Periodic-orbit bifurcations and superdeformed shell structure - art. no. 065201

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 ac tion-angle variables were performed using an improved stationary phase meth od. The resulting semiclassical level density oscillations and shell-correc tion energies are in good agreement with quantum-mechanical results. We fin d that the bifurcations of some dominant short periodic orbits lead to an e nhancement of the shell structure for "superdeformed" shapes related to tho se known from atomic nuclei.