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Exchange and correlation contributions to superconducting electron pairing.

The screening of the electron-phonon and Coulomb interactions in an electron gas is considered with use of various forms of the exchange correction term G(q). A solution of the Eliashberg equations including G(q) is achieved with conventional approximations, and the resulting superconducting transition temperatures T/sub c/ are found to be very sensitive to the form of exchange. Smooth functional forms of G(g), such as the Hubbard model, yield only small deviations from the random-phase approximation, which greatly overestimates T/sub c/ for simple metals such as Na and Li. However, an exchange function with a peak near qapprox. =2k/sub F/ (e.g., the forms proposed by Devreese and independently by Overhauser) greatly reduces T/sub c/ and may explain the mysterious absence of superconductivity in simple metals such as Na, Li, and Rb. These many-body effects may also be significant in superconductors with more complex energy-band structures.