THE EGS5 CODE SYSTEM

Final
Direction
x
φ
Θ
t( (1 − ζ) K1)
∆x
t(K1)
t(ζ K1)
Θ
∆y
z
y
s
Figure 2.10: Modified random hinge transport mechanics schematic.
Thus, instead of the hinge consisting of steps ζt and (1 − ζ)t, it consists of steps of the distances
corresponding to the accumulation of scattering strengths ζK 1 (t) and (1 − ζ)K 1 (t). In this way,
the total scattering strength K 1 (t) over the step is preserved, and the average location of the hinge
will correspond to that location which preserves the first moments of spatial displacements. The
modified random hinge transport mechanics of EGS5, illustrated in Figure 2.10, is therefore capable
of simulating accurately the average final positions of electrons moving long pathlengths through
materials, even when energy loss occurs continuously along the track. The length of an electron
step is therefore limited only by the accuracy of the multiple scattering p.d.f., any need to higher
order spatial moments (as would be required for some differential tallies), and the accuracy of the
method used to compute the integral in Equation 2.372 along the paths between hinge points.
Values of the scattering powers G 1 for electrons and positrons as a function of energy are
computed in PEGS in a new function G1E. For kinetic energies less than 100 MeV, values are taken
from cubic spline fits of data provided in the DCSLIB package described in the previous section.
Above 100 MeV, the Wentzel-shaped scattering cross section used by Molière is assumed, in which
case Equation 2.367 for l = 1 can be integrated analytically to yield
G 1 (E) = N [ ( )]
aρ 2πZ 2 e 4 π 2 + χ 2 a
M p 2 v 2 ln
χ 2 −
π2
a π 2 + χ 2 , (2.373)
a
where χ 2 a is taken from Equation 2.322. Discontinuities at 100 MeV between values of G 1 computed
from the partial-wave cross section data of DCSLIB and from the Wentzel cross section above are
usually small (on the order of fractions of 1 percent), and hence are smoothed only crudely.
Since the Goudsmit-Saunderson multiple scattering distributions are pre-computed in PEGS,
100