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Journal of Mathematical Physics

The sum rule for spectroscopic factors in the seniority scheme of identical particles

Masao Nomura

Published Jan 1, 1987• 6 citations
Publisher

Abstract

Spectroscopic factors partitioning an identical-particle state into a couple of substates with definite seniorities are summed into a simple form. This sum rule is an extension of the reduction relation for the fixed-seniority average of a many-body operator. The seniority projection operator is utilized throughout the present formulation

DOI
10.1063/1.527793

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Spectroscopic factors partitioning an identical-particle state into a couple of substates with definite seniorities are summed into a simple form. This sum rule is an extension of the reduction relation for the fixed-seniority average of a many-body operator. The seniority projection operator is utilized throughout the present formulation
The seniority scheme introduced by Racah is generalized in the case of degenerate levels. Many formulae for the pure configuration j n are modified in order to calculate matrix elements in this generalized seniority scheme. It is especially the most interesting result that the diagonal matrix element of two-body operators between the states with the same seniority v can be expressed in terms of the matrix elements in the v -particle system. This result, of course, holds in the case of the pure configuration.