Relaxation Constants of a Uniform Hard-Sphere Gas

A uniform hard-sphere gas with a small departure from a Maxwellian velocity distribution is considered, and the approach towards equilibrium investigated. Methods adapted from the theory of neutron thermalization are used to show that an infinite sequence of discrete relaxation constants λn exists, corresponding to exponentially decaying modes. The sequence begins with the degenerate eigenvalue λ0 = 0, and converges towards the lower bound of the continuous spectrum set by the minimum value of the scattering rate, Vmin = V(0).