A general yet simple and hence practical algorithm for calculating SU3⊃SU2×U1 Wigner coefficients is formulated. The resolution of the outer multiplicity follows the prescription given by Biedenharn and Louck. It is shown that SU3 Racah coefficients can be obtained as a solution to a set of simultaneous equations with unknown coefficients given as a by-product of the initial steps in the SU3⊃SU2×U1 Wigner coefficient construction algorithm. A general expression for evaluating SU3⊃R3 Wigner coefficients as a sum over a simple subset of the corresponding SU3⊃SU2×U1 Wigner coefficients is also presented. State conjugation properties are discussed and symmetry relations for both the SU3⊃SU2×U1 and SU3⊃R3 Wigner coefficients are given. Machine codes based on the results are available.

Results for ab initio no-core shell model calculations in a symmetry-adapted SU(3)-based coupling scheme demonstrate that collective modes in light nuclei emerge from first principles. The low-lying states of $^{6}\mathrm{Li}$, $^{8}\mathrm{Be}$, and $^{6}\mathrm{He}$ are shown to exhibit orderly patterns that favor spatial configurations with strong quadrupole deformation and complementary low intrinsic spin values, a picture that is consistent with the nuclear symplectic model. The results also suggest a pragmatic path forward to accommodate deformation-driven collective features in ab initio analyses when they dominate the nuclear landscape.