Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

1.83In certain applications, the kernel of multiplying processes is given in the formC..(P',P") = V,(P')C„(P',P")instead of the summed form of Equation (5.39). This is tr.of secondaries per multiplication, v r(P'), and a common m-(r i , .are known, and also when the postcollision density C nG r ' < " i !depend on the number of progenies:C n(P',F) = C„(P',P"), n = 1,2, .,In general, v, is not an integer and the simulation of the rnuk denote the integer part of iyk =CRt[V 1(P')]Then k progenies will leave the collision at P' with a probabilityq k(P') = k + 1 - P 1-(P')and k -f1 secondaries are born with a probabilityq kM(P') = V 1-(P') -kThe postcollision coordinates of all the progenies are selected from C,,(P',P"). Obviously,the expected number of progenies in a multiplication at P' iskq k+ (k + l)q k M= v f(P')Setting all the other probabilities q„ equal to zero, the kernel of the above procedure read-;k+ 1C 1-(P',P") = 2 nq k(P')C v(P',P")n kIf the multiplication event contributes to the final score a value f„(P\P"), the form alasderived in this chapter remain valid by puttingf„(P',P") = f„(P',P"), n = k,k + 1IV. FURTHEE GENERALIZATIONSAlthough the majority of the practically applied sirnui «>• \ < * " m >the cases discussed in the previous Chapters, certain corn ut > < i it' i • i,mentioned in the previous Chapter. This procedure implie hr u< ,.