Calculation of neutron spectra for hydrogen in zeolites: rotational motions and translational motions in the Born-Oppenheimer limit

Inelastically scattered neutrons can probe the location and dynamical behavior of molecular hydrogen absorbed within zeolites. Hydrogen may, at certain temperatures, display mixed quantum/classical dynamics associated with its rotational and center-of-mass (CM) motions. When hydrogen diffusion occurs within a zeolite containing a unique adsorptive site, the spectrum is a simple convolution of (quantum) rotational and (classical) CM contributions. We present a jump diffusion model with a faujasite-type host which illustrates this behavior. A more general case would be a host which induces a spatially-dependent distribution of rotational frequencies. In order to address this more general situation, we present a formalism in which the standard time correlation function for neutron intensity: C(q,t) = [e(i (H) over capt)(b) over cap (q)e(-i (H) over capt)(b) over cap (dagger)(q)] is approximated in the Born-Oppenheimer limit. A preliminary test of this formalism is performed for jump diffusion within a one-dimensional model system. (C) 2000 Elsevier Science B.V. All rights reserved.