dorsal/arxiv
View SchemaPeriodic Orbits and Shell Structure in Octupole Deformed Potentials
| Authors | W. Dieter Heiss, Rashid G. Nazmitdinov, Stefanel Radu |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9409024 |
| URL | https://arxiv.org/abs/nucl-th/9409024 |
| DOI | 10.1103/PhysRevB.51.1874 |
Abstract
The effect of an octupole term in a quadrupole deformed single particle potential is studied from the classical and quantum mechanical view point. 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 which 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 analysed 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.
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"abstract": "The effect of an octupole term in a quadrupole deformed single particle\npotential is studied from the classical and quantum mechanical view point.\nWhereas the problem is nonintegrable, the quantum mechanical spectrum\nnevertheless shows some shell structure in the superdeformed prolate case for\nparticular, yet fairly large octupole strengths; for spherical or oblate\ndeformation the shell structure disappears. This result is associated with\nclassical periodic orbits which are found by employing the removal of\nresonances method; this approximation method allows determination of the shape\nof the orbit and of the approximate octupole coupling strength for which it\noccurs. The validity of the method is confirmed by solving numerically the\nclassical equations of motion. The quantum mechanical shell structure is\nanalysed using the particle number dependence of the fluctuating part of the\ntotal energy. In accordance with the classical result this dependence turns out\nto be very similar for a superdeformed prolate potential plus octupole term and\na hyperdeformed prolate potential without octupole term. In this way the shell\nstructure is explained at least for some few hundred levels. The Fourier\ntransform of the level density further corroborates these findings.",
"arxiv_id": "nucl-th/9409024",
"authors": [
"W. Dieter Heiss",
"Rashid G. Nazmitdinov",
"Stefanel Radu"
],
"categories": [
"nucl-th",
"chao-dyn",
"chem-ph",
"cond-mat",
"nlin.CD"
],
"doi": "10.1103/PhysRevB.51.1874",
"title": "Periodic Orbits and Shell Structure in Octupole Deformed Potentials",
"url": "https://arxiv.org/abs/nucl-th/9409024"
},
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