Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

59By this technique the number of events and the number of score contributions is increased,which — assuming that splitting is applied really in important regions - increases theefficiency, even in spite of the increased number of simulations.It is worth noting that the above-described trivial ways are not the only possibilities.Splitting and Russian roulette are treated in full generality in Chapter 5.III.Russian roulette and splitting may — and frequently are — used together. In complexgeometries, sometimes each region can be assigned an importance. 23Then, when a panicleenters region n + 1 from region n, and the ratio I n, ,/I n> 1. the particle is to be split infov = I n+1ZI npieces, otherwise Russian roulette is to be played by a survival probability ofp = I n +,/I n. If v, in the splitting, is not an integer, one can either choose the nearest integer,or to split into n = ent(v) with a probability of n 4- 1 — v and into n = entOf) + 1 witha probability of v — n.In the previous paragraph we already assumed that importances can be assigned to certainregions of phase space. Such importances, however, can be exactly specified only if theproblem is solved. Thus, in a first step one can use estimated values. Such estimates car.be derived from non Monte Carlo (e.g., discrete ordinate] calculations carried out forsimplified problems, or the user can set ad hoc values based on his earlier experiences withmore-or-less similar problems. Sometimes the first estimates of the importances are successivelycorrected after a smaller number of simulations and the computation is followedby the better estimates.In the solution of real physical problems, with different materials in different zones;energy dependent cross-sections; region, energy and direction dependent importances; theproper selection of the survival and splitting criteria may strongly influence the efficiencyof the calculation and is a hard task. Investigations on finding optimum or near optimumparameters will be given in Chapter 7.II.I). EXPECTED VALUES IN SCORINGThe replacement of absorption by the reduction of the artificially introduced weightparameter, from a certain point of view, is equivalent to the analytical calculation of theexpected value of a random process.Specifically, if we assign a score of 0 to an absorption and 1 to a scattering event, andwe know that the probabilities of their occurrences are aja and a/a, respectively, then theweight reduction factor:cr — cr,, CT S1 •