Effect of infrared radiation on nonrelativistic Coulomb scattering

Abstract

The Bloch-Nordsieck treatment of infrared radiation in scattering theory, based on the use of coherent states of the radiation field, is generalized, within the context of a nonrelativistic model of the scattering, to include the case where the potential has a long-range Coulomb tail. The procedure followed here is based on a construction of modified asymptotic states which properly account for the motion of the projectile under the combined influence of the Coulomb tail and the low-frequency modes of the radiation field. The differential cross section for scattering accompanied by the emission of an arbitrary number of unobservable photons (those with frequencies below some cutoff value ${\ensuremath{\omega}}_{c}$) reduces, in lowest approximation, to the field-free cross section in agreement with the Bloch-Nordsieck sum rule for scattering in a short-range potential. In a more accurate approximation, corrections are obtained which differ from those derived previously for the short-range case through the appearance of terms depending logarithmically on ${\ensuremath{\omega}}_{c}$. A low-frequency theorem for single-photon bremsstrahlung in a Coulomb potential is derived as a special case of the formalism developed here.