Theory of the effective Debye–Waller factor in neutron scattering from high frequency molecular modes

Abstract

A theory is given of the incoherent scattering cross section from high frequency intramolecular vibrational modes (ωλ) in a molecular crystal. It is assumed that ωλ≫ωD, where ωD is the maxium frequency of the low frequency lattice phonon continuum. It is shown that the scattering from a ωλ mode is proportional to a Debye–Waller factor arising only only from the internal molecular modes, multiplied by Ss(K,ω−ωλ), where Ss(K, ω) is the self-correlation function of the molecular lattice. In the case when the Debye–Waller factor due to the lattice phonons is negligibly small, we show that Ss(K, ω−ωλ) is a Gaussian in ω−ωλ with Doppler broadening due to translational and rotational motion. Our theory is a development of the short-time approximation and explains the unexpectedly strong intensity of the C–H stretching and bending modes recently observed by Jobic, Ghosh, and Renouprez in hexamethylenetetramine (HMT). The present paper gives the theoretical basis for the quantitative interpretation of the high energy intramolecular vibrational spectrum measured by inelastic neutron scattering.