We want to stress again that the discussion we have given of the one-electron spectrum is based on the assumption that vertex corrections are small. As discussed in the next section recent work by Langreth [29] shows that vertex corrections in the core electron problem can have a quite large effect on the form of satellite structures, while their effect on the quasi particle properties seems to be small. Preliminary investigations by one of us (L.H.) show similar strong vertex effects on the conduction band satellite. The details of the plasmaron structure should thus not be taken very seriously.