On the evaluation of phonon widths and shifts

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Abstract
In this paper a method is described for the numerical evaluation of phonon widths and shifts due to three‐phonon processes in an anharmonic crystal. With this method the δ‐function and principal value restrictions on the frequencies of the phonons participating in the three‐phonon processes do not have to be taken into account explicitly. The method is based on a dispersion relation satisfied by the width and shift, and on their expansion in Legendre functions of the first and second kinds, respectively. It is illustrated by a numerical example.