JAEA Elastic Scattering Model

The \(\gamma\)-ray elastic scattering process in Geant4 is a process that takes into consideration the different mechanisms in which a high-energy photon may be elastically scattered by an atom. These mechanisms include Rayleigh scattering, nuclear Thomson scattering, and Delbrück scattering. A new model developed by JAEA includes all these scattering mechanisms collectively as elastic scattering. A more detailed description can be found in Ref. [OH18].

Total cross section

The total cross section is given by [OH17]

\[\sigma=4\pi \int^\pi_0\frac{d\sigma}{d\Omega}d \cos\theta\]

where

\[\frac{d\sigma}{d\Omega}=\lvert A\rvert ^2=\lvert A^R+A^T+A^D\rvert ^2\]

Here \(A^R\) is the Rayleigh scattering amplitude, \(A^T\) is the nuclear Thomson scattering amplitude, \(A^D\) is the Delbrück scattering amplitude, and \(A\) is the resultant scattering amplitude. The resultant amplitude is a function of the incident photon energy \(E\), scattering angle \(\theta\), and the atomic number of the scattering atom \(Z\). The total and differential cross sections are pre-calculated and prepared in data files for all elements with \(1\leq Z\leq 100\) and 10 keV \(\leq E\leq 3\) MeV over the whole angular range. The structure of the data file is explained in Ref. [OH18].

Sampling of the Final States

Sampling procedure is as the following:

  1. atom is selected randomly according to the total cross section.

  2. angular distribution functions are retrieved from data files according to the incident photon energy and atomic number of the scattering atom.

  3. polar angle is sampled based on the angular distribution function retrieved in 2.

  4. azimuthal angle is sampled uniformly.

Bibliography

OH17

Mohamed Omer and Ryoichi Hajima. Including delbrück scattering in geant4. Nucl. Instrum. Methods Phys. Res., Sect. B, 405:43 – 49, 2017. URL: http://www.sciencedirect.com/science/article/pii/S0168583X17306092, doi:https://doi.org/10.1016/j.nimb.2017.05.028.

OH18(1,2)

Mohamed Omer and Ryoichi Hajima. Geant4 physics process for elastic scattering of γ-rays. Technical Report 2018-007, Japan Atomic Energy Agency, June 2018. URL: https://jopss.jaea.go.jp/search/servlet/search?5059687, doi:http://dx.doi.org/10.11484/jaea-data-code-2018-007.