We have investigated multiphoton multiple ionization dynamics of argon and xenon atoms using a new x-ray free electron laser (XFEL) facility, SPring-8 Angstrom Compact free electron LAser (SACLA) in Japan, and identified that highly charged Xe ions with the charge state up to +26 are produced predominantly via four-photon absorption as well as highly charged Ar ions with the charge state up to +10 are produced via two-photon absorption at a photon energy of 5.5 keV. The absolute fluence of the XFEL pulse, needed for comparison between theory and experiment, has been determined using two-photon processes in the argon atom with the help of benchmark ab initio calculations. Our experimental results, in combination with a newly developed theoretical model for heavy atoms, demonstrate the occurrence of multiphoton absorption involving deep inner shells.
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