Polaronic effects in mixed and intermediate-valence compounds

From an exact calculation of the density of states for one electron in the Sherrington-von Molnar model of an s-f resonance coupled to a local optical phonon mode the authors find the conditions necessary for a polaronic reduction in the width of the resonance. With the notation nu for the relaxation shift, Delta 0 for the resonance width in zero coupling, omega 0 the phonon frequency and W the conduction band width, they find for nu in the range W> nu > Delta 0 very little reduction in the resonance width, and obtain the polaronic reduction exp(- nu / omega 0) only if nu >W. This condition is too strong to be satisfied in intermediate-valence systems. However, the model is not an adequate description of intermediate-valence materials as it is an essentially one-site model. The authors generalise the model to include two sites coupled to phonons such that the sites compete a favourable local lattice distortion. In this model they can examine the dependence of the intersite transfer on lattice coupling strength. For w> nu > Delta 0 (the plausible physical region), this intersite transfer is reduced by a polaronic reduction factor leaving the widths of the virtual bound-state resonance almost unaffected.