Quasiselection rules for multiphonon absorption in alkali halides

Abstract

A quasiselection rule is derived that multiphonon infrared absorption in alkali halides prefers final states containing an odd number of optical phonons. This quasiselection rule explains the recent observation of a well-defined peak in the low-temperature infrared absorption of several alkali halides at a frequency corresponding to the sum of three optical phonons. No corresponding peak occurs at the two- or four-opticalphonon summation-band frequencies. It is shown that the quasiselection rule results from the relative ionic displacements for optical modes being approximately in phase with the individual ion displacements, while the relative ionic displacements for acoustical modes are approximately 90\ifmmode^\circ\else\textdegree\fi{} out of phase. The further realization that, at least for optical modes, the magnitude of the Fourier-transformed relative displacement is nearly independent of the phonon wave number greatly reduces the effort of the calculation. This approximation reduces an extremely tedious momentum-dependent sum to a thermally and frequency weighted density of states in which the phonon branches are kept distinct.