Coherent Scattering of Slow Neutrons by a Liquid

Abstract

The convolution approximation of Vineyard to treat the coherent scattering of slow neutrons by a monatomic liquid is extended. The correction term, which takes care of correlations between neighboring atoms, is evaluated on the basis of a "quasicrystalline" model of a liquid. In the calculation proper account is, however, taken of the geometrical arrangement and dynamical behavior of atoms in a liquid. Expression for the width of the "quasielastic" scattering is derived which exhibits a characteristic oscillatory behavior as a function of momentum transfer. Explicit numerical calculations for the width have been made for liquid argon near the triple point, which are in reasonably good agreement with experiment. An interesting feature of the basic formula of the paper is the temperature dependence of the width for a given momentum transfer, which is also in qualitative agreement with experiment. There are other features which need to be tested by further experiments, suggestions for which have been outlined.