Electron-phonon relaxation in pure metals and superconductors at very low temperatures

The electron-phonon relaxation processes in pure metals and superconductors are considered at low temperatures when electrons interact with both longitudinal and transverse phonons. The screening of the electron-ion interaction is treated in a gauge-invariant form, so that both longitudinal and transverse electromagnetic fields are taken into consideration. The results obtained are applied to the analysis of the heating effect of the electron system. The interaction of electrons with transverse phonons increases the electron-phonon relaxation rate by a factor of ≃15 in comparison with the case when only longitudinal phonons are taken into consideration. The peculiarity of the screening effects in a superconductor leads to the conclusion that at low temperatures T≪Δ transverse phonons do not participate in the electron-phonon relaxation processes.