Adiabatic theory of multiphoton ionisation. I. Ionisation of an isolated level

An adiabatic approximation is developed for systems with a Hamiltonian periodic in time taking into account transitions in the continuum (multiphoton ionisation). The problem is reduced to three-term recurrent relations for which an approximation similar to the semiclassical one is applied. The quasi-energy level shift and width are found together with the energy spectra of the ejected electrons. The results are illustrated by the calculations for the model problem with the zero-range interaction. The non-monotonic dependence of the level width on the field frequency (or strength) is discussed. It is shown that the ejected electron spectra fall off more slowly in the adiabatic approximation than in perturbation theory. This result is in qualitative agreement with recent experiments on above-threshold multiphoton ionisation.