Factorized representation for parity-projected Wigner d^j (β) matrices

Authors

N.L. Manakov, Voronezh State UniversityFollow
A.V. Meremianin, Voronezh State UniversityFollow
Anthony F. Starace, University of Nebraska-LincolnFollow

Document Type

Article

Date of this Version

2-1-2000

Comments

Published by American Physical Society. Phys. Rev. A 61, 022103 (2000). http://pra.aps.org. Copyright © 2000 American Physical Society. Permission to use.

Abstract

An alternative representation for the parity-projected Wigner d^j(β) rotation matrix is derived as the product of two triangular matrices composed of Gegenbauer polynomials with negative and positive upper indices, respectively. We relate this representation for d^j(β) to the one presented by Matveenko [Phys. Rev. A 59, 1034 (1999)], which, in contrast with our result, requires for its evaluation a matrix inversion. In addition, identities for bilinear sums of Gegenbauer polynomials are derived. This work is based on our recently introduced invariant representations for finite rotation matrices [Phys. Rev. A 57, 3233 (1998)].