, K., Brack, M.
• Format: Journal Article
• Language: English
• Published: Dordrecht SP MAIK Nauka/Interperiodica 01.10.2011; Springer
• Subjects: ACTINIDE NUCLEI; CORRECTIONS; FERMIONS; FISSION; FISSION BARRIER; FISSION ISOMERS; HARMONIC OSCILLATORS; INTEGRAL CALCULUS; NUCLEAR DEFORMATION; NUCLEAR PHYSICS AND RADIATION PHYSICS; NUCLEAR STRUCTURE; Nuclei; OSCILLATIONS; Particle and Nuclear Physics; PERIODICITY; Physics; Physics and Astronomy; SEMICLASSICAL APPROXIMATION; SHELL MODELS; SUPERDEFORMED NUCLEI; WOODS-SAXON POTENTIAL; Atomic Nucleus; Shell Structure; Level Density; Trace Formula; Cavity Model
• ISSN: 1063-7788; 1562-692X
• DOI: 10.1134/S1063778811100061

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).