  We formulate a computationally efficient time-independent method based on the
multi-electron molecular R-matrix formalism. This method is used to calculate
transition matrix elements for the multi-photon ionization of atoms and
molecules under the influence of a perturbative field. The method relies on the
partitioning of space which allows us to calculate the infinite-range free-free
dipole integrals analytically in the outer region, beyond the range of the
initial bound wave function. This approach is valid for an arbitrary order,
that is, any number of photons absorbed both in the bound and the continuum
part of the spectrum (below- and above-threshold ionization). We calculate
generalized multi-photon cross sections and angular distributions of different
systems (H, He, H2, CO2) and validate our approach by comparison with data from
the literature.
