Electron g3 Configurations in LS Coupling

Total orbital momentum and total spin are good quantum numbers for a complete basis which we construct as explicit linear combinations of orthonormal vectors (m₁m₂m₃), where integers ${\mathrm{|\hspace{0.17em}m}}_i\text{\hspace{0.17em}|\hspace{0.17em} ≤ 4}$ . Matrix elements of generators of the orbital momentum group are found explicitly in the basis (m₁m₂m₃) and a one‐to‐one correspondence between (m₁m₂m₃) and Gel'fand—Tseitlin patterns of SU (9) is shown. The multiplicity problem is solved systematically by simplicity conventions similar to those introduced by Racah for the cases where his classification scheme for higher fⁿ configurations failed. Every angular momentum multiplet we construct belongs to one irreducible representation of O (9) only.