Symmetry Breaking and Bifurcations in the Periodic Orbit Theory: II -- Spheroidal Cavity --

Details Symmetry Breaking and Bifurcations in the Periodic Orbit Theory: II -- Spheroidal Cavity -- Symmetry Breaking and Bifurcations in the Periodic Orbit Theory: II -- Spheroidal Cavity --

2002-08-05

arxiv.org/abs/nlin/0208005v1

Prog.Theor.Phys. 108 (2002) 853-901

Nonlinear Sciences

Exactly Solvable and Integrable Systems

49 pages, 18 figures, using PTPTeX.cls(included), submitted to Prog. Theor. Phys

Scientific paper

10.1143/PTP.108.853

We derive a semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences and discontinuities occurring at bifurcation points and in the spherical limit, the trace integrals over the action-angle variables are performed using an improved stationary phase method. The resulting semiclassical level density oscillations and shell energies are in good agreement with quantum-mechanical results. We find that the births of three-dimensional orbits through the bifurcations of planar orbits in the equatorial plane lead to considerable enhancement of shell effect for superdeformed shapes.

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