Collision Term in the Boltzmann Transport Equation

The scattering probability $W(v,v′)$⁠, associated with particles of mass m interacting by means of hard elastic collisions with moving scatterers of mass M, is obtained in terms of the corresponding scattering probability associated with scattering from rigid elastic scatterers. The collision term in the Boltzmann transport equation can then be written in a form which is convenient for handling both equilibrium and transport phenomena. The conditions of equilibrium are discussed. The approximate collision term for a distribution function of the form $f(v) = f0(v) + vxg(v($ is derived, and the results applied to the problem of the conductivity to microwaves of a slightly ionized gas.