Statistical Group Theory and the Distribution of Angular Momentum States

The problem of developing relations for the statistical distribution of the angular momentum states of an electron configuration lN , where l and N are large, has been considered. If D(L) is the number of times the orbital angular momentum L occurs, then, using the theory of partitions and groups, w...

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Bibliographic Details
Published in:Journal of mathematical physics 1971-01, Vol.12 (1), p.45-52
Main Authors: Cleary, J. G., Wybourne, B. G.
Format: Article
Language:English
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Summary:The problem of developing relations for the statistical distribution of the angular momentum states of an electron configuration lN , where l and N are large, has been considered. If D(L) is the number of times the orbital angular momentum L occurs, then, using the theory of partitions and groups, we find that the numbers D(L) are approximately distributed with respect to L according to the Wigner‐type form D(L)=A(L+ 1 2 )  exp  [−(L+ 1 2 ) 2 /2σ 2 ] . A number of examples are examined.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1665484