On the Electron-Phonon Interaction in Normal Metals. II

By the use of Fröhlich's Hamiltonian and the method of Green's function, the electron-phonon interaction in a normal metal under a steady magnetic field is studied. It is shown that the period of the de Haas-van Alphen effect is not modified by the interaction. The resonance frequency of the Azbel'-Kaner effect, on the other hand, is modified and the cyclotron mass of the electron takes essentially the same value as the thermal mass which is also modified by the interaction as shown previously. The conclusion is in accord with the recent experimental results obtained by Kip and Grimes on Na and K. The same conclusion, however, is obtained also by applying Landau's theory of Fermi liquids to the inter-electronic Coulomb correlation without introducing the electron-phonon interaction, though the mass shift caused by the former seems too small.