  We investigate sum-rules applying to the Raman intensity in a strongly
correlated system close to the Mott transition. Quite generally, it can be
shown that, provided the frequency integration is performed up to a cutoff
smaller than the upper Hubbard band, a sum-rule applies to the non-resonant
Raman signal of a doped Mott insulator, resulting in an integrated intensity
which is proportional to the doping level. We provide a detailed derivation of
this sum-rule for the t-J model, for which the frequency cutoff can be taken to
infinity and an unrestricted sum-rule applies. A quantitative analysis of the
sum-rule is also presented for the d-wave superconducting phase of the t-J
model, using slave boson methods. The case of the Hubbard model is studied in
the framework of dynamical mean-field theory, with special attention to the
cutoff dependence of the restricted sum-rule, and also to the intermediate
coupling regime. The sum-rule investigated here is shown to be consistent with
recent experimental data on cuprate superconductors, reporting measurements of
Raman scattering intensities on an absolute scale.
