PENELOPE 2003 - OECD Nuclear Energy Agency

3.2. Inelastic collisions 103
In reality, the target electrons are not at rest and, therefore, the angular distribution
of emitted delta rays is broad. Since the average momentum of bound electrons is
zero, the average direction of delta rays coincides with the direction of q. Thus, our
simple emission model correctly predicts the average initial direction of delta rays, but
disregards the “Doppler broadening” of the angular distribution. This is not a serious
drawback, because secondary electrons are usually emitted with initial kinetic energies
that are much smaller than the initial energy of the projectile. This means that the
direction of motion of the delta ray is randomized, by elastic and inelastic collisions,
after a relatively short path length (much shorter than the transport mean free path of
the projectile).
3.2.6 Ionization of inner shells
As indicated above, the theory presented in sections 3.2.1 and 3.2.2 does not give realistic
values of the cross sections for ionization of inner shells. Hence, it is not appropriate
to simulate inner-shell ionization by electron and positron impact and the subsequent
emission of fluorescent radiation, i.e. Auger electrons and characteristic x rays. Nevertheless,
the GOS model does provide an appropriate description of the average (stopping
and scattering) effect of inelastic collisions on the projectile.
A consistent model for the simulation of inner-shell ionization and relaxation must
account for the following features of the process: 1) space distribution of inner-shell ionizations
along the projectile’s track, 2) relative probabilities of ionizing various atomic
electron shells and 3) energies and emission probabilities of the electrons and x rays released
through the de-excitation cascade of the ionized atom. The correlation between
energy loss/scattering of the projectile and ionization events is of minor importance and
may be neglected (it is observable only in single-scattering experiments where the inelastically
scattered electrons and the emitted x rays or Auger electrons are observed in
coincidence). Consequently, we shall consider inner-shell ionization as an independent
interaction process that has no effect on the state of the projectile. Accordingly, in the
simulation of inelastic collisions the projectile is assumed to cause only the ejection of
knock-on electrons (delta rays); in these collisions the target atom is considered to remain
unaltered to avoid double counting of ionizations. Thus, to determine the location
of ionizing events and the atomic shell that is ionized we only need to consider cross
sections for ionization of individual inner shells, which can be obtained from elaborate
theoretical models. The relaxation of the vacancies produced by inner-shell ionizations
is simulated as described in section 2.6. This kind of simulation scheme is trivial to
implement, but it may cause artifacts (in the form of small negative doses) in space regions
where the simulated dose distributions have large relative statistical uncertainties.
The reason is that simulated Auger electrons and x rays remove energy from their site
(volume bin) of birth, in quantities that may exceed the actual energy deposited by the
projectile.
To simulate the ionization of K shells and L subshells (with ionization energies
larger than 200 eV) by electron and positron impact, penelope uses total ionization