PENELOPE 2003 - OECD Nuclear Energy Agency

3.3. Bremsstrahlung emission 109
1 keV
1 keV
1 5
Al
0
10 keV
10 keV
Au
10 keV
10 0 keV
1 M eV
1 0
1 M eV
10 M eV
10 M eV
10 0 M eV
10 0 M eV
χ (Z, E, κ) (barn)
1 0
χ (Z, E, κ) (barn)
5
5
0
0.0 0.5 1 .0
κ=W/E
0
0.0 0.5 1 .0
κ=W/E
Figure 3.13: Numerical scaled bremsstrahlung energy-loss DCSs of aluminium and gold for
electrons with the indicated energies (Seltzer and Berger, 1986).
To simulate each radiative event in a compound, we should first select the element (X
or Y) where the emission occurs and then sample the photon energy and direction from
the corresponding atomic DCS. This is a lengthy process and requires storing the scaled
DCSs for all the elements present. To simplify the simulation, we shall express the
molecular DCS in the same form as the atomic DCS, eq. (3.131),
dσ br,mol
dW
= Z2 eq
β 2 1
W χ mol(Z eq , E, κ), (3.135)
where
is the “equivalent” atomic number Z eq and
Zeq 2 ≡ 1 (
xZ
2
x + y X + yZY)
2
(3.136)
χ mol (Z eq , E, κ) = xZ2 X
Z 2 eq
χ(Z X , E, κ) + yZ2 Y
χ(Z
Zeq
2 Y , E, κ) (3.137)
is the molecular scaled DCS. Radiative events will be sampled directly from the molecular
DCS (3.135). This method may introduce slight inconsistencies in the angular
distribution of the emitted photons (see below), which usually have a negligible effect
on the simulation results.