Effect of Target Gas Temperature on the Scattering Cross Section

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Abstract
If a beam of particles is scattered by a gas or plasma, the differential scattering cross section that is observed experimentally may, in some cases, be altered a discernible amount by the random thermal motion of the target particles. In order to explore the feasibility of using this effect as a means of measuring high temperatures, or to correct for the temperature of the target in the event that the desired cross section must be measured at high temperatures, this work presents a theoretical study of the temperature dependence of the cross section. A general expression is obtained for the observed differential scattering cross section in the laboratory frame in terms of the differential cross section in the center-of-mass frame for the general case of arbitrary initial motion of the target. Detailed results for the temperature dependence are given for hardsphere scattering (which is also applicable to low-energy neutron scattering) and for Coulomb scattering, in the approximation in which the projectiles are light and rapidly moving, compared to the targets. For hard-sphere scattering the case of equal projectile and target mass is also considered.

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