CERN Program Library Long Writeup W5013 - CERNLIB ...

may set:
f(ɛ) =
g(ɛ) =
α 1 =
f 1 (ɛ) =
[ ] 1
2∑
ɛ + ɛ = α i f i (E) for ɛ 0 >ɛ>1
[
i=1
1 − ɛ ]
sin2 θ
1+ɛ 2 rejection function
1
α 2 = 1 ln(1/ɛ 0 )
2 (1 − ɛ2 0)
1
2ɛ
f 2 (ɛ) =
ɛ ln(1/ɛ 0 )
1 − ɛ 2
The value of ɛ corresponding to the minimum photon energy (backward scattering) is given by:
ɛ 0 =
1
1+2E/m e
Given a set of random numbers r i uniformly distributed in [0,1], the sampling procedure for ɛ is the following:
1. decide which element of the f(ɛ) distribution to sample from. Let α T =(α 1 + α 2 )r 0 .Ifα 1 ≥ α T
select f 1 (ɛ), otherwise select f 2 (ɛ);
2. sample ɛ from the distributions corresponding to f 1 or f 2 .Forf 1 this is simply achieved by:
ɛ = ɛ 0 e α 1 r 1
For f 2 , we change variables and use:
ɛ ′ =
{
max(r2 ,r 3 ) for E/m ≥ (E/m +1)r 4
r 5
Then, ɛ = ɛ 0 +(1− ɛ 0 )ɛ ′ ;
for all other cases
3. calculate sin 2 θ =max(0,t(2 − t)) where t = m e (1 − ɛ)/E ′
4. test the rejection function, if r 6 ≤ g(ɛ) accept ɛ, otherwise return to step 1.
After the successful sampling of ɛ, GCOMP generates the polar angles of the scattered photon with respect
to the direction of the parent photon. The azimuthal angle, φ, is generated isotropically and θ is as defined
above. The momentum vector of the scattered photon is then calculated according to kinematic considerations.
Both vectors are then transformed into the GEANT coordinate system.
3 Restriction
The differential cross-section is only valid for those collisions in which the energy of the recoil electron is
large compared with its binding energy (which is ignored). However, as pointed out by Rossi [18], this has
a negligible effect because of the small number of recoil electrons produced at very low energies.
PHYS221 – 2 218