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The theory of the infra‐red absorption and dispersion of crystals due to lattice vibrations is reinvestigated. Dipole moments up to third order and cubic and quartic anharmonicity in the displacements of the nuclei are considered. Using Green functions and the functional method of Martin and Schwinger a dispersion formula is derived in terms of renormalized phonons. The introduction of a renormalized linear dipole moment causes the oscillator strength to become a complex function of frequency. In the case of diatomic ionic crystals the frequency shift and lifetime of the dispersion oscillator can be obtained from the measured optical parameters.

The two-phonon absorption bands of silicon and germanium are calculated taking into account the second-order dipole moment up to second-nearest neighbours. The agreement between the calculated and measured bands shows that the shell model used in our calculations gives quite good phonon dispersion curves. The detailed analysis of the remaining deviations between measured and calculated frequencies indicates that in some points of the Brillouin zone the shell model should be corrected.Die Zweiphononen-Absorptionsbanden von Silizium und Germanium werden berechnet, wobei das Dipolmoment zweiter Ordnung bis zu zweitniichsten Nachbarn berucksichtigt wird. Die Vbereinstimmung zwischen den berechneten und gemessenen Banden zeigt, daB das fur die Rechnungen zugrunde gelegte Schalenmodell die Phononendispersionskurven recht gut wiedergibt. Die niihere Betrachtung der restlichen Abweichungen zwischen gemessenen und berechnetenFrequenzen ergibt, daD in einem gewissen Bereich der Brillouinzone das Schalenmodell besser angepaBt werden sollte.

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