Semiclassical quantization of the shell model

R. D. Williams, S. E. Koonin

Research output: Contribution to journalArticle

Abstract

The classical limit of the nuclear shell model is shown to be a many-dimensional hamiltonian system in which the coordinates and momenta are the coherent-state parameters of the original quantum system. Several methods for semiclassical quantization of this system are discussed, including surfaces of section and the Birkhoff-Gustavson transformation to action-angle variables. Application to a schematic three-level shell model indicates some of the new problems involved in requantizing multi-dimensional systems which are not present in one-dimensional examples. These include difficulties in finding periodic orbits and the onset of stochasticity.

Original languageEnglish (US)
Pages (from-to)72-92
Number of pages21
JournalNuclear Physics, Section A
Volume391
Issue number1
DOIs
StatePublished - Dec 20 1982

Fingerprint

circuit diagrams
orbits
momentum

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Semiclassical quantization of the shell model. / Williams, R. D.; Koonin, S. E.

In: Nuclear Physics, Section A, Vol. 391, No. 1, 20.12.1982, p. 72-92.

Research output: Contribution to journalArticle

Williams, R. D. ; Koonin, S. E. / Semiclassical quantization of the shell model. In: Nuclear Physics, Section A. 1982 ; Vol. 391, No. 1. pp. 72-92.
@article{c8f4b2ec931f4cd5b571c8843dead3a0,
title = "Semiclassical quantization of the shell model",
abstract = "The classical limit of the nuclear shell model is shown to be a many-dimensional hamiltonian system in which the coordinates and momenta are the coherent-state parameters of the original quantum system. Several methods for semiclassical quantization of this system are discussed, including surfaces of section and the Birkhoff-Gustavson transformation to action-angle variables. Application to a schematic three-level shell model indicates some of the new problems involved in requantizing multi-dimensional systems which are not present in one-dimensional examples. These include difficulties in finding periodic orbits and the onset of stochasticity.",
author = "Williams, {R. D.} and Koonin, {S. E.}",
year = "1982",
month = "12",
day = "20",
doi = "10.1016/0375-9474(82)90220-2",
language = "English (US)",
volume = "391",
pages = "72--92",
journal = "Nuclear Physics A",
issn = "0375-9474",
publisher = "Elsevier",
number = "1",

}

TY - JOUR

T1 - Semiclassical quantization of the shell model

AU - Williams, R. D.

AU - Koonin, S. E.

PY - 1982/12/20

Y1 - 1982/12/20

N2 - The classical limit of the nuclear shell model is shown to be a many-dimensional hamiltonian system in which the coordinates and momenta are the coherent-state parameters of the original quantum system. Several methods for semiclassical quantization of this system are discussed, including surfaces of section and the Birkhoff-Gustavson transformation to action-angle variables. Application to a schematic three-level shell model indicates some of the new problems involved in requantizing multi-dimensional systems which are not present in one-dimensional examples. These include difficulties in finding periodic orbits and the onset of stochasticity.

AB - The classical limit of the nuclear shell model is shown to be a many-dimensional hamiltonian system in which the coordinates and momenta are the coherent-state parameters of the original quantum system. Several methods for semiclassical quantization of this system are discussed, including surfaces of section and the Birkhoff-Gustavson transformation to action-angle variables. Application to a schematic three-level shell model indicates some of the new problems involved in requantizing multi-dimensional systems which are not present in one-dimensional examples. These include difficulties in finding periodic orbits and the onset of stochasticity.

UR - http://www.scopus.com/inward/record.url?scp=0003114191&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0003114191&partnerID=8YFLogxK

U2 - 10.1016/0375-9474(82)90220-2

DO - 10.1016/0375-9474(82)90220-2

M3 - Article

AN - SCOPUS:0003114191

VL - 391

SP - 72

EP - 92

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

IS - 1

ER -