Multiplet Structure of Excitons in Ionic Crystals

Abstract

The excited states of crystals arising from the configuration in which an electron is transferred from a negative ion to a nearest neighbor positive ion are analyzed. It is concluded that 72 overlapping exciton bands results for crystals having the NaCl structure. Optical transitions from the ground state are allowed to only 5 of the 30 energy levels into which the 72 bands collapse at the center of the Brillouin zone. For crystals having the CsCl structure, 96 bands occur which collapse into 40 energy levels at $k=0, 6$ of which can be reached from the ground state by allowed optical dipole transitions. In the absence of spin-orbit interaction, only two transitions are allowed for both structures. It is concluded that the lifetime of exciton states, as limited by interaction with optical phonons, is sufficiently short to account for the width and temperature dependence of fundamental absorption lines. Approximate wave functions describing the exciton states are constructed and a procedure for calculating energy levels and relative intensities of absorption components is formulated.