Connection between configuration-mixing and quantum-defect treatments

Alternative formulations of atomic problems are connected in terms of the Green's function for the radial motion of a single electron in an effective potential field. The quantum-defect theory (QDT) represents an electron outside an ion by a Coulomb function with a phase shift contributed by the additional interactions that prevail inside the ion core. We interpret the phase-shifted portion of this radial function as arising from the application of a Green's function propagator to the short-range operator that represents the coupling to other channels of the electron + ion system. The alternative representation of the same radial function, as a superposition of zero-order functions for configurations with different energies, differs only by having the same Green's function expanded in a set of zero-order eigenfunctions. This analysis of configuration mixing leads to a reformulation of reaction matrices which extends the initial QDT treatment of bound states.