Deconvolution of thermal averaging in scattering experiments using integral transform methods

In several distinct types of scattering experiments the velocity distribution of some components of velocity of the primary and/or target particles is a Maxwell–Boltzmann distribution of known width, while other velocity components are known to far better precision. We derive inversion procedures using Fourier and Laplace transforms which permit the detailed microscopic rate constant k (Vrel) to be recovered from the measured quantities. Experiments using the beam–gas arrangement, velocity selection (of one component) by Doppler shift, and experiments conducted in complete thermal equilibrium are considered. Practical applications and limitations are discussed.