Continuum level-shift effects in the theory of multiphoton transitions

Publisher Website
Google Scholar
Abstract
A successive-approximation procedure for calculating multiphoton-transition amplitudes is presented. The theory, designed for use in the strong-field domain where ordinary perturbative methods are unsuitable, provides an extension of previous work along these lines by inclusion of the effects of free-free transitions, i.e., interactions with the field which take the atomic system from one continuum state to another. This approach is based on the introduction of an effective Hamiltonian which operates only in the subspace of states, degenerate or nearly degenerate, among which real transitions can take place. Contributions from virtual intermediate states are included in the structure of the effective potential. This approach provides the framework for the construction of models, defined by the approximations made for the effective potential, which build in the constraints of unitarity and which properly account for the effects of intermediate-state resonances. The present work is focussed on those new features of the problem which arise from the fact that both the electron and the residual atom to which it was originally bound can interact with the field in asymptotic states. To avoid complications associated with long-ranged Coulomb effects, the residual atom is assumed to be neutral. (The initial state is a negative ion.) An approximation procedure is described for calculating the field-modified asymptotic states appropriate for such a system. By way of an illustrative example a low-frequency approximation is given which leads to considerable simplification of the calculational procedure.