  We consider the interaction of atomic hydrogen with an intense laser field
within the strong-field approximation. By using a Faddeev-like formalism, we
introduce a new perturbative series in the binding potential of the atom. As a
first test of this new approach, we calculate the electron energy spectrum in
the very simple case of a photon energy higher than the ionisation potential.
We show that by contrast to the standard perturbative series in the binding
potential obtained within the strong field approximation, the first terms of
the new series converge rapidly towards the results we get by solving the
corresponding time-dependent Schroedinger equation.
