A Method for the Numerical Integration of the Photon Transport Equation in Slab Geometry

Abstract

A procedure for the direct numerical integration of the transport equation in slab geometry is introduced. The angular flux is expressed as a series of Legendre polynomials. The iteration process is utilized for the spatial integration of the transport equation. Prior to applying this method both to neutrons and to photons, a series of studies on the photon penetration problem has been performed to assess its validity. The first code, the EOS-1, was prepared for the NEAC 2206 computer to perform the above mentioned work and also to solve some practical problems of not very large scale.

A comparison of energy buildup factors obtained by the EOS-1 code with those from the moments method and from the Monte Carlo method indicates that the method presented in this paper provides a correct treatment of the attenuation of radiations in a slab. The results also agree well with the energy spectra from the moments method, with the energy spectrum measured in the Bulk Shielding Reactor and with the energy-angular flux distributions obtained with ⁶⁰Co and ¹³⁷Cs sources behind iron and aluminum plates, both with respect to spectrum pattern and to absolute values.