PHONON-PLASMON COOPERATIVE EFFECTS IN THE DILUTE LARGE-BIPOLARON GAS - A POSSIBLE MECHANISM FOR HIGH-TC SUPERCONDUCTIVITY

A Hamiltonian for two interacting electrons coupled with longitudinal phonons and plasmons is wt up. The phonons are treated in the Frohlich scheme and the plasmons in the single-pole approximation. We are inte rested in systems with low electron density (n less-than-or-equal-to 1 0(20)-10(21)) such as high-T(c) superconductors. It is shown that, in this density range, the electron dynamics do not simply screen the ele ctrostatic interaction but, also, cooperates to the bipolaron formatio n. Furthermore we find that the binding energies and the effective mas s depend on the electronic density. The features of the effective elec tron-electron potential are discussed, mainly for what concerns the se lf-energy terms and the long-range tail; the former depends on the pai r state and the second shows that the plasmon field tends to screen al l the electrostatic interactions, even the electron-phonon one. It is also shown that the Hamiltonian formulation is equivalent to a dielect ric formulation where the total dielectric function of the system is t he sum of the dielectric function appropriate for an ionic of the syst em is the sum of the dielectric function appropriate for an ionic mate rial and that appropriate for the electron gas. Within this model we c alculate the Bose-condensation critical temperature of a system of cor related pairs and free carriers in a two-fluid model at thermodynamica l equilibrium.