TIME-INDEPENDENT SCATTERING-THEORY FOR TIME-PERIODIC HAMILTONIANS - FORMULATION AND COMPLEX-SCALIGN CALCULATIONS OF ABOVE-THRESHOLD-IONIZATION SPECTRA

A time-independent scattering theory is introduced for time-periodic Hamiltonians. The theory is applicable in cases where at infinite time (t = +/- infinity) the relative motion between the colliders is free, and therefore the asymptotic kinetic energy can be defined experimentally. This asymptotic condition and the time periodicity of the Hamiltonian lead to time-independent expressions for the distribution of the kinetic energy in the relative motion of the fragments for a half-collision and for a full-collision experiment. These expressions are combined with the complex-coordinate method to give an efficient numerical algorithm for the calculation of multiphoton ionization-dissociation probabilities within the framework of the finite-range-potential approximations. The theory is applied to a model Hamiltonian of an atom in a strong ac field. The obtained above-threshold-ionization spectra are in excellent agreement with theoretical results previously obtained from time-dependent calculations.