sets and diffusion constants for specified material compositions for use in gamma ray diffusion calculations (incorporating a removal flight correction) from a library of microscopic cross sections. For the purpose of the first flight calculation the source is assumed to be composed of discrete energies; the diffusion calculation is performed in groups. The data supplied by the module for each material is as follows:
Total cross sections at the source energies.
Scattering cross sections from the source energies into each diffusion group.
Diffusion coefficient (D) and diffusion length (L) for each diffusion group.
Group to group transfer cross sections for the diffusion groups.
Energy deposition factors for each source energy and for each diffusion group.
The module extracts microscopic cross sections for the required elements from a library which contains data for a given set of source energies and a given diffusion group scheme. The standard library supplied with the module contains data for 33 elements. It employs 13 source energies and 32 diffusion groups. This data has been prepared using the GAMCON program which obtains cross sections from the data of Hubbel by reference to the subroutine HEITLER. The module can, however, handle any library of data prepared in the appropriate format.
The group diffusion length and consequent diffusion coefficient are obtained from standard formulae.
REMTWO (WRS system module No. 299) Calculates the uncollided flux due to a distributed source in a one-dimensional plane geometry system. A method is used in which the flux is approximated by a sum of diffusion equation solutions. From the calculated flux a first collision source may be obtained (externally) for use in the diffusion equations.
The REMTWO module may be used for a system which can be represented by a series of plane parallel sided slabs of infinite lateral extent, each composed of a uniform material. Some or all of these regions contain sources, which are of varying strength and have a range of energies. The source strength shows no lateral variation, and is therefore a function of a single spatial coordinate x. The source is defined as a function of x by values given at the points of a mesh which is uniform in each region, while a group treatment is used for the energy dependence. Two cases are distinguished by whether the source energy spectrum is the same throughout the system or varies with position.
In the latter case the spatial variation of source strength is defined separately for each group using a mesh which may be different for each group.
The cross section for each group is defined throughout the system by assigning a material to each region and a set of cross sections to each material. The uncollided flux in group g at position x is given by the integral over all volume of the source strength multiplied by exp(-t) (the number of mean free paths) divided by 4 Pi r**2.
When the integration over the lateral coordinates is performed in this expression, there remains an integral with respect to x in which the integrand involves the E1 function. By substituting an approximation of this function it is possible to express the flux throughout the system as the sum of three solutions of the diffusion equation. By this method, the module calculates flux values at the points of a mesh, and it can print out values at a specified spacing in each region. The mesh can be different from the source mesh and will be set automatically by the module if it is not supplied. The module does not solve the diffusion equations itself but sets the parameters which define them completely and then returns control to the calling program so that the solutions can be obtained externally.