On the Frenkel exciton theory of amorphous solids: II. Application to a simple three-dimensional model

Abstract

The theoretical results of the Frenkel exciton theory in an amorphous solid has been applied to a simple three-dimensional model. Explicit expressions are obtained for the longitudinal and transversal exciton energy in an averaged cubic crystal and in the corresponding amorphous phase. For an appropriate choice of the different parameters a quantity F( x), proportional to the exciton energy, can be explicitly calculated. By numerical calculations, a broadening of the exciton energy band is obtained in the amorphous phase, which rises appreciably for increasing values of the parameter, describing the disorder.