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

A. G. Magner·K. Arita·S. N. Fedotkin·K. Matsuyanagi
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Abstract

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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A. G. Magner, K. Arita, S. N. Fedotkin, K. Matsuyanagi. 2002-08-05. Symmetry Breaking and Bifurcations in the Periodic Orbit Theory: II -- Spheroidal Cavity --. https://doi.org/10.1143/ptp.108.853

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