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| Geant 3.12 | GEANT User's Guide | PHYS251 ##
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Author(s) : G.Tromba, P.Bregant Submitted: 10.10.89
Origin : Same Revised: 19.12.92
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|CALL GRAYL |
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GRAYL generates Rayleigh scattering of a photon by 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 automatically called by GTGAMA when a Rayleigh scattering occurs.
2 The Rayleigh differential cross section as a function of q is given by [bib-NELS]:
2 2 2 2 2
((dsigma (q ))/ (dOmega))= ((pir )/(k ))(((1 +mu )/ (2)))|F (q)| (1)
R T
0
where:
r electron radius
k0 incident wave vector
q= 2ksin(((theta)/(2))) momentum of scattered photon (theta is the
scatter2ng ang2e)
mu= cos(theta) = 1-((q )/ (2k ))
sigma total atomic cross section for coherent scattering
F (q)c molecular form factor.
T
Under the assumption that the atoms of a molecule are completely 2 independent, |F (q)| is given by: T
2 2
|F (q)| = sum ((W )/(A ))|F (q ,Z )| sigma (Z ,E) (2)
T i=1 i i i i i c i
i
where:
th
W percentual weight of the i element
i th
Z ,A atomic number and weight of the i element
i i
th
F form factor of the i element
i
N number of atoms in the molecule.
Using the combined composition and rejection sampling method described in GPAIRG (Phys-211) we may set:
N N 2 2 2 2
f(q) =sum alpha f (q)g (q) =sum A(q )((|F (q)| )/(A(q )))(((1+mu )/ (2)))(3)
i=1 i i i i=1 T
i n
where:
n number of energy binning
th
q momentum of the photon with energy E of the i
i i
binning
q lower limit for the momentum of the scattered
n-1 photon
q upper limit for the momentum of the scattered
n pho2on
alpha A(q )
i
i
2 2
f (q) |F (q)| / A(q )
i T n
2
g (q) ((1+ mu )/(2)) is the rejection function.
i
Therefore, for given values of the random numbers r and r , 1 2 GRAYL samples the momentum of the scattered photon and the scattering angle theta via the following steps:
2 2 2 2
q =(A(q )- A(q ))(((q -q )/ (A(q )-A(q )))) (4)
i i-1
i-1 i i-1
2 2