COMPETITION BETWEEN THE COULOMB AND PHONON FIELDS - SUPERCONDUCTIVITYIN A QUIESCENT FERMI GAS

Co-existence of and competition between the screened Coulomb and phono n fields are fundamental facts in superconductors. In the conventional superconductors the strong screening greatly suppresses the Coulomb i nteraction and the phonon field that mediates a given attractive inter action between electrons may thus play a leading role. A quiescent Fer mi sea hence applies, as proposed by Cooper and adopted in BCS. In thi s model a graphical derivative technique, based on Ward's identity, is developed to consider the contributions to the interparticle interact ion. This technique allows one to evaluate the effective two-particle interaction (T-matrix). It is shown that the conventional Cooper insta bility in a quiescent Fermi gas is only caused by a given attractive i nteraction. Of more importance is that the methodology presented in th is work can be extended to the investigation of the intermediate and s trong coupling cases where the well-known Migdal theorem is not applic able and the vertex corrections must be evaluated. (C) 1997 Academic P ress Limited.