Zur Theorie des Exzitons in den Alkalihalogeniden

Following the many-body treatment of exciton byHaken andSchottky we represent the electronic polarization of the lattice induced by the excess electron and the hole in the Hamiltonian as well as in the wave function by introducing localized pair states and their coupling with the exciton particles. By application of a unitary transformation the pair states may be eliminated and one obtains the effective Schrödinger equation of an exciton consisting of particles dressed with polarization clouds. The coupling coefficients are determined by a minimum condition for the polarization energy. The effective interaction law between electron and hole and their effective masses are investigated explicitly. By transformation of the Schrödinger equation into a system of difference equations and solution of the corresponding secular equation one obtains an expression for the binding energy of the lowest exciton state in the alkali halides, which represents a connection of the “excitation” and “transfer” models. For the iodides of Na, K and Rb the binding energies were calculated using an approximative estimate for the various matrix elements involved. They are in good agreement with the experimentally observed energy differences between the first absorption peak and the small shoulder which indicates the position of the band edge.