Selection Rules for Anharmonic Interactions of Nearest Neighbors in Crystals with the Zinc Blende or Diamond Structure

Selection rules are derived for multiple-phonon processes which are dominated by anharmonic interactions between nearest-neighbor lattice particles. These nearest-neighbor selection rules (NSR) are different from and supplementary to the usual group-theoretical selection rules. NSR for wave vectors at $X$ or $L$ are expressed in Born's (NSRB) and in Keating's (NSRK) formalism. The NSRB refer to anharmonic two-particle interactions; the NSRK allow interactions between two or more particles. The applicability of the NSR to various multiple-phonon processes—with emphasis on infrared two-phonon absorption—is investigated and the results of some relevant model calculations are given. Practical rules for further applications are proposed.