Kinematics of small angle scattering

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Abstract
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.