Theory of single-photon bound - free transitions: extension of the pole approximation

A theory of single-photon ionization, detachment, and dissociation of quantum systems (atom, molecule, ion, etc) is presented. A unified treatment of excitation from the ground and excited states is performed, via a consideration of the rotating- and counter-rotating-wave terms on equal footing. The familiar pole approximation (PA) is extended to obtain higher-order corrections, which allows one to establish the PA validity conditions and provide a unified description of the cases of above- and below-threshold excitation. As a specific example, photodetachment of negative ions is considered. An exact long-time solution is obtained for the general case. A familiar model of photodetachment is used to validate the present PA formalism. The latter has allowed us to derive the PA validity condition, which holds for all values of the parameters, involving quite different situations. The applicability of the existing versions of the rotating-wave approximation has been checked.