On the Use of the Langevin Equation of Brownian Motion for the Analyses of Cold and Slow Neutron Scattering by Liquid Methane

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Abstract
The Langevin equation of Brownian motion is used to analyze the experimental data on the scattering of cold and slow neutrons by liquid methane. Scattering of neutrons by a molecule in the liquid is treated analytically as for a gas except the translational mode of the molecule is assumed to obey the Langevin equation. To obtain agreement with the experimental data using this model, it is necessary to adjust the viscous damping coefficient η appearing in the Langevin equation as the magnitude of the momentum transfer κ in the collision between the neutron and the molecule changes. Plotting the value of η needed to best fit the observed quasielastic peak against the momentum transfer κ resulted in a straight line on a semilogarithm plot. An extrapolation of the straight line to zero momentum transfer gave a value of 1.7×1013 sec−1 for the viscous damping coefficient. This value is in agreement with the experimental value of the diffusion coefficient which is related to the viscous damping coefficient by the Einstein relation. It is pointed out that the analysis is, at least qualitatively, in accord with results on the scattering of neutrons by other liquids. There is evidence, although not conclusive, that the rotational motion is partially hindered.