PENELOPE 2003 - OECD Nuclear Energy Agency

66 Chapter 2. Photon interactions
penelope simulates the emission of characteristic radiation and Auger electrons that
result from vacancies produced in K shells and L subshells by photoelectric absorption,
Compton scattering and electron/positron impact (see chapter 3). The relaxation of
these vacancies is followed until the K and L shells are filled up, i.e. until the vacancies
have migrated to M and outer shells. Vacancies in these outer shells originate much less
energetic secondary radiation, whose main effect is to spread out the excitation energy
of the ion within the surrounding material. To get a reliable description of the dose
distribution, and other macroscopic transport characteristics, we only have to follow
secondary radiation that is able to propagate to distances of the order of, say, 1% of
the penetration distance (or range) of the primary radiation. Radiation with lower
energy does not need to be followed, since its only effect is to blur the “primary” dose
distribution on a small length scale.
To simplify the description of the ionization processes of outer shells (i.e. photoelectric
absorption, Compton scattering and electron/positron impact), we simply assume
that, when ionization occurs in M or outer shells, a secondary (delta) electron is emitted
from the parent ion with a kinetic energy E s equal to the energy deposited by the
primary particle,
⎧
⎪⎨ E − E ′ in Compton scattering,
E dep = E in photoelectric absorption,
⎪⎩ W in electron/positron impact (see chapter 3).
(2.107)
That is, the whole excitation energy of the ion is taken up by the ejected electron and
no fluorescent radiation is simulated. In reality, the emitted electrons have energies less
than the values (2.107) and can be followed by characteristic x rays, which have mean free
paths that are usually much larger than the Bethe range of photoelectrons. By giving
an artificially increased initial energy to the electron we allow it to transport energy
farther from the ion so as to partially compensate for the neglect of other radiation
emitted during the de-excitation cascade.
In the case of ionization of an inner shell i, i.e. a K shell or an L shell, we consider
that the electron is ejected with kinetic energy
E s = E dep − U i , (2.108)
where U i is the ionization energy of the active shell, and that the target atom is left with
a vacancy in shell i. As mentioned above, we consider only characteristic x-rays and
Auger electrons emitted in the first stages of the relaxation process. These secondary
radiations are assumed to be emitted isotropically from the excited atom. We use the
following notation to designate the possible transitions
• Radiative: S0-S1 (an electron from the S1 shell fills the vacancy in the S0 shell, leaving
a hole in the S1 shell). The considered radiative transitions (for elements with Z > 18
with the M-shell filled) are shown in fig. 2.3.
• Non-radiative: S0-S1-S2 (an electron from the S1 shell fills the vacancy in the S0 shell,
and the released energy is taken away by an electron in the S2 shell; this process leaves