Abstract
A projection operator formalism is employed in considering the T operator for describing a scattering or reaction event in which a system evolves from one continuum channel into another continuum channel. The formalism is based upon projections of the Lippmann-Schwinger equations for T and an operator generalization of Gauss's reduction for linear algebraic equations. A formal solution of the projected Lippmann-Schwinger equation is presented for the case in which the couplings involving the final-state continua satisfy a chosen separability condition. The simplifications that occur when the pole approximation is made on the final-state continua or on both the initial- and final-state continua are presented. The formalism is employed in considering the effects of an external dc electric field in photorecombination processes in a model atomic system which features two autoionizing states, two electron continua (one of which contains the initial state), and two photon continua (corresponding to radiatively stabilized atomic states). Particular attention is paid to the effects of the coupling between the two electron continua.
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