THE EGS5 CODE SYSTEM

ICRU37-compliant using the NIST database ESPA[148]. Effectively, this modification globally
renormalizes EGS4’s bremsstrahlung cross section so that the integral of the cross section (the
radiative stopping power) agrees with that of ICRU Report 37[20, 79]. This improvement can lead
to noticeable changes in the bremsstrahlung cross section for particle energies below 50 MeV[54]
and significant differences for energies below a few MeV where bremsstrahlung production is very
small[124]. These new capabilities were carried over to EGS5.
Low-energy elastic electron cross section modeling
It has long been acknowledged that the Molière multiple scattering distribution used in EGS4
breaks down under certain conditions. In particular: the basic form of the cross section assumed
by Molière is in error in the MeV range, when spin and relativistic effects are important; various
approximations in Molière’s derivation lead to significant errors at pathlengths less than 20 elastic
scattering mean free paths; and the form of Molière’s cross section is incapable of accurately
modeling the structure in the elastic scattering cross section at large angles for low energies and
high atomic number. It is therefore desirable to have available a more exact treatment, and in
EGS5, we use (in the energy range from 1 keV to 100 MeV) elastic scattering distributions derived
from a state-of-the-art partial-wave analysis (an unpublished work) which includes virtual orbits at
sub-relativistic energies, spin and Pauli effects in the near-relativistic range and nuclear size effects
at higher energies. Additionally, unlike the Molière formalism of EGS4, this model includes explicit
electron-positron differences in multiple scattering, which can be pronounced at low energies.
The multiple scattering distributions are computed using the exact approach of Goudsmit and
Saunderson (GS)[63, 64]. Traditionally, sampling from GS distributions has been either prohibitively
expensive (requiring computation of several slowly converging series at each sample)
or overly approximate (using pre-computed data tables with limited accuracy). We have developed
here a new fitting and sampling technique which overcomes these drawbacks, based on a scaling
model for multiple scattering distributions which has been known for some time[27]. First, a change
of variables is performed, and a reduced angle χ = (1−cos(θ))/2 is defined. The full range of angles
(0 ≤ θ ≤ π, or 0 ≤ χ ≤ 1) is then broken into 256 intervals of equal probability, with the 256 th
interval further broken down into 32 sub-intervals of equal spacing. In each of the 287 intervals or
sub-intervals, the distribution is parameterized as
f(χ) =
α
(χ + η) 2 [1 + β(χ − χ −)(χ + − χ)]
where α, β and η are parameters of the fit and χ − and χ + are the endpoints of the interval.
By using a large number of angle bins, this parameterization models the exact form of the
distribution to a very high degree of accuracy, and can be sampled very quickly (see Chapter 2 for
the details of the implementation).
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