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Physical Review A

Two-body-operator matrix elements in SU(n) for application to complex spectroscopy

R. D. Kent, M. Schlesinger

Published Nov 1, 1987• 5 citations
Publisher

Abstract

We present a derivation of closed-form algebraic expressions for two-body operators in the context of the special-unitary-group approach to complex spectroscopy. The method involves the use of a graphical representation of the permutational symmetry-adapted irreducible-representation basis which facilitates the decomposition of the matrix elements into simple factors. The results afford significant reductions of computational complexity in cases pertaining to higher-than-spin-1/2 N-particle systems.

DOI
10.1103/physreva.36.4737

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We present a derivation of closed-form algebraic expressions for two-body operators in the context of the special-unitary-group approach to complex spectroscopy. The method involves the use of a graphical representation of the permutational symmetry-adapted irreducible-representation basis which facilitates the decomposition of the matrix elements into simple factors. The results afford significant reductions of computational complexity in cases pertaining to higher-than-spin-1/2 N-particle systems.
A detailed exposition of explicit formulas used in the evaluation of raising-raising forms of two-body-operator matrix elements is presented. The methods are based on the use of the unitary-group distinct-row tabular-graphical representation of the many-particle basis. All matrix elements are expressible in the form of scalar and 2\ifmmode\times\else\texttimes\fi{}2 matrix factors. In order to facilitate the derivations of simple, computationally efficient forms for the matrix factors we develop a calculus based on elementary graphs. The methods are applicable to systems of particles involving spins greater than (1/2 and reduce to previously known results for the case of spin (1/2.
A detailed exposition of explicit formulas used in the evaluation of raising-lowering forms of two-body-operator matrix elements is presented. The methods are based on the use of the unitary group distinct row table and graphical representation of the many-particle basis. All matrix elements are expressible in terms of scalar and simple matrix factors. In order to facilitate the derivations of simple, computationally efficient forms for the matrix factors, we utilize a recently developed calculus based on elementary graphs. The methods are applicable to systems of particles involving spins greater than (1/2 and reduce to previously known results for the case of spin (1/2.
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