IL NUOV0 CIMENT0 VOL. 9 D, N. 1 Gennaio 1987 Many-Body Effects in the Electron Spectroscopies of Incompletely Filled Bands. ~I. CINI Istituto Metodologie Avanzate Inorganiche del Consiglio Nazionale delle Ricerche Casella Postale 20, 1-00016 Monterotondo Scalo, Roma, Italia (~. V:ERDOZZI Dipartimento di Fisica ~ G. Marconi, - Piazzale A. Moro 2, 00185 Roma, Italia (ricevuto il 20 Agosto 1986) Summary. -- Photoemission and Auger line shapes from almost com- pletely filled bands have been widely discussed in recent years within a simplified model based on an Anderson Hamiltonian in which the virtual level shift due to the interactions is suitably compensated for. Up to now, the theory has been much more successful with XPS than with AES, and the reason for this was obscured by the lack of an exact solution and by the difficulty to assess the degree of validity of various approximate treatments that have been proposed. Here we present a Green's function formalism that allows us to extend the closed band solution to the partially occupied case and lends itself to the exact numerical treatment of finite systems. By applying the theory to 27 and 125 atom clusters, we analyse the dependence of the spectra on hole-hole repulsion U with a degree of unfilling nh<~ 0.25. We also consider the case when one of the spin subbands is full as a rough model for ferromagnetic metals. Correlation effects on the one-hole density of states produce a narrowing of the band region, while a split-off structure develops below the band for U comparable to the band width. The low- density approximation is in good agreement with the exact results for n h ~ 0.1 and also for n h = 0.25 for small and moderate U. Our results on the Auger line shapes justify somewhat the suggestion by Haak and Bennet et al. that split-off states observed in photoemission must be discarded before computing the two-hole spectrum. Indeed self-energy corrections must be excluded also in bandlike cases, when the simple procedure of cutting off the unwanted structure is not applicable. This arises because, in a wide range of physical situations, the Auger line shape reflects the mutual scattering of undressed final-state holes. PACS. 79.20. - Impact phenomena, including electron spectra and sputtering. 1 - ll Nuovo Cimenfo D. I