Resonant scattering in the presence of an electromagnetic field

Abstract

The theory of resonant reactions, in the projection-operator formulation of Feshbach, is generalized to account for the presence of an external electromagnetic field. The theory is used as the basis for the construction of low-frequency approximations for the transition amplitude. Results obtained here for scattering in a laser field confirm earlier versions of the low-frequency approximation when the resonances are isolated. However, if there are several closely spaced resonances additional terms must be included (their importance magnified by the appearance of near singularities) which account for the effect of radiative transitions between pairs of nearly degenerate resonant states. The weak-field limit of this result yields a low-frequency approximation for single-photon spontaneous bremsstrahlung which, through the inclusion of correction terms associated with closely spaced resonances, provides an improvement over the Feshbach-Yennie version derived some time ago. A separate treatment is required to deal with the limiting case of a static external field and this is worked out here in the context of a time-dependent formulation of the scattering problem. Linear and quadratic Stark splitting of the resonance positions, and resonance broadening due to the tunneling mechanism, are expected to play a significant role in the static limit and these effects are included in the approximation derived here for the transition amplitude.