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The spectrum of two-particle excitations of the Hubbard Hamiltonian

The spectra of two-hole and two-electron excitations are calculated for a single-band Hubbard Hamiltonian. These spectra are directly connected with the intensity of CVV Auger spectra and with the appearance potential spectra of transition metals with strong electron-electron interactions. The theory is based on a local decoupling procedure applied to the retarded two-particle double-time Green functions in the site representation. It is exact in four important limiting cases: in the non-interacting limit (U to 0), in the atomic limit (band width W to 0), in the limit of low concentration of electrons (n to 0) and holes (n to 2), and it provides a physically reasonable interpolation between these limits. In contrast with previous similar theories, it has proper transformation properties under the electron-hole transformation. The theory is illustrated numerically in a simplified model.