Bremsstrahlung near reaction thresholds

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Abstract
Low-frequency approximations for both spontaneous and stimulated bremsstrahlung processes are derived that are applicable to cases in which an electron is scattered from an atom at an energy near the threshold for excitation of the target. Existing approximation procedures are modified to properly account for the strong energy dependence of the cross section, in the form of cusps or rounded steps, caused by the opening up of a new channel. These modifications preserve an essential feature of standard versions of the low-frequency approximation in that the physical, field-free scattering amplitude appears as input to the calculation. An estimate of the error in the Feshbach-Yennie approximation [Nucl. Phys. 37, 150 (1962)] for spontaneous bremsstrahlung is obtained through an evaluation of that contribution to the matrix element corresponding to radiation by the projectile following a virtual excitation of the target. To illustrate the effect of the anomalous energy dependence in a domain containing the threshold, as well as the significance of the above-mentioned correction to the Feshbach-Yennie approximation, calculations are described for a model system; the model is defined by a parametrization of the field-free scattering amplitude that reproduces the correct threshold behavior. A closely analogous treatment is given of laser-assisted scattering near a reaction threshold. A sum rule is derived for this external-field process which, in its simplest form, reproduces a recently conjectured approximation and provides higher-order corrections to it.