Theory of the Electronic Polaron and Ionization of a Trapped Electron by an Exciton

Abstract

Introducing the concept of the electronic polaron which is an analogue of the usual lattice polaron, we have considered its motion under the influence of a trapping potential, by using a simplified model for the electronically polarizable crystal such that the excited states of crystal electrons consist of a single exciton band. By a suitable transformation we obtain an expression for the Hamiltonian which consists of the following three parts: the first part describes the motion of an electron under the potential in an dielectric medium in the classical way, the second part represents the energy of the electronic polarization field the quanta of which are nothing but free excitons, and the last part is the interaction energy between these two parts which causes the production or annihilation of excitons in the neighbourhood of the potential by exchanging energy with the electron. Treating the last part as a perturbation, we have calculated the probability for the ionization of a traped electron by an exciton. After correcting the oversimplification of the model, we have applied the obtained result to actual crystals, leading to a conclusion that in alkali-halides the excitons annihilate rather by ionizing F-electrons than by spontaneous emission if the density of the F-centers is larger than 1016 per c.c., in consistence with the experimental results of Apker and Taft on the external photoelectric effect.