Kinematics of small angle scattering

In beam-recoil measurements of the scattering of molecules by electrons or photons, deflected molecules are observed at very small angles, comparable to the angular divergences of the observed and crossing beams. A kinematic analysis is presented that explicitly includes the effects of these divergences. Distinguishing features of the analysis include the transformation to apparatus fixed vs ``laboratory'' coordinates and the calculation of the integrals over a finite detector in center of mass coordinates. The latter feature permits a simple recipe for inversion of laboratory observations to obtain a center of mass differential cross section.