  A previous two-step hydrodynamic model calculation of angle-resolved
photoemission has been improved by modeling the surface with a soft analytic
function. The same ground-state potential is used to screen the photon field
and to calculate the electronic wave functions. The implemented code can be
used for arbitrary ground state densities along the perpendicular direction.
Mathematical and physical aspects of the model are discussed extensively. The
behavior of the main peak of the spectrum in response to the variation of some
parameters leads us to the conclusion that the peak cannot be interpreted as
the direct excitation of multipole modes. This conclusion was suggested in the
previous two-step model calculation.
