We have investigated the response of a multielectron atom to the strong (intensity of the order of 1 a.u.) VUV free-electron laser radiation. Our study shows that for such a high driving frequency a new physical mechanism for the generation of high harmonics emerges. The lack of harmonics via the simple man's model mechanism is replaced by the production of harmonics due to the vibration of inner-shell electrons. The highest photon energy found is well in excess of 1 keV. We predict the appearance of even harmonics in the spectrum which could be a sign of "touching" the consecutive electronic shells (more tightly bound assuming the driving frequency increases).
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