An isotropic model operator for three-phonon interactions and its application to the thermal conduction of phonons

A new model operator for Umklapp processes is formulated in such a way that it combines the Hamilton and Parrott approach (1968-9) with that of Simons (1975). In comparison with the models used in earlier work the present model has the advantage that the reciprocal lattice vectors need not be grouped in any particular manner to prove its negative-semi-definite property. It also yields a new expression for thermal conductivity which agrees quantitatively with the experimental data for Ge and LiF without using any fitting parameters.