SU3 recoupling and fractional parentage in the 2s-1d shell

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 [superset or implies] SU2 chain. The Wigner coefficients are those for the Kronecker products ([lambda]1[mu]1) x ([lambda]2[mu]2), where ([lambda]1[mu]1) is arbitrary and ([lambda]2[mu]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 ([lambda][mu]). 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 [lambda] and [mu]. The SU3 fractional parentage coefficients are used to give expressions for single-particle spectroscopic factors for 2s-1d shell nuclei.