Angular momentum adaptation of spinor basis

Abstract

Fermion operator realization of the Lie-algebra of SCX(N) (N = 2n, 2n + 1) has been used extensively to study the symmetry adaptation of the fundamental spinor space of SO(N) to SO(3). However, the multispinor basis cannot be handled directly using such fermion operators since they generate only the totally antisymmetric irreducible representation (irrep) of U(4l + 2). Thus, the required spin-free states, which belong to two column irrep of U(2l + 1), do not follow readily. Recently, the Lie-Algebra of SO(N) has been realized using the restriction U(2n) ↓ SO(2n + 1) and was further adapted to SO(2n + 1) = ⊃ SO(2n) ⊃ U(n) = ⊃ U(n − 1) ⊃ … ⊃U(1) for the CI studies in molecules. However, for spin-free electronic configurations in atoms, the total angular momentum is a good quantum number and hence the relevant subgroup chain is SO(2n + 1) = ⊃ SO(2n) ⊃ U(n) ⊃ SC(n) = SO(3) (n odd). It is interesting to generate the configuration space in complex atoms using, as the starting point, the symmetric two box Weyl states of U(2n) and then restrict it to the above chain. This has been attempted in the present note in the hope that it will lead to simpler procedures for MC SCF studies in atoms.