Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

154 Monte Carlo Particle Transport Methods: Neutron and Photon Calculationscoining out of the event. For example, for the multiplicative reaction f (say, nuclear fissiondue to a neutron)jdP"C,(P',P") = v f(P') (5.37)With the conventions above, the mean number of secondaries in a collision is expressed asc(P')= dP"C(P',P") = 2 c r(P> r(P') (5 38)JRThe kernels defining multiplying processes can be decomposed further. For example, forthe reaction fC f(P',P") = E nq, n(P')C,„(P',P") (5.39)where q fn(P') is the probability that n particles come out of the event if one enters at P\and C 1 n(P',P") is the density of the daughter particles' coordinates, P", i.e.,JdP"C f,„(P',P") = 1andX nq„„(P') = v f(P')N= 1Note that Equation (5.39) for the kernel implies that every secondary has the same distributionC 1n(P',P")- In most practical cases, this assumption is justified. If, for some specific reason,the distributions of the secondaries are different — e.g., for the i-th particle in an n-foldmultiplication, it is CP n(P',F') — then Equation (5.39) is replaced byC f(P',P") = 2 q, n(P') 2 Qi(P',P")II = iI - iThis case will not be discussed; in the following, extension of the considerations to thiscase is straightforward.With the notations above, the selection procedure in step 3 of the simulation presentedin the previous Section can be detailed as follows:1. The type of reaction, r, is selected with a probability C 1(P').2. If it is an absorption, then the tracking of the particle is terminated.3. If it is a scattering of type i, then the postcollision coordinates are selected fromQ,,(P',P").4. If it is a multiplicative event of type f, then the number of particles, n, coming outof the event is selected with a probability q fr,(P') and the coordinates of the particlesare selected from C f„(P',P").As was mentioned in the previous Section, in a general nonanalog game, the statisticalweight of a particle that undergoes an event must be properly changed in order to keep the