  The conditions behind the sudden approximation are critically examined. The
fuzzy band expression is derived in detail from first principles. We go beyond
the sudden approximation to account for both extrinsic losses and interference
effects. In an extension of earlier work we discuss both core and valence
satellites including both intrinsic and extrinsic amplitudes, and high energy
excitations as well as low energy electron-hole pairs. We show how the
extrinsic losses in photoemission can be connected with the electron energy
loss function. This is achieved by three approximations, to connect the
dynamically screened potential in the bulk solid to the loss function, to
account for the surface, and lastly to extrapolate zero momentum loss data to
include dispersion. The extrinsic losses are found to be weak for small loss
energies. For larger loss energies the extrinsic losses can be strong and have
strong interference with the intrinsic losses depending on the nature of the
solid. The transition from the adiabatic to the sudden regime is discussed for
atoms and localized systems and compared with the situation for solids. We
argue that in solids for photoelectron energies above some 10 eV the external
losses are mainly connected with spacially extended excitations. We discuss
strongly correlated quasi-two-dimensional solids with Bi2212 as example, and
find an asymmetric broadening of the main peak from shake up of acoustic
three-dimensional plasmons. In the superconducting state the loss function is
assumed to have a gap, which then leads to a peak-dip-hump structure in the
photoemission spectrum. This structure is compared with a corresponding
structure in tunneling.
