Abstract
The kinetic formula for collisional frequency as a product of particle concentration, cross section and relative velocity is based on the assumption that the latter is constant before and after the collision. This result is here generalized to include the case of collisions with relative acceleration and this is found to involve a cross section in velocity space and the number of particles per unit volume of velocity space. The argument proceeds from the relaxational Boltzmann equation satisfied by the probability density of localization in phase space. The Gauss divergence theorem is applied in the positional and velocity subspaces to convert a space integration and a velocity space integration into the corresponding surface integrations and under the assumptions of unidirectional relative velocity and relative acceleration the two kinds of cross section are obtained naturally.
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