Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

241surrounded by a black absorber and there is no return from outside V, or the particles enteringV are assumed to be independent of any particle previously left V and they are thought tobe part of the uniform surface source in Equation (5,246). The assumption will be relaxedin Section D by introducing an albedo-type quantity that accounts for the returning particlesThe present form of the model allows us to examine the score moments in V without regardto the surroundings.B. THE SEPARATION ASSUMPTIONIt is well known from transport theory that even in the specialized modea very limited number of problems can be exactly solved, and these solutionsmathematical foundations. Therefore, some further approximation is to beorder to obtain an easily treatable method of solution. The approximation is firstin the case of the analog first-moment equationM 1(P) = I 1(P) + JdP' T(P, P') JdP"C(P\P")M,(P")where, when the collision rate in Equation (5.242) is estimatedI 1(P) =j dP'T(P.P')JvWith the kernels in Equations (5.243) and (5.244), the moment equation takes on the form/•D(P)crM 1(P) = 1 - e~ a W n + o- dD e~«*> _ d*»'M,(r + Dw,') (5,247)Jo4 Tf Jwhere D(P) is the geometrical distance of the surface S from the point P along