Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

291single type are present and various events may only lead to the increase or decrease of suchparticles. In many particle transport problems, however, reactions may result in the appearanceof particles different from the one entering the reaction. For example, in neutrontransport problems, collisions of neutrons with matter often produce gamma particles, and.in radiation damage calculations, atoms of the structural material that are knocked out cfthe lattice may also be interesting from a simulational point of view. In such cases, differentparticles obey different transport equations. Similarly, the number of moment equations tobe established is equal to the number of different particle types if different particles scoredifferently in a Monte Carlo simulation. These equations are often coupled to each other.In this Section, we investigate a simple case when two types of particles may appearin the system. The first type originates from an external source, the second may only beproduced in collisions of the first type of particle. We shall assume that free flights of bothtypes of particles are described by transition kernels of the structure introduced in Section5.I.D. (This means that no charged particles are considered.) The collision kernel of thefirst type of particle (for brevity, we call them neutrons) is written in the general formC(P';P",P 7)dP"dP 7C 7(P') C 7(P',P") T n(P',P 7)+ E c r(P')C r(P',P")8(P 7- P) dP"dP 7(5.376)whereJdP"C 7(P',P") = 1 (5.377)JdP 7F n(P',P 7) = v, Y(5.378)C 7(P') + 2 c r(P') = 1 (5,379)The kernels C r(P',P") are analogous to those discussed in Section 5.1. 1). The kernel inEquation (5.376) has the following obvious meaning: a collision of a neutron gives rise tothe production of particles of the second type (they will be called gamma particles) with aprobability C 7and a reaction r, with the participation of neutrons only taking place with aprobability c r. The postcollision coordinates of the neutrons in a gamma-producing reactionare determined by the density C 7. [If gamma production is due to neutron absorption,C 7(P',P") = 8(P' — P), by analogy to the pure neutron absorption in Equation (5.35).] Thenumber of gamma particles born in the collision is v . The gamma particle starts from thedensity F n/v 7. The collision kernel may also be written in the shortened formC(P';P",P 7) = C 7(P')C 7(P',F)T n(P',P 7) + C 0(P',P")8(P 7- P) (.5.380)where C„ is equivalent to the kernel in a pure neutron problem. The collision kernel of thegamma particle has the formT(P',P") = 2g r(P')r r(P',P") (5.381)where2 g r(P') = i