  The strong field approximation (SFA) formulated in terms of so-called
"quantum orbits" led to much insight into intense-laser driven ionization
dynamics. In plain SFA, the emitted electron is treated as a free electron in
the laser field alone. However, with improving experimental techniques and more
advanced numerical simulations it becomes more and more obvious that the plain
SFA misses interesting effects even on a qualitative level. Examples are
holographic side lobes, the low-energy structure, radial patterns in
photoelectron spectra at low kinetic energies, and strongly rotated angular
distributions. For this reason increasing effort has been recently devoted to
Coulomb corrections of the SFA. In the current paper, we follow a similar line
but consider ionization of metal clusters. It is known that photoelectrons from
clusters can be much more energetic than those emitted from atoms or small
molecules, especially if the Mie resonance of the expanding cluster is evoked.
We develop a SFA that takes the collective field inside the cluster via the
simple rigid-sphere model into account. Our approach is based on
field-corrected quantum orbits so that the acceleration process (or any other
spectral feature of interest) can be investigated in detail.
