The total polycrystalline elastic and inelastic scattering cross sections are computed by means of the Born approximation with use of the Fermi (δ function) interaction between slow neutrons and bound nuclei. Isotopic disorder and magnetic interaction are neglected. Numerical calculation for iron scattering "300-degree" neutrons yields an inelastic cross section which rises from 0.006 at $T=0$^∘{}K to 0.192 for a scatterer temperature of 1000^∘{}K, in units of the "free" nuclear elastic scattering cross section. The total (elastic plus inelastic) cross section remains constant for scatterer temperature up to 250^∘{}K, but falls off from 0.97 at $T=0$^∘{}K to 0.90 at $T=1000$^∘{}K. High and low temperature approximate results are also computed. Comparison of the results for inelastic scattering with the theory of the diffuse scattering of x-rays as developed by Zachariasen is successful in the limiting cases in which the two theories overlap.
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Robert Weinstock (1944) studied this question.
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