We present experimental results showing that channeling measurements with fast stripped heavy ions incident on thin crystals can allow a detailed study of radiative electron capture. Charge-state measurements and photon-energy spectra have been used to deduce cross sections of radiative capture into the K, L, and M shells of 25-MeV/u Xe 53+ ions. The orientation dependence of the positions and shapes of associated photon lines has been observed. PACS numbers: 34.70.+e, 34.50.-s, 61.80.MkWe report on the new features observed in the study of the charge-exchange process of fast H-like xenon ions channeled in a thin silicon crystal. The simultaneous study of the charge state of the transmitted Xe ions and of the x rays they radiate has lead to the following results: (i) Channeled particles appear to be essentially "frozen" in their initial 53 + charge state (a feature already observed by Datz et al. l with lighter ions), while the mean charge state for nonchanneled particles is 49.5. (ii) In the x-ray spectrum, strong, or at least well resolved, lines show up that are due to radiative electron capture (REC) into the K, L, and M shells of channeled projectiles. Both results are due to the fact that REC is the only capture process available for channeled particles, as nonradiative capture, which is by far dominant 2 for nonchanneled Xe ions of the energy used here, is excluded like any other low-impact-parameter process. This type of experiment has been undertaken by Appleton et al.,3 who have obtained information on A^-REC cross sections and have shown that the line shape could be explained by the velocity distribution of target electrons, as suggested by Schnopper et al. 4 who first observed REC. The swift heavy ions used in our experiment have great advantages; K, L and M REC can be studied precisely, and the cross sections have been measured and compared with theoretical predictions. The line shapes appear very clearly and can be analyzed in great detail. This will be done in a forthcoming paper. Moreover the joint study of charge states and REC intensity shows that electron capture by channeled particles is completely accounted for by REC.We used 25-MeV/u Xe 53+ ions delivered at Grand Accelerateur National dTons Lourds (GANIL) in the LISE beam line, which provided a beam of angular divergence lower than 0.5 mrad. Before reaching the crystal, the beam passes through a rotating chopper used for beam monitoring. The chopper blades are covered with silver and the Ag x-ray yield is measured by a Si-Li x-ray detector. The crystal, a 17-pm-thick (ill) Si crystal of area about 1 cm 2 , is viewed by a solid-state Ge detector positioned at 90° to the beam. The transmitted ions are charge and energy analyzed by a magnetic spectrometer associated with a wire chamber (the angular acceptance allows the detection of all the particles). The experiment has been performed around the (110) axial direction. The charge-state measurements are performed as follows: The electric charges collected on each wire are integrated over an ad...