PENELOPE 2003 - OECD Nuclear Energy Agency

70 Chapter 3. Electron and positron interactions
The possible interactions of electrons and positrons with the medium are elastic
scattering, inelastic collisions and bremsstrahlung emission; positrons can also undergo
annihilation, either in flight or at rest. The atomic DCSs adopted in penelope are
defined either as analytical functions or by means of numerical tables, or as a combination
of both. These DCSs, which are sufficiently accurate for most practical simulation
purposes, allow fast and accurate random sampling of the individual interactions. It
is worth pointing out that multiple scattering distributions are quite insensitive to the
fine details of the single scattering DCSs. If the adopted DCSs have a physically reasonable
shape, only the values of a few integrals of the DCS have a direct influence
on the simulation results (Liljequist, 1987; Fernández-Varea et al., 1993b). As a consequence,
a general-purpose simulation procedure can be made fairly simple by using
approximate DCSs with the proviso that they exactly reproduce the correct values of
the relevant integrals. The DCSs described below represent a compromise between reliability
and simplicity; they are simple enough to allow the use of fast sampling methods
and, at the same time, they are flexible enough to account for the relevant features of
the interactions.
Owing to the large number of interactions suffered by a fast electron or positron
before coming to rest, detailed simulation is unfeasible at high energies. In penelope
we overcome this practical difficulty by using a mixed simulation procedure (see chapter
4) instead of the habitual condensed simulation schemes adopted in other high-energy
simulation codes —e.g. etran (Berger and Seltzer, 1988), its3 (Halbleib et al., 1992),
egs4 (Nelson et al., 1985), geant3 (Brun et al., 1986). The formulation of mixed
simulation is complicated by the fact that the sampling of hard interactions is done from
restricted DCSs, with cutoffs that vary with the particle energy during the evolution
of a track. This limits the complexity of the DCSs that can be efficiently used in a
simulation code.
3.1 Elastic collisions
In this section we consider the theoretical description of elastic collisions of electrons and
positrons with isolated neutral atoms of atomic number Z at rest. By definition, elastic
interactions are those in which the initial and final quantum states of the target atom
are the same, normally the ground state. The angular deflections of electron trajectories
in matter are mainly (but not completely) due to elastic scattering. Notice that there
is a certain energy transfer from the projectile to the target, which causes the recoil of
the latter (see section A.1.1). Because of the large mass of the target (∼ 3600Zm e ), the
average energy lost by the projectile is a very small fraction of its initial energy (a few
meV for scattering of 30 keV electron by aluminium atoms) and is usually neglected,
which is equivalent to assuming that the target has an infinite mass and does not recoil.
For a wide energy range (say from a few hundred eV to ∼1 GeV), elastic interactions
can be described as scattering of the projectile by the electrostatic field of the target
(Mott and Massey, 1965). The charge distribution of the target atom consists of the