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The three-photon detachment cross sections of the ions F-, Br-and Iare measured, using the fundamental 1064.2 nm wavelength of a single-mode Nd:YAG laser. The detachment signal is measured by detecting the neutral atoms produced from an ionic beam of kinetic energy 1.2 keV. The data analysis takes into account the laser pulse time profile, the actual spatial profile of the laser beam in the interaction region, and the fast motion of the ions through the laser beam during the laser pulse. Saturation of the threephoton process is observed and used to normalise the detachment signal. We obtain u(F-) = 6.1' ::8 x s2 m6. These measured cross sections are compared with theoretical predictions. The result obtained for Fagrees with a very recent measurement performed with a different technique. s2 m6, u(Br-) = 1.6' ;:: x s2 m6 and u(I-) = 3.3:;:: x i. This work was supported by the DRET office (Direction des Recherches, Etudes et Techniques) under contract No 84/079.