  In a recent experiment at the VUV free-electron laser facility at DESY in
Hamburg, the generation of multiply charged ions in a gas of atomic xenon was
observed. This paper develops a theoretical description of multiphoton
ionization of xenon and its ions. The numerical results lend support to the
view that the experimental observation may be interpreted in terms of the
nonlinear absorption of several VUV photons. The method rests on the
Hartree-Fock-Slater independent-particle model. The multiphoton physics is
treated within a Floquet scheme. The continuum problem of the photoelectron is
solved using a complex absorbing potential. Rate equations for the ionic
populations are integrated to take into account the temporal structure of the
individual VUV laser pulses. The effect of the spatial profile of the
free-electron laser beam on the distribution of xenon charge states is
included. An Auger-type many-electron mechanism may play a role in the VUV
multiphoton ionization of xenon ions.
