Quantum Corrections to the Neutron Transport Equation

The singular behaviour of the neutron transport equation, in the limit of zero neutron velocity, comes into play in an essential manner when one wants to study the nature of its asymptotic solutions. From the physical point of view, the consistency of such a study can be checked only if one knows explicitly the behaviour of the quantum correction terms which are usually neglected. These terms are derived and explicitly exhibited using techniques of the statistical mechanics of irreversible processes. Neglecting terms of order greater than the second in the interaction potential between neutron and scattering centers and in the "short memory" approximation it is shown that the quantum correction terms can be expressed by means of Van Hove's scattering function $S(\overrightarrow{\kappa }, \omega )$. Some models for the dynamics of the scattering centers (moderators) are discussed, and it is found that the correction terms are critically dependent on the detailed balance condition being satisfied.