© D. Pines. *Elementary Excitations in Solids*, W.A. Benjamin, 1963, p 238.

The background of polarizable conduction electrons and phonons present in a metal modifies the interaction between electrons in two ways. On the left we sketch the way in which the interaction between electrons of momentum p and p + q is modified by their coupling to phonons, the quantized lattice vibrations, as one electron emits a phonon of momentum q, and the second electron absorbs it, leading to an attractive interaction. On the right we sketch the way in which the repulsive electrostatic interaction between the electrons is modified by electronic polarization processes in the metal, with one electron acting to induce a density fluctuation of momentum q, and the second electron absorbing it. Bardeen and the author developed a self-consistent treatment of both (a) and (b), in which both the electron-electron and electron-phonon interactions were screened, and the phonon energies were modified by their coupling to electrons. We found that within the RPA, at very low frequencies, the attractive phonon-induced interaction could win out over the repulsive screened interaction; subsequent work by the author showed that when one took into account the influence of the periodic ionic potential on both processes, this provides a good criterion for finding superconductivity in the periodic system, explaining why monovalent metals do not superconduct, etc. (Unit: 8)