We present KnudsenModel, an open-source Python implementation of the Knudsen model for computing evaporative cooling of microscopic liquid jets in vacuum. The code builds on widely used scientific Python packages and provides a transparent and flexible framework that can be applied to both cylindrical jets and spherical droplets. A fixed-mass radial discretization is employed to consistently account for the coupled evolution of mass loss and density, ensuring physically accurate predictions of both temperature and jet or droplet diameter. We analyze the numerical behavior of the method, including convergence properties and comparisons with literature calculations based on alternative discretization schemes, revealing that, in particular for water droplets, the present formulation captures a shallow minimum in the diameter that reflects the interplay between evaporation-induced mass loss and water's density anomaly-a feature absent in previous results. PROGRAM SUMMARY Program Title: temp_liq_jet Python package CPC Library link to program files: (to be added by Technical Editor) Developer's repository link: https://github.com/rgrisenti/temp_liq_jet Licensing provisions(please choose one): MIT Programming language: Python Nature of problem: Evaporative cooling drives the temperature evolution of microscopic liquid jets in vacuum. Accurate predictions of their temperature are essential for interpreting experiments employing such microjets. This evolution results from the coupled dynamics of evaporative mass loss at the liquid-vapor interface and radial heat transport within the fluid. While the Knudsen model provides a well-established theoretical framework, practical numerical implementations are often developed independently, with limited documentation or validation. Seemingly minor numerical choices-particularly in the radial discretization-can lead to inconsistencies that affect physically relevant observables, including droplet or jet radius. A physically consistent, reproducible implementation is therefore required to obtain reliable predictions and ensure reproducibility across studies. Solution method: The KnudsenModel class, provided in the temp_liq_jet Python package, implements a physically consistent numerical solution of the coupled mass and energy balance equations describing evaporative cooling of liquid jets or droplets. The liquid cross section is discretized into concentric shells of fixed mass, avoiding the inconsistencies associated with remapping procedures in previous implementations and addressing the radial discretization issues noted above. Evaporative mass loss at the surface is calculated using the Hertz-Knudsen expression, while radial heat transport is described by thermal conduction between neighboring shells. The resulting system of coupled ordinary differential equations is integrated along the propagation coordinate using robust ODE solvers from scipy.integrate. The code outputs the evolution of temperature and droplet or jet diameter, correctly capturing subtle physical effects arising from the interplay between evaporation and thermophysical properties, providing a transparent and reproducible reference implementation.

The fate of a metastable substance is governed by rare nucleation events, whose full microscopic details still remain elusive despite over 150 years of study. Experimental nucleation rates often differ by many orders of magnitude from theory and simulations, limiting predictive power. In this Perspective, after a general overview on nucleation, we focus on crystallization in three representative systems: metastable water, colloidal suspensions, and Lennard-Jones liquids. The latter, which are well realized by rare-gas liquids, provide a touchstone for nucleation theory. Recent femtosecond X-ray diffraction experiments on supercooled argon and krypton deliver accurate crystal nucleation statistics and direct insight into structural defects such as stacking faults. These advances establish rare-gas liquids as uniquely well-controlled systems bridging experiment, simulation, and theory, and pave the way toward a more complete microscopic understanding of nucleation.

Pair distribution functions from individual femtosecond X-ray pulses have the potential to elucidate the structure of transient states in matter, such as those found in liquid systems. To demonstrate this possibility an experiment was conducted at the Materials Imaging and Dynamics instrument of European X-ray Free Electron Laser Facility. We utilized the large field of view detector configuration, exploiting single high-flux X-ray pulses of femtosecond duration at 23 keV photon energy. After deconvolution from the pattern termination function, we show here pair distribution functions of liquid water at approximately 260 K. These results demonstrate that current X-ray free electron laser methods can acquire pair distribution functions on the femtosecond timescale that have potential to capture transient state of liquids.

We demonstrate an advanced scattering method for accessing the 3D reciprocal space of crystalline structures forming in a rapidly supercooled noble-gas liquid using a combination of femtosecond X-ray diffraction and X-ray cross-correlation analysis. The preservation of angular information from the scattering signal allows probing the structure factor along selected directions in reciprocal space and identifying signatures undetectable in azimuthally integrated scattering curves. Therefore, more information from serial diffraction experiments on stochastic crystallization processes can be retrieved despite the inherent variation of the crystal orientation and morphology for each single probe. We also demonstrate how different features in the correlation maps can be associated with certain forms of stacking faults, which enables studying such defects in situ and disentangling them from simultaneous changes in crystal size and temperature.

Quantum electrodynamics (QED), the quantum field theory that describes the interaction between light and matter, is commonly regarded as the best-tested quantum theory in modern physics. However, this claim is mostly based on extremely precise studies performed in the domain of relatively low field strengths and light atoms and ions 1 – 6 . In the realm of very strong electromagnetic fields such as in the heaviest highly charged ions (with nuclear charge Z ≫ 1), QED calculations enter a qualitatively different, non-perturbative regime. Yet, the corresponding experimental studies are very challenging, and theoretical predictions are only partially tested. Here we present an experiment sensitive to higher-order QED effects and electron–electron interactions in the high- Z regime. This is achieved by using a multi-reference method based on Doppler-tuned X-ray emission from stored relativistic uranium ions with different charge states. The energy of the 1 s 1/2 2 p 3/2 J = 2 → 1 s 1/2 2 s 1/2 J = 1 intrashell transition in the heaviest two-electron ion (U 90+ ) is obtained with an accuracy of 37 ppm. Furthermore, a comparison of uranium ions with different numbers of bound electrons enables us to disentangle and to test separately the one-electron higher-order QED effects and the bound electron–electron interaction terms without the uncertainty related to the nuclear radius. Moreover, our experimental result can discriminate between several state-of-the-art theoretical approaches and provides an important benchmark for calculations in the strong-field domain.

The performance of time-resolved photoelectron spectroscopy for the study of subpicosecond dynamics of laser-heated solids is often limited by space charge effects. The consequent shift and distortion of the photoelectron spectrum induced by electrons emitted by the ultrashort pump pulse is studied here using a fully coherent approach based on experimental measurements and space charge calculations. The temporal dynamics of the valence band of a copper sample is recorded before and after an 800 nm laser pump excitation at a fluence of 750 mJ/cm2. The probe pulse is produced using a laboratory-based high-harmonics source delivering 25 fs pulses up to 100 eV photon energy. We extract the laser-heating contribution by comparing these measurements with space charge calculations based on particle-in-cell simulations of the pump and probe electron clouds mutual interaction on their way to the detector. The deduced picosecond dynamics associated to the electronic density of states shift is attributed to lattice changes with the help of hydrodynamic simulations including the two-temperature model.

The liquid-to-solid phase transition is a complex process that is difficult to investigate experimentally with sufficient spatial and temporal resolution. A key aspect of the transition is the formation of a critical seed of the crystalline phase in a supercooled liquid, that is, a liquid in a metastable state below the melting temperature. This stochastic process is commonly described within the framework of classical nucleation theory, but accurate tests of the theory in atomic and molecular liquids are challenging. Here, we employ femtosecond x-ray diffraction from microscopic liquid jets to study crystal nucleation in supercooled liquids of the rare gases argon and krypton. Our results provide stringent limits to the validity of classical nucleation theory in atomic liquids, and offer the long-sought possibility of testing nonclassical extensions of the theory.

We present a here a non-parametric analysis of x-ray spectra for experiment E125 performed at GSI-FAIR in Darmstadt. This experiment measured intra-shell transitions of highly charged uranium with a twin-arm Bragg spectrometer equipped with x-rays CCDs. The method consists in slicing the CCD image and calculating the centroids of the lines, then adjusting the slice size in order to remove background. Due to the low count rate, we reveal the limitations of this method which provides an accuracy of only a few pixels, far from the sub-pixel requirement.

Knowledge of the refractive index of water in the deeply supercooled metastable liquid state is important, for example, for an accurate description of optical reflection and refraction processes occurring in clouds. However, a measurement of both the temperature and wavelength dependence of the refractive index under such extreme conditions is challenging. Here, we employ Raman spectroscopy in combination with microscopic water jets in vacuum to obtain the refractive index of supercooled water to a lowest temperature of 230.3 K. While our approach is based on the analysis of Mie resonances in Raman spectra measured by using a single excitation wavelength at 532 nm, it allows us to obtain the refractive index in a wide visible wavelength range from 534 to 675 nm. Because of a direct link between the refractive index and density of water, our results provide a promising approach to help improve our understanding of water's anomalous behavior.

P.-M. Hillenbrand , 2 S. Hagmann , Y. S. Kozhedub , E. P. Benis , C. Brandau , 5 R. J. Chen, D. Dmytriiev , 6 O. Forstner , 7 J. Glorius , R. E. Grisenti , 2 A. Gumberidze , M. Lestinsky , Yu. A. Litvinov , 6 E. B. Menz , 7, 8 T. Morgenroth, 7, 8 S. Nanos , 4 N. Petridis, Ph. Pfäfflein , 7, 8 H. Rothard, M. S. Sanjari , 11 R. S. Sidhu , 6 U. Spillmann , S. Trotsenko, I. I. Tupitsyn , L. Varga, 6 and Th. Stöhlker 2, 7, 8 Institut für Kernphysik, Goethe-Universität, 60438 Frankfurt, Germany GSI Helmholtzzentrum für Schwerionenforschung, 64291 Darmstadt, Germany Department of Physics, St. Petersburg State University, 199034 St. Petersburg, Russia Department of Physics, University of Ioannina, 45110 Ioannina, Greece I. Physikalisches Institut, Justus-Liebig-Universität, 35392 Giessen, Germany Fakultät für Physik und Astronomie, Ruprecht-Karls-Universität, 69117 Heidelberg, Germany Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität, 07743 Jena, Germany Helmholtz-Institut Jena, 07743 Jena, Germany Tandem Accelerator Laboratory, INPP, NCSR “Demokritos”, 15310 Agia Paraskevi, Greece Centre de Recherche sur les Ions, les Matériaux et la Photonique CIMAP, Normandie Université, ENSICAEN, UNICAEN, CEA, CNRS, 14000 Caen, France Aachen University of Applied Sciences, 52066 Aachen, Germany (Dated: January 26, 2022)

In this paper, we present an experimental and theoretical study of excitation processes for the heaviest stable helium-like ion, that is, He-like uranium occurring in relativistic collisions with hydrogen and argon targets. In particular, we concentrate on angular distributions of the characteristic Kα radiation following the K → L excitation of He-like uranium. We pay special attention to the magnetic sub-level population of the excited 1s2lj states, which is directly related to the angular distribution of the characteristic Kα radiation. We show that the experimental data can be well described by calculations taking into account the excitation by the target nucleus as well as by the target electrons. Moreover, we demonstrate for the first time an important influence of the electron-impact excitation process on the angular distributions of the Kα radiation produced by excitation of He-like uranium in collisions with different targets.

We study the electron-loss-to-continuum (ELC) cusp experimentally and theoretically by comparing the ionization of U$^{89+}$ projectiles in collisions with N$_2$ and Xe targets, at a beam energy of 75.91 MeV/u. The coincidence measurement between the singly ionized projectile and the energy of the emitted electron is used to compare the shape of the ELC cusp at weak and strong perturbations. A significant energy shift for the centroid of the electron cusp is observed for the heavy target of Xe as compared to the light target of N$_2$. Our results provide a stringent test for fully relativistic calculations of double-differential cross sections performed in the first-order approximation and in the continuum-distorted-wave approach.

Surface chemistry of gold nanoparticles produced by laser ablation in liquids has been investigated using synchrotron radiation and the X-ray Photoelectron Spectroscopy technique. Thanks to the recorded core-level and valence spectra, combined with a detailed analysis based on Bayesian statistical methods, the oxide presence and its proportion on the nanoparticle surface have been determined.

Crystallization is a fundamental process in materials science, providing the primary route for the realization of a wide range of new materials. Crystallization rates are also considered to be useful probes of glass-forming ability1–3. At the microscopic level, crystallization is described by the classical crystal nucleation and growth theories4,5, yet in general solid formation is a far more complex process. In particular, the observation of apparently different crystal growth regimes in many binary liquid mixtures greatly challenges our understanding of crystallization1,6–12. Here, we study by experiments, theory and computer simulations the crystallization of supercooled mixtures of argon and krypton, showing that crystal growth rates in these systems can be reconciled with existing crystal growth models only by explicitly accounting for the non-ideality of the mixtures. Our results highlight the importance of thermodynamic aspects in describing the crystal growth kinetics, providing a substantial step towards a more sophisticated theory of crystal growth. The contribution of non-ideal mixing for the crystallization of supercooled mixtures of argon and krypton is reported, showing that this process is well described by classical crystal growth theories when such thermodynamics is considered.

We present the Aurore platform for ultrafast sciences. This platform is based on a unique 20 W, 1 kHz, 26 fs Ti:sapphire laser system designed for reliable operation and high intensity temporal contrast. The specific design ensures the high stability in terms of pulse duration, energy, and beam pointing necessary for extended experimental campaigns. The laser supplies 5 different beamlines, all dedicated to a specific field: attosecond science (Aurore 1), ultrafast phase transitions in solids (Aurore 2 and 3), ultrafast luminescence in solids (Aurore 4), and femtochemistry (Aurore 5). The technical specifications of these five beamlines are described in detail, and examples of the recent results are given.

This work demonstrates efficient micro-lensing of laseraccelerated proton beams by transient electromagnetic (EM) fields in coil targets. In an all-optical principle, hig intensity ps-laser pulses are used to charge solid density t argets and induce EM target-discharges [1]. The strong transient EM-fields are guided by the target geometry. Such EM-mode propagation along wire targets [2] has already been used for the guiding of a proton beam [3]. Our collaboration aims at a more easily tunable energy-selective collimation and focusing with independent discharge and particle source targets: A sub-mm coil shaped part of the discharge target’s rod produces lensing effects. Protons with in an energy range of approximately ±2MeV, with energies up to12MeV, are focused over cm-scale distances.

For U89+ projectiles colliding at a beam energy of 75.91 MeV/u with a N-2 target, we present a coincidence measurement between the cusp electrons emitted under an angle of 0. with respect to the projectile beam and the photons emitted under a polar angle of 90 degrees. This radiative-electron-capture-to-continuum cusp directly probes the theory of electron-nucleus bremsstrahlung up to the high-energy endpoint in inverse kinematics. In the present study, significant improvement with respect to the experimental accuracy has been achieved, resulting in a finer agreement between experimental and theoretical results.

An experiment addressing electron capture (EC) decay of hydrogen-like Pm60+142 ions has been conducted at the experimental storage ring (ESR) at GSI. The decay appears to be purely exponential and no modulations were observed. Decay times for about 9000 individual EC decays have been measured by applying the single-ion decay spectroscopy method. Both visually and automatically analysed data can be described by a single exponential decay with decay constants of 0.0126(7)s−1 for automatic analysis and 0.0141(7)s−1 for manual analysis. If a modulation superimposed on the exponential decay curve is assumed, the best fit gives a modulation amplitude of merely 0.019(15), which is compatible with zero and by 4.9 standard deviations smaller than in the original observation which had an amplitude of 0.23(4).

We have studied the K-shell excitation of He-like uranium (U90+) in relativistic collisions with hydrogen and argon atoms. Performing measurements with different targets, as well as with different collision energies, enabled us to explore the proton- (nucleus-) impact excitation as well as the electron-impact excitation process for the heaviest He-like ion. The large fine-structure splitting in uranium allowed us to partially resolve excitation into different L-shell levels. State-of-the-art relativistic calculations which include excitation mechanisms due to the interaction with both protons (nucleus) and electrons are in good agreement with the experimental findings. Moreover, our experimental data clearly demonstrate the importance of including the generalized Breit interaction in the treatment of the electron-impact excitation process.