The temperature dependence of inelastic neutron scattering in rotational tunnelling systems. II. Calculation of the time-dependent correlation functions

Abstract

For pt.I see ibid., vol.15, p.3841 (1982). The problem of explaining the temperature dependence observed in the inelastic neutron scattering spectrum of rotational tunnelling systems was considered in an earlier paper and based on a model in which a threefold molecular group in a hindering potential is coupled to a spectrum of phonon modes. An expression was derived for the neutron scattering function in terms of the correlation functions of the standard basis operators of the uncoupled system. Here the authors extends the perturbational approach for the calculation of these correlation functions that was developed earlier to include the effects of line broadening. The temperature dependence of the shifting and broadening of the peaks in the neutron spectrum is then calculated for different assumed forms for the density of the coupled-phonon states. Not enough is known about the coupling to the phonon spectrum for a complete quantitative comparison with experiment for any one system. However, the author shows that the theory can be used to explain the range of the experimentally observed behaviour, and the form of the temperature dependence of the shifting and broadening of the peaks.