CERN Program Library Long Writeup W5013 - CERNLIB ...

As in the conditions (22), (23) and (24) the value of c is as minimum 4, one gets n 3 ≥ 16. In order to speed
the simulation, the maximum value is used for α.
The number of collisions with energy loss in the interval B (the number of interactions which has to be
simulated directly) increases slowly with the total number of collisions n 3 . The maximum number of these
collisions can be estimated as
n B,max = n 3 − n A,min ≈ n 3 (〈n A 〉−σ A ) (27)
From the previous expressions for 〈n A 〉 and σ A one can derive the condition
n B ≤ n B,max = 2n 3c 2
n 3 + c 2 (28)
The following values are obtained with c =4:
n 3 n B,max n 3 n B,max
16 16 200 29.63
20 17.78 500 31.01
50 24.24 1000 31.50
100 27.59 ∞ 32.00
Special sampling for lower part of the spectrum
If the step length is very small (≤ 5 mm in gases, ≤ 2-3 µm in solids) the model gives 0 energy loss for
some events. To avoid this, the probability of 0 energy loss is computed
P (∆E =0)=e −(〈n 1〉+〈n 2 〉+〈n 3 〉)
(29)
If the probability is bigger than 0.01 a special sampling is done, taking into account the fact that in these
cases the projectile interacts only with the outer electrons of the atom. An energy level E 0 =10eV is
chosen to correspond to the outer electrons. The mean number of collisions can be calculated from
〈n〉 = 1 dE
∆x (30)
E 0 dx
The number of collisions n is sampled from Poissonian distribution. In the case of the thin layers, all the
collisions are considered as ionisations and the energy loss is computed as
∆E =
n∑
i=1
3 Implementation
E 0
1 − Emax
E max+E 0
u i
(31)
The method to be used for energy loss straggling is chosen in GFLUCT. Ifδ-rays are produced (DRAY = 1)
above the cut value DCUTE and the detailed PAI simulation for straggling in thin layers (see PHYS334) is
not chosen (STRA = 0, default), GLANDZ is called always as it samples from the restricted distribution (the
energy loss of the δ-rays which are explicitly produced should not be taken into the energy loss distribution).
If δ-rays are not produced, the values of κ and ξ/I are computed, and Urbán, Landau, Vavilov or Gaussian
model is chosen accordingly. If Urbán model is used, GLANDZ will be called with infinite (BIG) value for the
δ-ray production.
When Landau model is chosen, it is possible to use a routine from the CERN Program Library to sample
random numbers from the Landau distribution : GENLAN written by James and Hancock [64] and copied
into GEANT source file as GLANDG. This routine has been modified in order to reproduce the tail for large
values of X. The original routine did not give values of X larger than 200.
CALL GENLAN(X)
It should be noted that over the years considerable confusion has arisen over the precise form and features
of the Landau distribution. As an example, a simpler form of φ(λ) had been proposed by Moyal [65] and
used on occasions which has little in common with the function defined in section 2.1 [66].
For the Vavilov distribution we have used the function GVAVIV by Rotondi and Montagna [67].
266 PHYS332 – 9