Reduced matrix element of an irreducible spherical tensor operator—New derivation and applications

Abstract

A new derivation is given of the result that the reduced matrix element of an irreducible spherical tensor operator T( kq) is (gamma;J‖ T (k) ‖γJ) = [(2J + k + 1)!k!/(2J − k)!(2k − 1)!!] 1 2 [f(J)] k , where f(J) = [(2J)(2J + 1)(2J + 2)] − 1 2 (γJ‖ T (1) ‖γJ) ; the reduced matrix is assumed diagonal in γ and J. Applications of this result to problems of molecular structure and spectroscopy and solid state physics are discussed. These are cases in which high order polynomials in angular momentum operators make the use of the irreducible spherical tensor formalism advantageous.