THE EGS5 CODE SYSTEM

from appropriate distribution functions. Discrete interactions can interrupt these steps at randomdistances, just as in the case of photon transport.Several factors complicate this model. First, because of continuous nature of the energy lossthat occurs over t, the discrete collision cross section varies along the path of the electron. Thus,mean free paths between between discrete electron interactions vary between the time they arefirst computed and the time the interaction position is reached. More importantly, electron pathsover simulated transport distances t are not straight lines, and so in addition to changing particles’energies and directions, continuous collisions also displace them laterally from their initial paths.Relatedly, these lateral displacements result in the actual straight-line transport distances beingsomething less than t. The models used in EGS5 to treat all of the implications of the continuousenergy loss and multiple elastic scattering methodology is examined in section 2.15.2.5 Particle InteractionsWhen a point of a discrete interaction has been reached it must be decided which of the competingprocesses has occurred. The probability that a given type of interaction occurred is proportionalto its cross section. Suppose the types of interactions possible are numbered 1 to n. Then î, thenumber of the interaction to occur, is a random variable with distribution functioni∑σ jj=1F (i) =σ t, (2.33)where σ j is the cross section for the jth type of interaction and σ t is the total cross section(= ∑ nj=1 σ j ). The F (i) are the branching ratios. The number of the interaction to occur, i, isselected by picking a random number and finding the i which satisfiesF (i − 1) < ζ < F (i). (2.34)Once the type of interaction has been selected, the next step is to determine the parameters forthe product particles. In general, the final state of the interaction can be characterized by, say, nparameters µ 1 , µ 2 , · · · , µ n . The differential cross section is some expression of the formd n σ = g(⃗µ) d n µ (2.35)with the total cross section being given by∫σ = g(⃗µ) d n µ. (2.36)Then f(⃗µ) = g(⃗µ)/ ∫ g(⃗µ) d n µ is normalized to 1 and has the properties of a joint density function.This may be sampled using the method given in a previous section or using some of the moregeneral methods mentioned in the literature. Once the value of ⃗µ determines the final state, theproperties of the product particles are defined and can be stored on the stack. As mentioned before,the particle with the least energy is put on top of the stack. The portion of code for transportingparticles of the type corresponding to the top particle is then entered.29