Inelastic Scattering of Cold Neutrons by Polycrystals

The method given by Sjölander to calculate the one phonon differential inelastic cross section in the case of single crystals has been extended to polycrystals. Initially a graphical method is used. It is shown that the method could be converted to a form in which graphical calculations are replaced by an analytic expression. This is similar to the one obtained by Weinstock's approach, except for a factor. Calculations are made for polycrystalline lead for seven different scattering angles. The incident energy corresponds to neutron of temperature 13.6°K or wavelength 8.3 A. The temperature of lead is taken as 300°K. The mean energy of the scattered neutron is also calculated. Comparison with the method of incoherent approximation shows that the results obtained by this method are widely different from the method in which we sum over the allowed reciprocal vectors.