On the Interaction of the Lattice Vibrations with the Conduction Electrons

Abstract

G. Wentzel') and W. Kohn and Vachaspati2) made comments on Frohlich's theory of superconductivity.3) The latter confimled that the shell construction in the momentum space is hardly possible if the interaction of the conduction electrons with the lattice phonons is so strong that Frohlich's condition of superconductivity is satisfied. The former applied Tomonaga's tneory of sound quanta4) to derive a similar result pointing out that the frequency of the lattice vibration becomes imaginary so far as Frohlich's condition is adopted. The objective of this report is two-fold; first we confirm the results, of the abovementioned authors by an extension of Tomonaga's theory given in our paperS) and next we examine Wentzel's suggestion that the motion of atom might become stable if the Coulomb interaction forces are taken into calculation. The result obtained is compared with that of the hydrodynamical treatment, the validity of which is computed from our point of view. When a conduction electron with wave number k absorbs a lattice phonon with wave number w, its wave number becomes k+w. Such a process and the reciprocal process are represented by the following operator