NONLINEAR SELF-CONSISTENT SCREENING APPLIED TO METALLIC HYDROGEN

Non-linear self-consistent screening of a proton by a high density electron gas has been used to find effective electron-proton potentials for metallic hydrogen for a number of densities and for both face-centered cubic and body-centered cubic structures. The resulting proton-proton potentials have been employed to calculate the phonons in the self-consistent harmonic approximation, following which the effective distributions alpha **2F( omega ) were evaluated in the plane wave, spherical approximation. From these, the superconducting transition temperatures T//c and functional derivatives were found. Non-linear effects are seen to be important. For both structures, dynamical instabilities occur for r//s greater than equivalent to 1. 0, indicating densities higher than those predicted by linear theory are required. In addition, for the fcc case, T//c is enhanced. T//c is found to depend sensitively on the structure assumed; for the bcc case, it is very small. For fcc H, McMillan's equation overestimates T//c by about 40%, even when lambda equals 0. 5. Leavens' formula agrees with solutions of the Eliashberg gap equations to within about 10%.