Resonance Absorption in Materials with Randomly Dispersed Grains

The resonance integrals and associated temperature coefficients in a mixture of graphite and randomly dispersed grains of ThO₂ are calculated. Two methods of dealing with the random distribution of grains are used. The first is one developed by Lane, Nordheim, and Sampson, which is based upon a random Dancoff factor, and the second uses the dichotomic Markov process. The numerical results are compared for a range of grain sizes and ranges of temperature. The differences in the two methods do not exceed 4% for resonance integrals and 2.5% for temperature coefficients. Bearing in mind the radically different stochastic procedures involved, it is remarkable and useful to know that the results are so insensitive to the stochastic model used. In addition we give a measure of the variance in the results.