Effective Coulomb interaction in metallic 3dsystems: Comparison of theory and experiment for Mn in Ag

We study the photoemission (PES) and bremsstrahlung isochromat (BIS) spectra of Mn in Ag to determine the effective Coulomb interaction ${\mathit{F}}^0$ between the Mn 3d electrons. We show that, due to many-body and multiplet effects together with the large degeneracy of the the 3d level, the main peak in PES and the main peak in BIS tend to be moved towards the Fermi energy by hybridization effects. As a result, the experimental separation beween these peaks leads to an underestimate of ${\mathit{F}}^0$ unless these effects are included. For Mn in Ag these effects, however, appear to be insufficient to obtain agreement between experiment and ab initio calculations for ${\mathit{F}}^0$.