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Prog. Theor. Phys. Vol. 108 No. 5 (2002) pp. 853-901

[ Full Text PDF : FREE ACCESS (1185K) ]

Symmetry Breaking and Bifurcations in the Periodic Orbit Theory. II

— Spheroidal Cavity —

Alexander G. Magner,1,2,3 Ken-ichiro Arita,4 Sergey N. Fedotkin2,3 and Kenichi Matsuyanagi5

1Research Center for Nuclear Physics, Osaka University, Ibaraki 567-0047, Japan
2Institute for Nuclear Research, 03680 Prospekt Nauki 47, Kiev-28, Ukraine
3Institute for Theoretical Physics, University of Regensburg, D-93040 Regensburg, Germany
4Department of Physics, Nagoya Institute of Technology, Nagoya 466-8555, Japan
5Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan

(Received August 5, 2002)

Abstract:

We derive a semiclassical trace formula for the level density of a 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 the shell effect for superdeformed shapes.


URL : http://ptp.ipap.jp/link?PTP/108/853/
DOI : 10.1143/PTP.108.853

[ Full Text PDF : FREE ACCESS (1185K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 115 No. 3 (2006) pp. 523-546 :
    Semiclassical Approach for Bifurcations in a Smooth Finite-Depth Potential
    Alexander G. Magner, Ken-ichiro Arita and Sergey N. Fedotkin

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