PENELOPE 2003 - OECD Nuclear Energy Agency

F
2.2. Photoelectric effect 43
1E+7
1E+6
σ ph
(barn)
1E+5
1E+4
1E+3
e
U
1E+2
C
1E+1
1E+2 1E+3 1E+4 1E+5 1E+6
E (eV)
Figure 2.5: Atomic photoelectric cross sections for carbon, iron and uranium as functions of
the photon energy E.
PDF
p i = σ ph,i (Z, E)/σ ph (Z, E), (2.22)
where σ ph,i (Z, E) is the cross section for ionization of shell i and σ ph (Z, E) is the total
photoelectric cross section of the atom. penelope incorporates a detailed description
of photoabsorption in K- and L-shells (including the subsequent atomic relaxation).
The ionization probabilities of these inner shells are determined from the corresponding
partial cross sections. The probability of ionization in an outer shell is obtained as
p outer = 1 − (p K + p L1 + p L2 + p L3 ). (2.23)
When the ionization occurs in an inner K- or L-shell, the initial energy of the photoelectron
is set equal to E e = E − U i ; the residual atom, with a vacancy in the shell,
subsequently relaxes to its ground state by emitting x rays and Auger electrons. If the
ionization occurs in an outer shell, we assume that the photoelectron leaves the target
atom with kinetic energy equal to the energy deposited by the photon, E e = E, and we
disregard the emission of subsidiary fluorescent radiation (see section 2.6).
Initial direction of photoelectrons
The direction of emission of the photoelectron, relative to that of the absorbed photon,
is defined by the polar and azimuthal angles θ e (fig. 2.1) and φ e . We consider that the
incident photon is not polarized and, hence, the angular distribution of photoelectrons
is independent of φ e , which is uniformly distributed in the interval (0, 2π). The polar
angle θ e is sampled from the K-shell cross section derived by Sauter (1931) using K-shell