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A new formalism is developed, based on the memory function approach, to treat many particle systems. The formalism is applied to the Ramirez-Falicov-Kimball (RFK) Hamiltonian, suitable to describe photoemission spectra in many light rare earth intermetallics. We obtain a quasi particle 4f-energy in the weak correlation regime and we discuss the bimodal structure of the f-f propagator in this regime comparing with the Hubbard-type structure in the strong correlation regime

QUASI PARTICLE ENERGY OF 4f-STATES IN THE RAMIREZ-FALICOV-KIMBALL (RFK) MODEL : MEMORY FUNCTION FORMALISM