The theory of laser-assisted collisions is carefully analysed in the weak-field regime to identify the implicit expansion parameter of the well known Kroll-Watson formula for free-free transitions. The theory is generalized in such a way that it applies under conditions where the ordinary Kroll-Watson formula fails. Most critical are situations where the laser polarization and the electron momentum transfer are almost perpendicular, in which case the Kroll-Watson expansion parameter diverges. The present theory applies generally for one-photon processes and the relevant amendments for multiphoton processes are readily identified. The strict comparison with recent measurements by Wallbank and Holmes (1994) is not impressive but the observed structure in the relative laser-assisted signal can be understood qualitatively. It is indicated that the departure between theory and experiment might be associated with comparatively large but not clearly identified uncertainties in the experimental definition of the momentum transfer vector.
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