Anisotropy in the scattering of thermal neutrons in crystalline moderators - beryllium

To study the anisotropy in scattering of thermal neutrons in beryllium, elastic as well as inelastic differential cross sections were calculated. Anisotropy in elastic scattering is studied by replacing the delta function by a Gaussian function of suitable width. To study the anisotropy in inelastic scattering, we have calculated one-phonon coherent inelastic differential cross sections. The differential cross sections for the one- and two-phonon processes have also been calculated in the incoherent approximation. The angle dependence of the cross section is also expanded in terms of the Legendre polynomials. Using the above differential cross sections, the intensity of scattered neutrons in various angular directions has been calculated, and the results have been compared with the corresponding observed results of Aizawa et al. Calculated results are found in good agreement with the corresponding observed results. The effect of anisotropy in scattering on steady-state angular spectra inside small beryllium assemblies was investigated. The calculated results have been compared with the observed results of Lake and Kallfelz and also with those obtained in the isotropic scattering approximation of Garg et al. It is found that the calculated spectra in the first angular direction theta1 approx. = 28 deg at various distances from the source plane are in better agreement with the correspondingobserved results in the entire energy range than those obtained in the isotropic scattering approximation