Transformations and Averaging Processes for Differential Cross-Section Measurements at Thermal Energies

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Abstract
Theoretical predictions on differential cross sections apply to the center‐of‐mass system of the colliding particles but not to the laboratory system. In order to compare theoretical results with measurements it is necessary either (a) to approximate the center‐of‐mass system by a suitable choice of the colliding particles, and the region of energy, or (b) to transform the differential cross section from the center‐of‐mass system into the laboratory system. If the target particles are at rest before collision, this transformation is simple and well known. If the target particles are not stationary before collision, the problem of transformation becomes more difficult, especially if the target particles have a distribution of velocities. In this paper, formulas are derived which allow the transformation from the center‐of‐mass system to the laboratory system (and vice versa). Both elastic and inelastic collisions are treated. In addition, the averaging process over all initial relative velocity vectors is described, i.e., for a given differential cross section in the center‐of‐mass system, the intensity distribution as measured in the laboratory system is calculated.