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The charged environment within a dense plasma leads to the phenomenon of ionization potential depression (IPD) for ions embedded in the plasma. Accurate predictions of the IPD effect are of crucial importance for modeling atomic processes occurring within dense plasmas. Several theoretical models have been developed to describe the IPD effect, with frequently discrepant predictions. Only recently, first experiments on IPD in Al plasma have been performed with an x-ray free-electron laser (XFEL), where their results were found to be in disagreement with the widely-used IPD model by Stewart and Pyatt. Another experiment on Al, at the Orion laser, showed disagreement with the model by Ecker and Kröll. This controversy shows a strong need for a rigorous and consistent theoretical approach to calculate the IPD effect. Here we propose such an approach: a two-step Hartree-Fock-Slater model. With this parameter-free model we can accurately and efficiently describe the experimental Al data and validate the accuracy of standard IPD models. Our model can be a useful tool for calculating atomic properties within dense plasmas with wide-ranging applications to studies on warm dense matter, shock experiments, planetary science, inertial confinement fusion and studies of non-equilibrium plasmas created with XFELs.

We investigate ultrafast (fs) electron dynamics in a liquid hydrogen sample, isochorically and volumetrically heated to a moderately coupled plasma state. Thomson scattering measurements using 91.8 eV photons from the free-electron laser in Hamburg (FLASH at DESY) show that the hydrogen plasma has been driven to a nonthermal state with an electron temperature of 13 eV and an ion temperature below 0.1 eV, while the free-electron density is 2:8 Â 10 20 cm À3 . For dense plasmas, our experimental data strongly support a nonequilibrium kinetics model that uses impact ionization cross sections based on classical free-electron collisions. The investigation of warm dense matter (WDM) is one of the grand challenges of contemporary physics [1]. WDM is a plasma state characterized by moderate-tostrong interparticle coupling which takes place at freeelectron temperatures of several eV and free-electron densities around solid density [1]. It is present in many physical environments, such as planetary interiors [2,3], gravitationally collapsing protostellar disks, laser matter interaction and particularly during the implosion of an inertial confinement fusion capsule [4]. While in the astrophysical context WDM exists under stable conditions, in the laboratory it is achieved only as a transient state bridging condensed matter and hot plasma regimes. Here, we report on the first investigation of the nonequilibrium transition of hydrogen from a liquid to a moderately coupled plasma on the fs time scale, induced by highly intense soft-x-ray irradiation. This is an important step towards the investigation of strongly-coupled plasmas which are within reach of current light sources such as the Linac Coherent Light Source (LCLS). Our measurement enables unprecedented direct tests of nonequilibrium statistical models beyond mean field theories in a regime where collision and relaxation processes are dominant [5][6][7].The use of x-ray scattering for the investigation of dense, strongly-coupled plasmas was successfully demonstrated in the past decade [5,[7][8][9][10][11]. This technique is the x-ray analog of optical Thomson scattering (TS) [12] and enables the experimental determination of plasma parameters in dense systems where optical light cannot penetrate. While previous experiments were carried out using highenergy laser facilities, the advent of soft-and hard-x-ray free-electron lasers (FELs) makes ultrashort high brightness beams available for this type of research [13,14]. This Letter reports on ultrafast heating of liquid hydrogen and TS measurement of dense plasma parameters using softx-ray FEL radiation. For the first time, nonequilibrium distributions are observed and the underlying relaxation dynamics are compared with kinetic models showing electron relaxation times in the order of 20 fs, thus, shorter than the pulse duration.The scattering taking place is collective TS, which is characterized by a spectrally blue and red shifted response due to collective electron motion, plasmons, and nearly elastic scattering due t...