Symmetry-decomposed reduced transition operators for degenerate atomic states-Their generation and their utility

Abstract

The p-particle reduced transition operator between the (ML = L, Ms = S) member of one degenerate (L, S) manifold and the (ML′ = V, MS′ = S′) member of a (possibly different) (L′, S′) manifold of eigenstates of a nonrelativistic atomic Hamiltonian contains sufficient information to construct the p-particle reduced transition operator between any member of the first manifold and any member of the second manifold. The procedure for such a construction has been given, and applied computationally to generate the symmetry-decomposed one-particle reduced transition operators among all the ML, MS states of a degenerate (L, S) manifold, from the nondecomposed one-particle reduced density operator of the (ML = L, MS = S) member of this manifold; thereby expediting the calculation of the one-particle reduced density operator of an arbitrary linear superposition of these degenerate states. To illustrate their applicability, these results were used to obtain the densities of the cubic-symmetry-adapted states of an atomic 1D manifold, (in a configuration-interaction approximation) which densities are shown graphically (using the PLOT79 graphics program). The computer program uses the coding of Carlos Bunge's atomic CI program, and can be appended directly to it or to its wavefunction or density-matrix output.