At the soft-x-ray free-electron laser FLASH in Hamburg, we have studied multiphoton ionization on neon and helium by ion mass-to-charge spectroscopy. The experiments were performed in a focused beam at 42.8 and 38.4 eV photon energy and irradiance levels up to 10(14) W/cm(2). Direct, sequential, and resonant two-, three-, and four-photon excitations were investigated by quantitative measurements as a function of the absolute photon intensity. The atomic and ionic photoionization cross sections derived indicate a clear dominance of sequential compared to direct multiphoton processes.
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