The temperature dependence of inelastic neutron scattering in rotational tunnelling systems. I. Formulation and perturbation theory

Abstract

In recent years inelastic neutron scattering experiments have revealed marked variations in the temperature dependence of the rotational tunnelling spectra of molecular groups in various local environments. A new theoretical approach is developed here to explain these results. A microscopic model of a rigid molecular group, whose rotational degree of freedom is coupled to lattice modes, is formulated in terms of standard basis operators for states of the uncoupled system. It is shown that a complete description of the neutron spectrum can be found in terms of the time-dependent correlation functions of these operators. As a preliminary to a fuller treatment of this problem a perturbational approach is developed, which allows the conditions for a treatment-dependent shift to lower tunnelling frequencies, which is commonly observed experimentally, to be thoroughly examined.