PENELOPE 2003 - OECD Nuclear Energy Agency

4.3. Combined scattering and energy loss 143
(ii) If s > s max , move the electron a path length s max and determine the soft energy
loss ω along this path length. Modify the electron energy 2 , E ← E − ω, and
assume that a delta interaction occurs at the end of the step.
(iii) If s < s max , move the electron a step of length s. Determine the energy loss ω and
update the energy, E ← E − ω. Sample a random number ξ.
(1) If ξΣ h,max < Σ h (E), simulate a hard interaction
(2) Otherwise, assume that the particle undergoes a delta interaction.
(iv) Return to (i).
It is clear that the path-length s to the first hard interaction generated with this algorithm
follows the PDF (4.95). The interesting peculiarity of this algorithm is that it
makes no explicit reference to the CSDA. Therefore, it can be adopted in mixed simulations
with soft-energy-loss straggling, provided only that an upper bound exists for
the energy ω lost along the path length s max .
1/λ (h) (E ) (cm −1 )
1Ε+7
1Ε+6
1Ε+5
1Ε+4
C 1
= C 2
= 0. 01
C 1
= C 2
= 0. 05
C 1
= C 2
= 0. 1 0
Al, e − C 1
= C 2
= 0
1/λ (h) (E ) (cm −1 )
1Ε+7
1Ε+6
1Ε+5
C 1
= C 2
= 0. 01
C 1
= C 2
= 0. 05
C 1
= C 2
= 0. 1 0
Au, e − C 1
= C 2
= 0
1Ε+2 1Ε+3 1Ε+4 1Ε+5 1Ε+6 1Ε+7 1Ε+8
E (eV)
1Ε+2 1Ε+3 1Ε+4 1Ε+5 1Ε+6 1Ε+7 1Ε+8
E (eV)
Figure 4.4: Inverse mean free path (interaction probability per unit path length) for hard
interactions of electrons in aluminium and gold for the indicated values of the simulation
parameters. The plotted curves were calculated with W cc = W cr = 100 eV.
Fortunately, the energy loss generated from the artificial distribution G a (ω; s), eqs.
(4.59)-(4.63), is always less than ω max , eq. (4.64). Indeed, in case I we use the truncated
2 In the description of the algorithms we use the symbol ← in expressions such as “a ← b” to indicate
that the value b replaces the value of a.