Unitary group approach to the treatment of mixed-orbital configurations

Recent advances in the unitary group, or Weyl tableau, approach to the theory of complex spectra have provided great simplification of calculations in atomic and molecular applications. We show that the subduction coefficients employed by Patterson and Harter to generate mixed-orbital-configuration $\mathrm{LS}$-adapted states can be derived using simple vector-coupling considerations. Using lowering and projection operator techniques based on the idea of "highest tableau," which we show are automatically eigenstates of the $L^2$ operator, we generate equivalent states. These states are used to calculate reduced matrix elements of the spin-own-orbit operator for the case ${}_{}{}^2{}_{}{}^{}\left(p^{2}d\right)$. We discuss the generalization of the existing minicomputer programs to treat mixed-orbital configurations.