Spatial-dispersion and relativistic effects in the optical sum rules

We describe a procedure to take into account the spatial dispersion of the optical excitations in the susceptibility sum rules. We show that this implies that relativistic corrections of the same order must be considered. The final result is a decrease of the total oscillator strength equal to the ratio of the average electron kinetic energy with mc. We propose experiments with synchrotron radiation sources on crystals of heavy elements to observe the described effect. PACS. 78.20.Ci Optical constants (including refractive index, complex dielectric constant, absorption, reflection and transmission coefficients, emissivity) – 78.40.-q Absorption and reflection spectra: visible and ultraviolet – 71.15.Rf Relativistic effects