An exact solution to the monoenergetic Boltzmann equation isobtained for the case of a plane isotropic burst of neutrons introducedat the interface separating two adjacent, dissimilar, semi-infinitemedia. The method of solution used is to remove the time dependenceby a Laplace transformation, solve the transformed equation by thenormal mode expansion method, and then invert to recover the timedependence.
The general result is expressed as a sum of definite, multipleintegrals, one of which contains the uncollided wave of neutronsoriginating at the source plane. It is possible to obtain a simplifiedform for the solution at the interface, and certain numerical calculationsare made there.
The interface flux in two adjacent moderators is calculated andplotted as a function of time for several moderator materials. Foreach case it is found that the flux decay curve has an asymptotic slopegiven accurately by diffusion theory. Furthermore, the interface currentis observed to change directions when the scattering and absorptioncross sections of the two moderator materials are related in acertain manner. More specifically, the reflection process in twoadjacent moderators appears to depend initially on the scatteringproperties and for long times on the absorption properties of the media.
This analysis contains both the single infinite and semi-infinitemedium problems as special cases. The results in thesetwo special cases provide a check on the accuracy of the generalsolution since they agree with solutions of these problems obtainedby separate analyses.
