Periodic-Orbit Bifurcations and Superdeformed Shell Structure

Details Periodic-Orbit Bifurcations and Superdeformed Shell Structure Periodic-Orbit Bifurcations and Superdeformed Shell Structure

2001-01-19

arxiv.org/abs/nlin/0101035v2

Phys.Rev.E63:065201,2001

Nonlinear Sciences

Exactly Solvable and Integrable Systems

4 pages including 3 figures

Scientific paper

10.1103/PhysRevE.63.065201

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 action-angle variables were performed using an improved stationary phase method. The resulting semiclassical level density oscillations and shell-correction energies are in good agreement with quantum-mechanical results. We find that the bifurcations of some dominant short periodic orbits lead to an enhancement of the shell structure for "superdeformed" shapes related to those known from atomic nuclei.

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