PENELOPE 2003 - OECD Nuclear Energy Agency

3.3. Bremsstrahlung emission 111
1Ε+10
1Ε+10
1Ε+9
1Ε+9
S br
/ρ (eV cm 2 /g)
1Ε+8
1Ε+7
1Ε+6
¤
¤¦¥
§ ¨©
§ ¨©
¤
S br
/ρ (eV cm 2 /g)
1Ε+8
1Ε+7
1Ε+6
1Ε+5
1Ε+5
1Ε+4
1Ε+4
positrons
e l e c trons
1Ε+4 1Ε+5 1Ε+6 1Ε+7 1Ε+8 1Ε+9
E (eV)
1Ε+4 1Ε+5 1Ε+6 1Ε+7 1Ε+8 1Ε+9
E (eV)
Figure 3.14: Radiative stopping power S br /ρ for electrons and positrons in aluminium, silver
(×10) and gold (×100) as a function of the kinetic energy. Solid and dashed curves are results
from the present model. Crosses are data from the ICRU37 report (1984) (also in Berger and
Seltzer, 1982).
from the DCS given by eq. (3.131) practically coincide with ICRU37 (1984) values
(also Berger and Seltzer, 1982). To leave room for future improvements, penelope
reads the radiative stopping power for electrons from the input material data file, and
renormalizes the DCS, eq. (3.131), (i.e. multiplies it by a κ-independent factor) so as to
exactly reproduce the input radiative stopping power.
CSDA range
As mentioned above, the stopping power gives the average energy loss per unit path
length. Thus, when an electron/positron with kinetic energy E advances a small distance
ds within a medium, it loses an (average) energy dE = −S(E)ds, where
S(E) = S in (E) + S br (E) = − dE
ds
(3.144)
is the total (collisional+radiative) stopping power. Many electron transport calculations
and old Monte Carlo simulations are based on the so-called continuous slowing down
approximation (CSDA), which assumes that particles lose energy in a continuous way
and at a rate equal to the stopping power. Evidently, the CSDA disregards energy-loss
fluctuations and, therefore, it should be used with caution.