Slow Neutron Scattering and Thermalization by Benzene

The moderation of neutrons in benzene has been studied and a kernel for benzene was obtained. The cross-sections were calculated in the incoherent approximation. The dynamics of the benzene molecule were determined, assuming a model of the molecule in which the atoms make harmonic oscillations about the equilibrium position. The harmonic potential was formed with the set of force constants calculated by Crawford and Miller from the assigned frequency spectrum. The vibrational frequencies and the amplitude vectors determined in this way were used in the calculation of the scattering law. The hindered translations and rotations corresponding to the liquid state were included as free translations of the molecule with an associated effective mass. The numerical calculations of the scattering law for benzene were performed with the code GASKET, which calculates the scattering law from the vibrational spectrum of the molecule. The total cross-section, the average of the scattering angle, and the single-differential cross-section were obtained and compared with experimental data. The agreement between theory and experiment is very good. (author)