Calculation of the Total Cross Section from Angular Measurements in Crossed‐Beam Experiments

Abstract

The total cross section is written as the sum of an integral taken over the scattered intensity measured in the plane of the initial velocity vectors and a correction term which itself is the sum of two integrals of the center‐of‐mass (c.m.) differential cross section. One of these integrals is taken from 0 to ε, the other from π—ε to π, where ε is the angle between the center‐of‐mass velocity and the relative velocity. In certain atomic or molecular scattering experiments, the angle ε is small; for these cases, it is shown that only a small error is made by dropping this correction term. This error is estimated for the case of isotropic scattering and for the case of glory scattering. In the latter case, the range of parameters for which the method is useful is given. In the event that the shape of the differential cross section is known a priori, the correction term can be calculated and the total cross section found exactly.