  The interaction of atomic clusters with short, intense pulses of laser light
to form extremely hot, dense plasmas has attracted extensive experimental and
theoretical interest. The high density of atoms within the cluster greatly
enhances the atom--laser interaction, while the finite size of the cluster
prevents energy from escaping the interaction region. Recent technological
advances have allowed experiments to probe the laser--cluster interaction at
very high photon energies, with interactions much stronger than suggested by
theories for lower photon energies. We present a model of the laser--cluster
interaction which uses non-perturbative R-matrix techniques to calculate
inverse bremsstrahlung and photoionization cross sections for Herman-Skillman
atomic potentials. We describe the evolution of the cluster under the influence
of the processes of inverse bremsstrahlung heating, photoionization,
collisional ionization and recombination, and expansion of the cluster. We
compare charge state distribution, charge state ejection energies, and total
energy absorbed with the Hamburg experiment of Wabnitz {\em et al.} [Nature
{\bf 420}, 482 (2002)] and ejected electron spectra with Laarmann {\em et al.}
[Phys. Rev. Lett. {\bf 95}, 063402 (2005)].
