The effect of large $U_d$ on the Raman spectrum in the copper-oxide superconductors

The effect of the charge fluctuations on the electronic and Raman spectrum of high temperature superconductors is examined, using the slave boson approach to the large Coulomb repulsion $U_d$ on the copper site. Instead of the saddle point approximation $\srv{b}\ne 0$ for the slave boson, characteristic for various $N\ide\infty$ approaches, we confine ourselves to the non-crossing approximation (NCA) diagrams for the Green functions. In this way the effects of charge fluctuations and of the constraint of no double occupancy on the copper site on the shape of the electronic spectrum are studied primarily, while the slave boson diagrams responsible for copper-copper spin correlations are intentionally not included. The novel feature of the charge fluctuation dynamics shows up in the slave boson spectrum as the plateau extending over the range of 1eV below $\omega=0$. This is further reflected in the electronic Raman spectrum that we calculate for various combinations of the polarization of the incoming and scattered light. The Raman spectrum shows the characteristic featureless behaviour up to frequencies of the order of 1eV while the polarization dependence is also in qualitative agreement with experiment.