Virtual Phonon Exchange in Glasses

Abstract

The phonon field has long been recognized to provide an efficient coupling of particles or excitations in crystals. The most famous example is the case of superconductivity where a pair of electrons is bound by virtual exchange of phonons. The same mechanism has also been invoked in the case of paramagnetic impurities in crystals (1). However because of the small value of the coupling constant of each spin with the lattice even for non Kramers ions, this mechanism yields a negligible contribution to the linewidth measured in E.P.R. (2). On the contrary, in the case of helium 3 or 4 impurities in helium 4 or 3 single crystals, the coupling between the impurities via the phonon field seems to be rather strong and probably contributes to the anomalous value of the diffusion coefficient of impurities, as observed in NMR (3). One might also ask whether the anomalous value at low temperatures of the dielectric constant of KC1 crystals containing molecular impurities (OH-) is not due to the appearance of a collective effect ordered by the phonon field (4).