Periodic orbits and shell structure in octupole deformed potentials

Journal Article · Sun Jan 15 04:00:00 EST 1995 · Physical Review, B: Condensed Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.51.1874· OSTI ID:6640336

Heiss, W D ^[1]; Nazmitdinov, R G ^[2]; Radu, S ^[1]

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1. Centre for Nonlinear Studies and Department of Physics, University of the Witwatersrand, P.O. Wits 2050, Johannesburg (South Africa)
2. Departamento de Fisica Teorica C-XI, Universidad Autonoma de Madrid, E-28049 Madrid (Spain)

The effect of an octupole term in a quadrupole deformed single-particle potential is studied from the classical and quantum-mechanical viewpoint. Whereas the problem is nonintegrable, the quantum-mechanical spectrum nevertheless shows some shell structure in the superdeformed prolate case for particular, yet fairly large octupole strengths; for spherical or oblate deformation the shell structure disappears. This result is associated with classical periodic orbits that are found by employing the removal of resonances method; this approximation method allows determination of the shape of the orbit and of the approximate octupole coupling strength for which it occurs. The validity of the method is confirmed by solving numerically the classical equations of motion. The quantum-mechanical shell structure is analyzed using the particle-number dependence of the fluctuating part of the total energy. In accordance with the classical result, this dependence turns out to be very similar for a superdeformed prolate potential plus octupole term and a hyperdeformed prolate potential without octupole term. In this way the shell structure is explained at least for some few hundred levels. The Fourier transform of the level density further corroborates these findings.

• OSTI ID: 6640336
• Journal Information: Physical Review, B: Condensed Matter; (United States), Journal Name: Physical Review, B: Condensed Matter; (United States) Vol. 51:3; ISSN 0163-1829; ISSN PRBMDO
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
664500 -- Special Atoms & Molecules-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ATOMIC CLUSTERS
DEFORMATION
DIFFERENTIAL EQUATIONS
ENERGY LEVELS
EQUATIONS
EQUATIONS OF MOTION
FERMI GAS
FLUIDS
GASES
MATHEMATICAL MODELS
MULTIPOLES
NUCLEAR MODELS
OCTUPOLES
ORBITS
PARTIAL DIFFERENTIAL EQUATIONS
SHELL MODELS