Effective Electron–Hole Interaction for Intermediate and Strong Electron–Phonon Coupling

The interaction of an electron‐hole pair is studied in a polar semiconductor, each particle being coupled to the lattice by the Fröhlich interaction. The theory of Gross and Tulub is used for the description of a single polaron. This theory which gives satisfactory results for both intermediate and strong coupling is then generalized to the problem of two interacting polarons. For not too strong coupling the effective electron‐hole potential will be presented in form of a series with increasing powers of the coupling constant. The first term of this series gives the well known Haken potential, whereas the higher terms are corrections to the potential which will become important for stronger coupling. The results are discussed in connection with exciton screening in the thallous and cuprous halides.