  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.
