Time expansion of correlation functions and the theory of slow neutron scattering

Abstract

The velocity correlation function for a classical system of particles interacting with a two-particle potential is expanded in powers of t. The coefficients in this expansion are averages of derivatives of the interaction potential and can be expressed in terms of instantaneous two, three, etc., particle distribution functions. For the special case of a harmonic crystal these expressions reduce to the respective moments of the frequency distribution function. For liquid argon the range of values of t, for which the velocity correlation is well represented by the first new terms of its time expansion, is determined from a comparison with the computer results obtained by one of us (A. R.). Similarly, the range of values of the momentum transfer is investigated, for which this time expansion leads to a useful representation of the incoherent scattering cross section for slow neutrons. For coherent scattering analogous formulae are given, but no numerical comparison with the computer results has been made. In addition, it is shown that the non-Gaussian behavior of G s ( r, t) obtained from the computer results has considerable influence on the shape of the incoherently scattered slow neutron spectrum. It is pointed out that slow neutron scattering with large values of momentum transfer can be used as an experimental technique for the determination of the mean square acceleration in any system.