CERN Program Library Long Writeup W5013 - CERNLIB ...

Geant 3.16 GEANT User’s Guide PHYS251
Origin : G.Tromba, P.Bregant Submitted: 10.10.89
Revision : Revised: 16.12.93
Documentation :
Simulation of Rayleigh scattering
CALL GRAYL
GRAYL generates Rayleigh scattering of a photon using the random-number composition and rejection technique
to sample the momentum of the scattered photon and the scattering angle, according to the form-factor
distribution. In this reaction no new particles are generated and the kinematical quantities of the scattered
photon replace the original ones in the /GCTRAK/ common block.
Activation of the Rayleigh scattering is done via the FFREAD data record RAYL. If this process is activated,
GRAYL is called by GTGAMA when a Rayleigh scattering occurs.
1 Method
The Rayleigh differential cross section as a function of q 2 is given by [35]:
(
dσ R q
2 ) ( )
= πr2 0 1+µ
2
dΩ k 2 |F T (q)| 2 (1)
2
where:
r 0
electron radius
k
incident wave vector
q =2ksin θ 2
momentum of scattered photon (θ is the scattering angle)
µ = cosθ =1− q2
2k 2
F T (q) molecular form factor
Under the assumption that the atoms of a molecule are completely independent, |F T (q)| 2 is given by:
|F T (q)| 2 =
N∑
i=1
W i
A i
|F i (q i ,Z i )| 2 σ ci (Z i ,E) (2)
where the index i runs on the N atoms in the molecule and:
W i
Z i ,A i
F i
σ ci
proportion by weight
atomic number and weight
form factor
total atomic cross section for coherent scattering
Using the combined composition and rejection sampling method described in GPAIRG ([PHYS211]) we may
set:
N∑
N∑ ( )
f (q) = α i f i (q) g i (q) = A qi
2 |FT (q)| 2 ( )
1+µ
2
A (qn 2) (3)
2
i=1
230 PHYS251 – 1
i=1