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Resonant two-electron states are examined in attractive Hubbard model on simple cubic lattice and exact formula for scattering cross section in the limit of low density (empty lattice) is calculated. S-wave pair is considered by means of lattice Green functions (LGF). Analytical form of these functions found by Joyce is used facilitating calculations, which were greatly hindered before by the necessity...
The analytic formula for the on-site Green function on the two-dimensional rectangular lattice is shown for arbitrary energy, both within the band (complex Green function) and outside the band (real Green function), expressed by means of elliptic integrals. The recursion formulae enabling calculation of the Green functions on other lattice sites are shown.
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