Impact Broadening of Spectral Lines

Abstract

An evaluation is made of the error introduced into current impact broadening theory by the two incorrect assumptions usually made,—the adiabatic approximation, and the neglect of the rotation of the adiabatic electron states in the computation of the interaction between these states and the radiation field. A simple case of resonance broadening is examined, with the aid of wave functions in a nonrotating coordinate system, and the emitted intensity is shown to be reduced by a factor of two in the first approximation from the value given by the usual impact formula. This discrepancy is no greater than other errors in the present theory of line broadening, and will be less for dispersion, van der Waals, and other second-order forces since these forces do not vanish on the average and will show little tendency to do so in a single encounter. The Weisskopf formula, despite its theoretical imperfections, may therefore be used to give approximate results for impact broadening. A criterion is also given for the transition between impact and statistical broadening; for resonance forces under normal conditions the impact broadening formulas are shown to be irrelevant, since they apply only within a distance of ${10}^{-1\mathrm{}}$ angstrom from the line center, and outside this range the statistical formulas must be applied. Although this is substantially the range of Doppler broadening, accurate measurements of line centers at low pressures should provide a qualitative test of the present theory in the case of resonance broadening. The influence of the previously neglected "rotation effect" on the interaction between a hydrogen atom perturbed by a passing ion and the radiation field is calculated with relative exactness for the first excited state.