Multiphoton processes are detected in the scattering of electrons on argon atoms in the presence of a strong C0 2 -laser field. The observations are in accordance with a recently developed semiclassical model.We present here what we believe to be the first direct observation multiphoton absorptions and emissions by electrons in a strong laser field. Measurements were made in an electron-argonatom scattering experiment in the field of a focused, pulsed C0 2 laser with a peak power of 50 MW. The following multiphoton absorption [Eq.(1)] and emission [Eq.(2)] processes were studied:^"(.E^+Ar + laser -<* e~ {E { +nhv) + Ar +laser;(1) e~(£ t .)+Ar + laser-e~(E { -nhv) +Ar +laser;where E { is the incident electron energy, hv is the energy of a laser photon, and n can be any positive integer. The one-photon (n = l) processes have recently been reported by Andrick and Langhans 1 using a 50-W continuous-wave C0 2 laser as a light source, which after focusing resulted in a flux density of 6x 10 4 W/cm 2 . At this flux density, a first-order perturbation expansion with respect to the laser field is suitable and provides in the soft-photon limit the following simple relation 2 between the one-photon absorption (emission) cross section <2a ff {1) /da and the cross section without laser field do el /dQ: da p { da with T 2 given by 5 =4.86xl0-13 X 4 F£ j [ €# fc^] 2 ,where the laser wavelength X is expressed in units of microns, the flux density F in units of watts per square centimeter, the incoming electron en-ergy E { in eV, and the polarization e is normalized according to ?-?=l such that, for all incoming and outgoing electron momenta p t . and py, the quantity in brackets in always between 0 and 1. In the present experiment, however, flux densities in the order of at least F = 10 9 W/cm 2 have been achieved in the scattering center. At these F values the quantity T 2 in Eq. (4) is about 50, which means that a perturbation expansion with respect to the laser field no longer applies and multiphoton processes are expected to contribute significantly. In the case of a C0 2 laser, however, a semiclassical soft-photon approach 3 " 5 can be applied, which yields the following cross-section formula for a free-free transition with a net absorption (emission) of n laser photonsHere J n (T) is the Bessel function of the first kind and order n, and T is given by Eq. (4). Clearly, if |r|« 1 and w = ±l, Eq. (5) reduces to Eq.(3), which shows the connection between the nonperturbative and the perturbative treatments of the laser field. From J 0 2 (*) + 2SJ" 2 (*) = 1,we note the sum rule (n< 0 correspond to emissions; n> 0 correspond to absorptions of a net number of nhv)

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