Inelastic Scattering of Slow Neutrons

The total polycrystalline elastic and inelastic scattering cross sections are computed by means of the Born approximation with use of the Fermi ($\delta$ 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 $T=0\mathrm{}$°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 $T=0\mathrm{}$°K to 0.90 at $T=1000\mathrm{}$°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.