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

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Abstract Explicit algebraic expressions have been calculated for both the SU3 Wigner coefficients and the SU3 Racah coefficients which are of particular interest in the recoupling problem involving 2s-1d shell nucleons and basis functions of SU3 symmetry involving the SU3 ⊃ SU2 chain. The Wigner coefficients are those for the Kronecker products (λ1μ1)×(λ2μ2), where (λ1μ1) is arbitrary and (λ2μ2) 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 SU3 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 SU3 fractional parentage coefficients are used to give expressions for single-particle spectroscopic factors for 2s-1d shell nuclei.