Angular and hyperangular momentum recoupling, harmonic superposition and Racah polynomials: a recursive algorithm

Generalized 6j symbols are defined in terms of orthonormalized Racah polyno mials of a discrete variable and given explicitly as hypergeometric F-4(3)( 1) series. They extend the recoupling coefficients of ordinary angular mome nt-am algebra, including multiples of 1/4 as quantum numbers. A three-term recurrence relationship is exploited for extensive calculations and illustr ation of their properties. Their role is outlined as matrix elements for su perpositions (or overlaps) both between alternative spherical and hypersphe rical harmonics and between alternative Sturmian sets, an important case be ing that of four-dimensional harmonies of S-3, which apply to the momentum- space hydrogen atom orbitals. (C) 2001 Elsevier Science B.V. All rights res erved.