PENELOPE 2003 - OECD Nuclear Energy Agency

4.4. Generation of random tracks 149
a) Sample the polar angular deflection µ = (1 − cos θ)/2 from the distribution
F a (s; µ), eq. (4.30), corresponding to the current energy E. Sample the azimuthal
scattering angle as φ = 2πξ. Perform a rotation R(θ, φ) of the vector ˆd according
to the sampled polar and azimuthal angular deflections (as described in section
1.4.2) to obtain the new direction: ˆd ← R(θ, φ)ˆd.
b) Sample the energy loss ω due to soft stopping interactions along the step s
from the distribution G a (s; ω), eqs. (4.59)-(4.63), and reduce the kinetic energy:
E ← E − ω.
These two actions are performed in random order to account for the energy dependence
of the soft transport mean free paths (see section 4.3.3).
Go to (xi) if E < E abs .
(vii) Let the particle advance the distance s − τ in the direction ˆd: r ← r + (s − τ)ˆd.
(viii) Do as in (v).
(ix) If in step (iii) the step length was truncated, i.e. s = s max , simulate a delta
interaction.
Go to (ii).
(x) Simulate the hard event:
Sample the kind of interaction according to the point probabilities,
p el = N σ(h) el
,
Σ h,max
p in = N σ(h) in
,
Σ h,max
p br = N σ(h) br
,
Σ h,max
p si = N σ si
Σ h,max
,
p δ =
Σ δ
Σ h,max
, and p an = N σ an
Σ h,max
in the case of positrons. (4.120)
If the event is a delta interaction, return to (ii).
If the event is an inner-shell ionization, sample the active shell, simulate the relaxation
cascade of the residual ion and return to (ii). Notice that in this case the
state of the projectile remains unaltered.
Sample the polar scattering angle θ and the energy loss W from the corresponding
DCS. Generate the azimuthal scattering angle as φ = 2πξ. Perform a rotation
R(θ, φ) of the vector ˆd to obtain the new direction: ˆd ← R(θ, φ)ˆd.
Reduce the kinetic energy of the particle: E ← E − W .
If, as a result of the interaction, a secondary particle is emitted in a direction ˆd s ,
with energy E s > E abs , store its initial state (r, E s , ˆd s ).
Go to (ii) if E > E abs .
(xi) Simulate the tracks of the secondary electrons and photons produced by the primary
particle (or by other secondaries previously followed) before starting a new
primary track.
4.4.1 Stability of the simulation algorithm
The present simulation scheme for electrons/positrons is relatively stable under variations
of the simulation parameters, due mostly to the effectiveness of the energy-loss
corrections. This implies that the simulation parameters can be varied amply without