Shell structure and orbit bifurcations in finite fermion systems

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 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)

References in corpus (4)

• Transcritical bifurcations in non-integrable Hamiltonian systems
• Normal forms and uniform approximations for bridge orbit bifurcations
• On the ground--state energy of finite Fermi systems
• Closed-orbit theory for spatial density oscillations

Cited by in corpus (16)

• Nuclear Theory and Science of the Facility for Rare Isotope Beams
• Periodic-orbit approach to the nuclear shell structures with power-law potential models: Bridge orbits and prolate-oblate asymmetry
• Chaoticity and Shell Effects in the Nearest-Neighbor Distributions
• Level density within a micro-macroscopic approach
• Semiclassical shell-structure micro-macroscopic approach for the level density
• Semiclassical trace formula for the two-dimensional radial power-law potentials
• Semiclassical catastrophe theory of simple bifurcations
• Shell-structure and asymmetry effects in level densities
• Semiclassical trace formula for truncated spherical well potentials: Toward the analyses of shell structures in nuclear fission processes
• Shells, orbit bifurcations and symmetry restorations in Fermi systems
• Semiclassical treatment of symmetry breaking and bifurcations in a non-integrable potential
• Semiclassical approaches to nuclear dynamics
• Microscopic-macroscopic level densities for low excitation energies
• Surface corrections to the moment of inertia and shell structure in finite Fermi systems
• Semiclassical and quantum shell-structure calculations of the moment of inertia
• Particle-number fluctuations near the critical point of nuclear matter