Slow-Neutron Inelastic Scattering from Beryllium Powder

The inelastic scattering of slow neutrons by a sample of beryllium powder has been measured using the Materials Testing Reactor phased-chopper velocity selector. Data were obtained at incident neutron energies of 0.040, 0.0415, 0.070, and 0.10 eV and at room temperature for a sample which had a transmission of 87%. The data were converted to partial differential cross sections and to the scattering-law presentation $S(\kappa , \hslash \omega )$. In contrast to previous measurements, the scattering-law presentation of the data displays considerable structure which correlates directly with the interference condition for coherent scattering. Factors which contribute to the observed structure include the structure factor for neutron-phonon interactions and the phonon dispersion relation itself. Data from this experiment are compared with the dispersion relation for single-crystal beryllium and the calculated frequency distribution of beryllium.