On Scattering Induced Curvature for Fast Charged Particles

Abstract

The exact solution recently obtained for the small-angle plural and multiple scattering of fast charged particles is used to derive several theorems of interest concerning scattering-produced curvatures, and calculations are reported of the probability distribution of such curvatures. Formulas are provided for obtaining the probability of occurrence of curvatures greater than any given amount, for any scattering material and energy, as long as the scattering is not too large. The types of curvature measurement dealt with are: (a) three-point observation, (b) mean curvature using the tangents to the track at each end, and (c) difference between the two curvatures obtained in (b). Asymptotic formulas allow the calculations to be extended for unusually rare events.