SU 3 recoupling and fractional parentage in the 2s-1d shell

Abstract

Explicit algebraic expressions have been calculated for both the SU 3 Wigner coefficients and the SU 3 Racah coefficients which are of particular interest in the recoupling problem involving 2s-1d shell nucleons and basis functions of SU 3 symmetry involving the SU 3 ⊃ SU 2 chain. The Wigner coefficients are those for the Kronecker products ( λ 1 μ 1)×( λ 2 μ 2), where ( λ 1 μ 1) is arbitrary and ( λ 2 μ 2) is the six-dimentional representation (20) of a single 2s-1d shell nucleon or one of the representations (02), (40), (21) for two coupled 2s-1d shell nucleons or the basic eight-dimensional representation (11). The racah coefficients are those involved in the coupling of two 2s-1d shell nucleons to a function of arbitrary (λμ). Calculations of SU 3 fractional parentage coefficients are illustrated by a few examples which have been evaluated without recourse to a full chain calculation for representations with large values of λ and μ. The SU 3 fractional parentage coefficients are used to give expressions for single-particle spectroscopic factors for 2s-1d shell nuclei.