A previous two-step hydrodynamic model calculation of angle-resolved photoe
mission has been improved by modeling the surface with a soft analytic func
tion. The same ground state potential is used to screen the photon field an
d to calculate the electronic wave functions. The implemented code can be u
sed 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 inter
preted as the direct excitation of multipole modes. This conclusion was sug
gested in the previous two-step model calculation.