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 ($\ensuremath{\delta}$ 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 $T=0$\ifmmode^\circ\else\textdegree\fi{}K to 0.192 for a scatterer temperature of 1000\ifmmode^\circ\else\textdegree\fi{}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\ifmmode^\circ\else\textdegree\fi{}K, but falls off from 0.97 at $T=0$\ifmmode^\circ\else\textdegree\fi{}K to 0.90 at $T=1000$\ifmmode^\circ\else\textdegree\fi{}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.