Abstract
The differential cross sections of particle scattering accompanied by n-photon exchanges are derived and compared, through an amplification factor, to those calculated when a single-mode laser assists the collision. A strong averaging is found, even in the two-mode case, with an increase (a decrease) of the probabilities of the processes less (more) favoured in the single-mode case, depending on the parameters of the scattering process. As in this problem the laser field is treated exactly, the information obtained sheds light on the known discrepancy between theory and experiment in multiphoton ionisation of atoms by a multimode laser in that it is shown that perturbative approaches are inadequate to treat problems where many photons are exchanged.