  Metallic K3C60 shows pronounced structure and a sharp Fermi edge in
integrated photoemission spectra (PES) while the insulating K4C60 and K6C60
phases display only a broad structureless peak. We find that both types of
spectra can be explained by the coupling to the optic vibrations of the
K+/C60n- ionic lattice. This is suppressed in K3C60 due to metallic screening
but is strong in the insulating phases. We use the non-crossing approximation
to calculate the density of states (DOS) of electrons in K3C60 coupled to the
intramolecular Hg modes in good agreement with the experiment. For K4C60 and
K6C60 strong coupling to the low energy optic K+/C60n- modes controls the DOS
and yields broad peaks in the PES. A moment expansion is used to calculate the
position and width of these peaks which agree well with the experiment.
