On the Evaluation of the Thermal Neutron Scattering Law

The magnitude of the scattering cross section for slow neutrons by atomic systems (gases, liquids, and polycrystalline solids) is governed by the correlated motions of atoms in the system. A major contribution to the scattering is determined by the motion of single atoms. The dominant part of this contribution is determined by the velocity autocorrelation function for an atom in the system. The aim of this paper is (i) to show how the autocorrelation function can be derived from experimental scattering data for small momentum transfers and (ii) to give methods of evaluation of the corresponding part of the cross section for all momentum and energy transfers in terms of the experimentally observed quantities. The methods are chosen to minimise computational difficulties and inaccuracies. The comparison of the recomputed data with the experimental results permits the estimate of other contributions to the scattering. Some simple examples of these methods are given, and the relevance of this work to thermal neutron transport calculations is mentioned.

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