dorsal/arxiv
View SchemaStatistics of electromagnetic transitions as a signature of chaos in many-electron atoms
| Authors | V. V. Flambaum, A. A. Gribakina, G. F. Gribakin |
|---|---|
| Categories | |
| ArXiv ID | physics/9802003 |
| URL | https://arxiv.org/abs/physics/9802003 |
| DOI | 10.1103/PhysRevA.58.230 |
Abstract
Using a configuration interaction approach we study statistics of the dipole matrix elements (E1 amplitudes) between the 14 lower odd states with J=4 and 21st to 100th even states with J=4 in the Ce atom (1120 lines). We show that the distribution of the matrix elements is close to Gaussian, although the width of the Gaussian distribution, i.e. the root-mean-square matrix element, changes with the excitation energy. The corresponding line strengths are distributed according to the Porter-Thomas law which describes statistics of transition strengths between chaotic states in compound nuclei. We also show how to use a statistical theory to calculate mean squared values of the matrix elements or transition amplitudes between chaotic many-body states. We draw some support for our conclusions from the analysis of the 228 experimental line strengths in Ce [J. Opt. Soc. Am. v. 8, p. 1545 (1991)], although direct comparison with the calculations is impeded by incompleteness of the experimental data. Nevertheless, the statistics observed evidence that highly excited many-electron states in atoms are indeed chaotic.
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"abstract": "Using a configuration interaction approach we study statistics of the dipole\nmatrix elements (E1 amplitudes) between the 14 lower odd states with J=4 and\n21st to 100th even states with J=4 in the Ce atom (1120 lines). We show that\nthe distribution of the matrix elements is close to Gaussian, although the\nwidth of the Gaussian distribution, i.e. the root-mean-square matrix element,\nchanges with the excitation energy. The corresponding line strengths are\ndistributed according to the Porter-Thomas law which describes statistics of\ntransition strengths between chaotic states in compound nuclei. We also show\nhow to use a statistical theory to calculate mean squared values of the matrix\nelements or transition amplitudes between chaotic many-body states. We draw\nsome support for our conclusions from the analysis of the 228 experimental line\nstrengths in Ce [J. Opt. Soc. Am. v. 8, p. 1545 (1991)], although direct\ncomparison with the calculations is impeded by incompleteness of the\nexperimental data. Nevertheless, the statistics observed evidence that highly\nexcited many-electron states in atoms are indeed chaotic.",
"arxiv_id": "physics/9802003",
"authors": [
"V. V. Flambaum",
"A. A. Gribakina",
"G. F. Gribakin"
],
"categories": [
"physics.atom-ph",
"chao-dyn",
"cond-mat.mes-hall",
"nlin.CD"
],
"doi": "10.1103/PhysRevA.58.230",
"title": "Statistics of electromagnetic transitions as a signature of chaos in many-electron atoms",
"url": "https://arxiv.org/abs/physics/9802003"
},
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