THE EGS5 CODE SYSTEM

2.4 Particle Transport Simulation
The mean free path, λ, of a particle is given in terms of its total cross section, σ t , or alternatively,
in terms of its macroscopic total cross section, Σ t , according to the expression
where
λ = 1 Σ t
=
N a = Avogadro ′ s number,
ρ = density,
M = molecular weight,
The probability of an interaction is given by
σ t = total cross section per molecule.
P r{interaction in distance dx} = dx/λ.
M
N a ρσ t
, (2.28)
In general, the mean free path may change as the particle moves from one medium to another, or
when it loses energy. The number of mean free paths traversed will be
N λ =
∫ x
x 0
dx
λ(x) . (2.29)
If ˆNλ is a random variable denoting the number of mean free paths from a given point until the
next interaction, then it can be shown that ˆN λ has the distribution function
P r{ ˆN λ < N λ } = 1 − exp(−N λ ) for N λ > 0. (2.30)
Using the direct sampling method and the fact that 1 − ζ is also uniform on (0, 1) if ζ is, we can
sample N λ using
N λ = − ln ζ. (2.31)
This may be used in Equation 2.29 to obtain the location of the next interaction.
Let us now consider the application of the above to the transport of photons. Pair production,
Compton scattering, and photoelectric processes are treated by default in EGS5. Explicit treatment
of Rayleigh scattering is included as a non-default option. These processes all have cross sections
which are small enough that all interactions may be simulated individually, so that photons in
EGS5 travel in straight lines with constant energies between interactions. Thus, if the overall
volume in which a simulation takes place is composed of a finite number of regions, each of which is
a homogeneous material with uniform density, then the integral in Equation 2.29 reduces to a sum.
If x 0 , x 1 , · · · are the region boundary distances between which λ is constant, then Equation 2.29
becomes
∑i−1( ) ( )
xj − x j−1 x − xi−1
N λ =
+
, (2.32)
λ j λ i
j=1
where x ∈ (x i−1 , x i ). The photon transport procedure is then as follows. First, pick the number of
mean free paths to the next interaction using Equation 2.31. Then perform the following steps:
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