Slow Electrons in Polar Crystals: Self-Energy, Mass, and Mobility

The parameters for the Feynman model of a polaron are evaluated numerically for various values of the electron lattice interaction $\alpha$, in the usual idealization of the problem of a slow electron in a polar crystal. The self-energy and effective mass thus obtained are compared with earlier polaron theories, indicating the superiority of the Feynman model for a wide range of $\alpha$. The polaron size and the effect of the continuum approximation are estimated, and it is concluded that the alkali halides, at least, may be in the border region for the validity of this approximation. The problem of calculating polaron mobility as determined by scattering with longitudinal optical mode phonons is analyzed and previous theories are critically reviewed. A new theory based on the Feynman model is developed in which the Boltzmann equation is used with resonance scattering considered as the fundamental scattering process. A comparison with previous theories shows some improvements and stresses still doubtful points. A comparison with various experiments suggests the possible inadequacy of the usual idealization.