Point-Kernel Shielding Applications of Sievert Integral

Abstract

The application of a point-kernel technique in gamma radiation shielding calculations has a long and successful history. Using this approach radiation sources of various shapes such as point, linear, planar, or volumetric can be subdivided using the linear superposition principle to calculate total radiation received at a detector. Mathematically, any form of a distributed source may be treated as a summation i.e. integration of the radiation received from an equivalent number of point sources, for which exponential point-kernel function is analytically known. Fundamental assumption is that there is no interaction of individual, point sources which together represent total distributed radiation source. The effects of geometrical boundaries and gamma scattering are not included in this treatment, so user should be aware of these inherent limitations when comparing with reference results, such as Monte Carlo (MC) solution. This paper presents specific case of gamma flux attenuation from a distributed line source of photons in front of a slab shield, but is actually part of a larger effort, whose final goal is a general-purpose point-kernel code development. The solution of a line source with slab shield is known as the secant or Sievert integral, which cannot be evaluated analytically, so auxiliary tabulated function is introduced to facilitate bilinear interpolation on angle and shield thickness. Such code written in C-language will provide graphical user interface to assist user with necessary input data preparation and selection of predefined shielding materials for which Taylor buildup factors are provided. This paper gives programming and numerical aspects of such point-kernel code for which results of the test cases are compared with a MC solution of SCALE6.1.3 code package.