Coulomb Correlations and Pseudo-gap Effects in a Pre-formed Pair Model for the Cuprates

We extend previous work on pre-formed pair models of superconductivity to incorporate Coulomb correlation effects. For neutral systems, these models have provided a useful scheme which interpolates between BCS and Bose Einstein condensation with increasing coupling and thereby describes some aspects of pseudo-gap phenomena. However, charge fluctuations (via the plasmon, $\omega_p$) significantly modify the collective modes and therefore the interpolation behavior. We discuss the resulting behavior of the pseudo-gap and thermodynamic quantities such as $T_c$, $\chi$ and $C_v$ as a function of $\omega_p$.