Projection-operator approach to the unified treatment of radiative and dielectronic recombination

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Abstract
A formalism that is based on projection operators is employed to obtain a general recipe for constructing matrix elements of the transition or T operator for electron-ion photorecombination processes in model systems featuring a limited number of discrete states and continua. The projection-operator formalism allows for a natural separation of the total transition operator into a direct, or radiative recombination, contribution and a resonance, or dielectronic recombination contribution. Implementation of the general recipe is discussed, and expressions for matrix elements of needed propagators in the combined Hilbert space of electron and photon continua are derived for model systems in which one makes the pole approximation on the photon continua, but not on the electron continua. The simplifications that occur when the pole approximation is made on all continua are presented. Finally, the recipe is employed to describe photorecombination for two model systems that feature an isolated autoionizing state. One model includes an arbitrary number of possible final-state photon continua, and the second model includes an arbitrary number of possible final-state electron continua. For the former model, it is shown how the various terms entering into the expression for the recombination transition amplitude can be obtained from a perturbation series and interpreted in terms of Feynman-like diagrams.