  We generalize the Wannier interpolation of the electron-phonon matrix
elements to the case of polar-optical coupling in polar semiconductors. We
verify our methodological developments against experiments, by calculating the
widths of the electronic bands due to electron-phonon scattering in GaAs, the
prototype polar semiconductor. The calculated widths are then used to estimate
the broadenings of excitons at critical points in GaAs and the electron-phonon
relaxation times of hot electrons. Our findings are in good agreement with
available experimental data. Finally, we demonstrate that while the Fr\"ohlich
interaction is the dominant scattering process for electrons/holes close to the
valley minima, in agreement with low-field transport results, at higher
energies, the intervalley scattering dominates the relaxation dynamics of hot
electrons or holes. The capability of interpolating the polar-optical coupling
opens new perspectives in the calculation of optical absorption and transport
properties in semiconductors and thermoelectrics.
