Slow-Neutron Scattering by Molecules

The operator formalism in slow-neutron scattering theory introduced by Wick and by Zemach and Glauber is considered in an approximation in which molecular rotational and vibrational effects are explicitly separated. The combined effects of rotation and translation are treated in terms of the Sachs-Teller "mass-tensor" concept, which is rederived on the basis of a rigid molecule Hamiltonian and extended to include interference effects. Only elastic vibrational transitions from the ground vibrational state are considered. The applicable neutron energy range is restricted to values large compared to the rotational level separation but below the vibrational threshold.The method is applicable to the calculation of differential as well as total scattering cross sections and to molecules of arbitrary structure. Expressions in closed form for these cross sections are obtained through use of an approximate procedure for averaging over molecular orientations. In the case of hydrogenous molecules, where direct scattering is dominant, the scattering by a given nucleus is described in terms of two parameters, viz., an effective nuclear mass for rotation and translation, and a vibrational constant. The relative simplicity of the method is illustrated in the calculation of the differential and total cross sections of CH₄ and the total cross section of H₂. Agreement of these calculations with experiment and with other calculations is good.