Multiphonon mechanism of neutron scattering in glasses

Abstract

A multiphonon mechanism of neutron scattering in glasses is considered. It is due to the interaction of the neutrons with strongly fluctuating double-well potentials characteristic of glasses which may be of importance at not too low temperatures (above the liquid helium temperature). The cross section of this process is calculated and its dependence on the temperature and the neutron energy transfer is found. It is shown that, contrary to the relaxation mechanism, the multiphonon mechanism produces a cross section without a maximum in its temperature dependence. This, as well as some other features, corresponds better to the experimental observations.

Multiphonon mechanism of light scattering in glasses

“…that will be used later on. The term proportional to bUa has been omitted in a similar expression in our previous paper (Fleurov and Levanda 1992) where the multiphonon neutron scattering is discussed. It is unimportant there since it does not contribute to the multiphonon interaction with rigid D w P s in the first order of the perturbation theory.…”

“…Therefore, we may substitute it by a constant, 1989). The principal details of these calculations are given in Fleurov and Levanda (1992). Using these results the Raman cross section can be represented as…”

“…The quantity r(T) in equation (3.5) is the multiphonon relaxation time in arigid DWP. The calculation carried out in our previous papers (Fleurov and 'Itakhtenberg (1986), see also Fleurov and Levanda (1992)) assumes that the fluctuations in the DWP barrier are mainly caused by its interaction with only one phonon mode characterized by the frequency Cl and reduced mass M . The equation obtained there reads where sinh(phCl/4)/ cosh3(phCl/4)…”

“…The two dimensionless parameters in equation (3.6) are Equation (3.5) enables an analysis of the temperature and frequency dependence of the cross section of the Raman scattering due to the multiphonon interaction of the light with the rigid DWPs. If we average over the DWPs in the manner described in Fleurov and Levanda (1992) assuming a broad distribution of the asymmetry parameter , tat and a narrow distribution of the tunnelling parameter, Jo, then the principal factors determining the behaviour of the cross section are the relaxation time T(T) and exponential function. The latter also determines the dependence of the cross section (3.1) on the frequency shift w2 -w1 in the scattering process.…”

“…According to this mechanism tunnelling by the particle in such a DWP is essentially renormalized due to the strong fluctuations of the potential barrier. As a result a multiphonon packet is involved in the interaction of the absorbed particle with the DWP (for the phonon see Fleurov and Trakhtenberg (1986); for the neutron, Fleurov and Levanda (1992); the photon is to be considered in this paper). The multiphonon absorption of the electromagnetic wave is similar in many respects to the multiphonon ultrasonic attenuation considered in Fleurov and Trakhtenberg (1986).…”