The non-linear itinerant oscillator model: the effect on the polarisability spectrum of including barrier-crossing by dipoles

Analysis of the itinerant oscillator model of polar fluids has hitherto been concentrated on the small-oscillation approximation. This has neglected one important contribution to the dynamic polarization, namely relaxation due to crossing ofdipoles over the hills of the cosine potential for dipole-dipole coupling. In this Letter a numerical algorithm for solution of the Fokker-Planck equation due to Reid is used to calculate the Fourier transform of the angular velocity autocorrelation function for this model when barrier-crossing is included. The results are used to calculate the frequency dependence of the polarizability. They indicate that (i) the far-infrared absorption peak is centred at a lower frequency than in the harmonic approximation, and (ii) the bandwidth of the far-infrared absorption is increased significantly over the harmonic approximation leading to additional contributions at frequencies below the far-infrared peak, in qualitative agreement with recent experimental observations.