Angular resolution corrections in total atomic collision cross section measurement

An important aspect of the measurement of the total atomic collision cross section at thermal velocities by beam attenuation is the correction for beam atoms which are scattered through small angles and still reach the detector. The correction requires an algorithm for the small angle differential cross section in the laboratory frame, Q(θ)dθ. An algorithm will be presented for a long range potential of the form C/rs. The result is obtained by expanding the general expression in a power series to second order in x, where x = (target gas velocity)/(beam atom velocity). The cross section correction is then obtained by integrating Q(θ)η(θ) over laboratory angle θ, where η is the probability of a beam atom scattered through an angle θ being detected