Approach to Equilibrium of a Neutron Gas

We have calculated the relaxation constants (time eigenvalues) associated with the time-dependent Boltzmann equation for the relaxation of a neutron gas in contact with a heat bath (moderating material). The eigenvalues were calculated by explicit and implicit matrix methods, and for monatomic-gas and crystalline models of the moderator. The discrete eigenvalues were found to lie in a finite piece of the λ axis. Our results strongly suggest that in many crystalline moderators, only the fundamental eigenvalue exists. In these cases, the approach to equilibrium is not exponential.