Two-Quantum Excitations in Alkali Halides

Optical excitations involving the simultaneous production of two or more excitons by a single photon in alkali halides are considered. The electron-electron interaction is approximated by a term derived from Toyozawa's theory of the electronic polaron. Using a Lee-Low-Pines transformation for the c.m. motion and the Hartree approximation for the internal motion of an exciton, dipole matrix elements are calculated for many-exciton transitions. Specifically, for typical alkali halides we find the oscillator strength ratio $\frac{f^{\mathrm{}\left(2\right)\mathrm{}}}{f^{\mathrm{}\left(1\right)\mathrm{}}}\sim {10}^{-2\mathrm{}}$, in disagreement with the ratio 1.5 obtained by Miyakawa for LiF. Ultraviolet and x-ray data in the two-exciton region are briefly discussed.