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Prog. Theor. Phys. Vol. 28 No. 1 (1962) pp. 1-23
On the Energy Distribution of Terms and Line Arrays in Atomic Spectra
Steven A. Moszkowski
The RAND Corporation, Santa Monica, California, U.S.A.
and
University of California, Los Angeles, California, U.S.A.
(Received December 4, 1961)
Abstract:
The Coulomb interaction leads to a splitting of the different terms belonging to the same many-electron configuration. We have studied the resulting energy distributions of terms and also of line arrays for transitions between different configurations. Expressions are derived for the first two moments of the distributions, namely, the average energy shift and the mean square deviation, as a function of the number of particles. The detailed shapes of the distributions are investigated both for (d)n configurations and for a simplified two-dimensional model.
URL :
http://ptp.ipap.jp/link?PTP/28/1/
DOI : 10.1143/PTP.28.1
References:
- Such relations between mean interactions energies are, in fact, well known.
- Strengths of individual lines and sum rules involving line strengths but not energies, have previously been studied in the literature.
See, for example, D. H. Menzel and L. Goldberg, Astrophys. J. 84 (1936), 1[CrossRef];
F. Rohrlich, Astrophys. J. 129 (1959), 441[CrossRef].
For comprehensive discussions of line strengths see Condon and Shortley, Theory of Atomic Spectra, and W. Slater, Quantum Theory of Atomic Structure, (McGraw-Hill Company, New York, 1960) Vol. II, Chap. 25.
The latter contains an extensive bibliography.
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See G. Racah, Phys. Rev. 63 (1943), 347, [APS]for a simple discussion of the method of fractional parentage coefficients and its applications.
- For a more detailed discussion of this model and some general considerations regarding term and line array distributions, see S. A. Moszkowski, Some Statistical Properties of Level and Line Distributions in Atomic Spectra, The RAND Corporation, Research Memorandum RM-2610-AEC, November 8, 1960.
- The dominant central-field term in the multipole expansion (Slater integral F°) does not lead to any splitting of terms, and consequently it does not affect the shape of our distribution.
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G. Racah, Phys. Rev. 62 (1942), 438[APS].
- Properties of the Racah coefficients and other quantities used in this Appendix are summarized by H. Horie and T. Ishidzu, ed., in Part I of Tables of the Racah Coefficients, (Pan Pacific Press, Tokyo, 1960).
See also, A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, 1957); M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957); and Rotenberg, Bivins, Metropolis and Wooten, The 3-j and 6-j Symbols (Cambridge University Press, MIT, 1959).
Citing Article(s) :
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Progress of Theoretical Physics Vol. 43 No. 2 (1970) pp. 556-557
:
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The Moszkowski's Relation and the Second Moment of Energy for a Given Seniority or Isospin in a Single Shell
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Masao Nomura
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Progress of Theoretical Physics Vol. 47 No. 6 (1972) pp. 1858-1877
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Sum Rules for Many-Particle Matrix Elements in the Seniority Scheme
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Masao Nomura
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Progress of Theoretical Physics Vol. 48 No. 1 (1972) pp. 110-132
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Reduction Relations for the Third and the Fourth Moments of Energy Spectra in a Many-Particle Configuration
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Masao Nomura
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Progress of Theoretical Physics Vol. 48 No. 2 (1972) pp. 442-458
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Distribution of Energy Spectra in a Large j Shell
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Masao Nomura
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Progress of Theoretical Physics Vol. 51 No. 2 (1974) pp. 489-505
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A Calculation Method for a High Moment of Energy Spectra
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Masao Nomura
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Progress of Theoretical Physics Vol. 59 No. 4 (1978) pp. 1199-1212
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Study of Gaussian Distribution in Nuclear Spectroscopy
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Masao Nomura
