Symmetry Breaking and Bifurcations in the Periodic Orbit Theory: II --   Spheroidal Cavity --
  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. 
A.G. Magner, K. Arita, S.N. Fedotkin and K. Matsuyanagi