We present a comprehensive experimental and theoretical study on superfluorescence in the extreme ultraviolet wavelength regime. Focusing a high-intensity free-electron laser pulse in a cell filled with Xe or Kr gas, the medium is quasi instantaneously population-inverted by inner-shell ionization on the giant resonance followed by Auger decay. On the timescale of 100 ps a macroscopic polarization builds up in the medium, resulting in superfluorescent emission of several Xe and Kr lines in the forward direction. As the number of emitters in the system is increased by either raising the pressure or the pump-pulse energy, the emission shows an exponential growth of over 4 orders of magnitude and reaches saturation. With increasing yield, we observe line broadening, a manifestation of superfluorescence in the spectral domain. Our novel theoretical approach, based on a full quantum treatment of the atomic system and the irradiated field, shows quantitative agreement with the experiment and supports our interpretation.Superfluorescence [1] is the spontaneous, collective decay of an extended ensemble of atoms that have been prepared in a population-inverted state, resulting in collimated, highintensity radiation pulses. The pulses are emitted at a certain delay following excitation and have a duration that can be several orders of magnitude smaller than the typical upper-state lifetimes. Long before the advent of short-wavelength free-electron lasers (FELs), strong superfluorescence in optically thick media was proposed as a source of highly intense and pulsed extreme-ultraviolet (XUV) or X-ray radiation [2]. Strong X-ray K-α superfluorescence following ionization of the 1s shell with a focused X-ray FEL (XFEL) beam was demonstrated in neon gas [3,4], solid copper [5] and manganese salts in aqueous solution [6]. Extremely high gains were observed in these experiments [3,6], with exponential amplification factors surpassing 20 compared to spontaneous emission. In the vacuum ultraviolet and XUV regions, superfluorescence following inner-shell ionization has so far not been demonstrated.The difficulty to obtain transient gain in this wavelength regime is a consequence of the very different time scales of two competing processes: on the one hand, short (fs) Auger lifetimes of inner-valence vacancies, and, on the other hand, comparatively long (ns) radiative transition times -a highly unfavorable combination to sustain a sizable population inversion and gain. Here, we present combined experimental and theoretical work, giving strong evidence for XUV superfluorescence of Xe and Kr gases. Population inversion is

We have studied Xe + 4d inner-shell photoionization in a direct experiment on Xe + ions, merging an ion and a photon beam and detecting the ejected electrons with a cylindrical mirror analyzer. The measured 4d photoelectron spectrum is compared to the 4d core valence double ionization spectrum of the neutral Xe atom, obtained with a magnetic bottle spectrometer. This multicoincidence experiment gives access to the spectroscopy of the individual Xe 2+ 4d −1 5p −1 states and to their respective Auger decays, which are found to present a strong selectivity. The experimental results are interpreted with the help of ab initio calculations.