Livermore Model
Rayleigh scattering is described by G4LivermoreRayleighModel.
Total Cross Section
The total cross section for the Rayleigh scattering process is based on either EPDL97 or EPICS2017 data as described in Low Energy Livermore Model, and determined from the data as described in Generic Calculation of Total Cross Sections.
Sampling of the Final State
The coherent scattered photon angle \(\theta\) is sampled according to the distribution obtained from the product of the Rayleigh formula \((1+\cos^2\theta)\sin\theta\) and the square of Hubbel’s form factor \(FF^2(q)\) [eal79] [Cul95]
where \(q = 2 E \sin(\theta/2)\) is the momentum transfer.
Form factors introduce a dependency on the initial energy \(E\) of the photon that is not taken into account in the Rayleigh formula. At low energies, form factors are isotropic and do not affect angular distribution, while at high energies they are forward peaked. For effective sampling of final state a method proposed by D.E. Cullen [Cul95] has been implemented: form factor data were fitted and fitted parameters included in the G4RayleighAngularGenerator.
The sampling procedure is following:
atom is selected randomly according to cross section;
\(\cos\theta\) is sampled as proposed in [Cul95];
azimuthal angle is sampled uniformly.