The Impulse Approximation Scattering Function and Its Use in Monte Carlo Photon Transport Simulations

Abstract

The viability of using the impulse approximation scattering function in Monte Carlo photon transport simulations is explored. This scattering function can be constructed from the double differential incoherent scattering cross section developed by Ribberfors and Berggren [Phys. Rev. A., Vol 26, p. 3325 (1982)]. A commonly used method for modeling photon Doppler broadening, which is referred to as the hybrid Doppler broadening method, can also be derived from this cross section. A new photon Doppler broadening method, called the consistent Doppler broadening method, is derived and discussed. This method eliminates some of the commonly employed approximations in the hybrid Doppler broadening method, in part, by using the impulse approximation scattering function. Integrated incoherent cross sections generated using the impulse approximation scattering function and the widely used Waller-Hartree scattering function are in good agreement above 20 keV. Below 20 keV, differences as high as 70% are observed, which differs from the roughly 5% differences observed by Ribberfors [Phys. Rev. A., Vol. 27, p. 3061 (1983)] for some of the materials. Integral and spectral quantities for two problems are also generated using the Monte Carlo photon transport capabilities of the Framework for Research in Nuclear Science and Engineering. Due to the small, relative result differences observed when using the impulse approximation scattering function, it is considered a viable alternative to the Waller-Hartree scattering function. In addition, some small, but expected, differences in spectral fluxes at low energies can be avoided by adopting the consistent Doppler broadening method.

Keywords:

• Impulse approximation
• incoherent scattering
• photon Doppler broadening
• adjoint
• Monte Carlo

Acknowledgments

This work describes objective technical results and analyses. Any subjective views or opinions that might have been expressed do not necessarily represent the views of the U.S. Department of Energy or the U,S. government. The authors would also like to thank Jürgen Henniger, Dorothea Gabler, and Uwe Reichelt of the Technische Universität Dresden for their helpful discussions related to portions of this work and their generosity as hosts.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

^a In EGS4 the method is slightly different to account for circularly polarized photons.

Additional information

Funding

This work was partially supported by U.S. Nuclear Regulatory Commission Fellowship grants [NRC-28-09-994 and NRC-38-10-954] and the Domestic Nuclear Detection Office: Academic Research Initiative grant 15DNARI0013-04-00. This work was also partially performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344.