Periodic-Orbit Bifurcations and Superdeformed Shell Structure

Abstract

We have derived a semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences occurring at bifurcations and in the spherical limit, the trace integrals over the action-angle variables were performed using an improved stationary phase method. The resulting semiclassical level density oscillations and shell-correction energies are in good agreement with quantum-mechanical results. We find that the bifurcations of some dominant short periodic orbits lead to an enhancement of the shell structure for "superdeformed" shapes related to those known from atomic nuclei.

4 pages including 3 figures

References in corpus (4)

• Symmetry Breaking and Bifurcations in the Periodic Orbit Theory: I: Elliptic Billiard
• Uniform trace formulae for SU(2) and SO(3) symmetry breaking
• Semiclassical Origin of Superdeformed Shell Structure in the Spheroidal Cavity Model
• Classical orbit bifurcation and quantum interference in mesoscopic magnetoconductance

Cited by in corpus (6)

• Gross shell structure at high spin in heavy nuclei
• Shell structure and orbit bifurcations in finite fermion systems
• Semiclassical catastrophe theory of simple bifurcations
• Shells, orbit bifurcations and symmetry restorations in Fermi systems
• Semiclassical approaches to nuclear dynamics
• Quantum Mechanical Approach to Bifurcation Point Detection in Hamiltonian Dynamical Systems