The Line Shape in a Harmonic Lattice

Abstract

A general formalism is developed for the treatment of lattice vibrations. The problem is reduced to the mathematics of noncommuting operators. Hausdorff's equation is then solved for a lattice interacting with linear forces. The cases treated in detail are the line shapes of a radiating atom as affected by the displacement (Franck‐Condon effect) and by the nuclear recoil (Mössbauer effect). Only formal results are obtained, which are more difficult to compute than those of the method of normal modes. However, they are more general and do not require the data of vibrational frequencies.