Dynamics of Neutron Scattering by Molecules

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Abstract
The scattering of low-energy neutrons by molecules is investigated by a method which facilitates the treatment of inelastic processes. Dynamical systems characterized by the degrees of freedom of gas molecules are examined in detail. The formalism is applied first to the derivation of the differential cross section for scattering by an ensemble of coupled harmonically oscillating nuclei in thermal equilibrium. Rotator scattering is investigated in the limits of high and low energy, and inelastic corrections to the static approximation are also calculated. The cross section of a thermally excited monatomic gas is presented in a closed form which shows its dependence on the ratio of the mean velocity of thermal motion to the neutron velocity. Results appropriate to large and to small values of the velocity ratio are derived. Quantitative estimates for the validity of the various approximations are given.

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