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DOE OSTI2025

Extending the capillary wave model to include the effect of bending rigidity: X-ray reflectivity and diffuse scattering

The surface roughness of a thin film at a liquid interface exhibits contributions of thermally excited fluctuations. This thermal roughness depends on temperature (𝑇), surface tension (𝛾), and elastic material properties, specifically the bending modulus (𝜅) of the film. A nonzero 𝜅 suppresses the thermal roughness at small length scales compared to an interface with zero 𝜅, as expressed by the power spectral density of the thermal roughness. The description of the x-ray scattering of the standard capillary wave model (CWM), which is valid for zero 𝜅, is extended to include the effect of 𝜅. The extended CWM (eCWM) provides a single analytical form for both the specular x-ray reflectivity (XRR) and the diffuse scattering around the specular reflection, and recovers the expression of the CWM at its zero 𝜅 limit. This theoretical approach enables the use of single-shot grazing incidence x-ray off-specular scattering (GIXOS) measurements for characterizing the structure of thin films on a liquid surface. The eCWM analysis approach decouples the thermal roughness factor from the surface scattering signal, providing direct access to the intrinsic surface-normal structure of the film and its bending modulus. Moreover, the eCWM facilitates the calculation of reflectivity at any desired resolution (pseudo-XRR approach). The transformation into pseudo-XRR provides the benefit of using widely available XRR software to perform GIXOS analysis. The extended range of the vertical scattering vector (𝑄 𝑧 ) available with the GIXOS pseudo-XRR approach allows for a higher spatial resolution than with conventional XRR. Experimental results are presented for various lipid systems, showing strong agreement between conventional specular XRR and pseudo-XRR methods. This agreement validates the proposed approach and highlights its utility for analyzing soft, thin films.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Neutron Scattering in Sodium-Ion Battery Research: Progress and Prospects

Sodium-ion batteries have attracted renewed interest in recent years and are widely studied as a complementary power source to Li-ion batteries for large-scale stationary energy storage and small electric vehicles. Compared with Li-ion batteries, Na-ion batteries offer several advantages, including elemental abundance, lower cost, improved safety, and better low-temperature performance. An in-depth understanding of Na-ion batteries across multiple length and time scales has further accelerated the rapid development of this technology. Among the various advanced characterization techniques used to study Na-ion batteries, neutron scattering has gained significant traction in recent years. It has become a powerful and versatile tool for probing structure, morphology, and sodium-ion dynamics over a wide range of length and time scales. In this article, we will briefly review the development of neutron scattering technology and highlight recent advances in applying neutron-based techniques—including neutron diffraction, total scattering, small-angle scattering, quasi-elastic/inelastic scattering, and neutron imaging—to Na-ion battery materials. We also provide perspectives on future technique developments, particularly in the realm of in situ and operando neutron scattering characterization, and discuss how these approaches could further enhance our understanding of Na-ion battery systems.

Liu, Jue [ORNL] (ORCID:000000024453910X)↗

DOE OSTI2022

Extracting structural insights from soft X-ray scattering of biological assemblies

Resonant soft X-ray scattering (RSoXS), a technique that combines X-ray absorption spectroscopy and X-ray scattering, can probe the nano- and meso-scale structure of biological assemblies with chemical specificity. RSoXS experiments yield scattering data collected at several photon energies, for example across an elemental absorption edge of interest. Collecting a near-edge X-ray absorption fine structure (NEXAFS) spectrum complements RSoXS experiments and determines X-ray energies that are best suited for RSoXS measurements. The analysis of RSoXS data is similar in many ways to analysis of small angle X-ray scattering using hard X-rays, with an added dimension that includes an X-ray energy dependence. This chapter discusses procedures for predicting scattering contrast and thereby identifying energies suitable for RSoXS measurements using NEXAFS spectra, analyses of 2D RSoXS images through integration into 1D profiles, and strategies for elucidating the origin of RSoXS scattering features. As a result, it also discusses existing and potential methods for interpretation of RSoXS data to gain detailed structural insights into biological systems.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Understanding Solution State Conformation and Aggregate Structure of Conjugated Polymers via Small Angle X-ray Scattering

Donor-acceptor (D-A) conjugated polymers are high-performance organic electronic materials that exhibit complex aggregation behavior. Understanding the solution state conformation and aggregation of conjugated polymers is crucial for controlling morphology during thin-film deposition and the subsequent electronic performance. However, a precise multiscale structure of solution state aggregates is lacking. Here, we present an in-depth small-angle X-ray scattering (SAXS) analysis of the solution state structure of an isoindigo-bithiophene-based D-A polymer (PII-2T) in chlorobenzene and decane as our primary system. Modeling the system as a combination of hierarchical fibrillar aggregates mixed with dispersed polymers, we extract information about conformation and multiscale aggregation and also clarify the physical origin of features often observed but unaddressed or misinterpreted in small-angle scattering patterns of conjugated polymers. The persistence length of the D-A polymer extracted from SAXS agrees well with a theoretical model based on the dihedral potentials. Additionally, we show that the broad high q structure factor peak seen in scattering profiles can be attributed to lamellar stacking occurring within the fibril aggregates and that the low q aggregate scattering is strongly influenced by the polymer molecular weight. Overall, the SAXS profiles of D-A polymers in general exhibit a sensitive dependence on the co-existence of fibrillar aggregate and dispersed polymer chain populations. We corroborate our findings from SAXS with electron microscopy of freeze-dried samples for direct imaging of fibrillar aggregates. Finally, we demonstrate the generality of our approach by fitting the scattering profiles of a variety of D-A polymers based on thieno-isoindigo (PTII-2T), diketopyrrolopyrrole (DPP2T-TT, DPP-BTZ, PDPP2FT-C- 16 ), naphthalenediimide (P(NDI2OD-T2)), and a conjugated block copolymer P3HT-b-DPPT-T. The results presented here establish a picture of the D-A polymer solution state structure and provide a general method of interpreting and analyzing their scattering profiles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Quantifying the Effect of Magnetic Field Line Curvature Scattering on the Loss of Ring Current Ions

During geomagnetic storms, the ring current ions sometimes exhibit rapid loss as suggested by the fast recovery of the Dst index on a time scale of a few hours. Here, the effects of magnetic field line curvature (FLC) scattering on the loss of ring current ions, which have not been well quantified, are studied here by test particle simulations under the T89c magnetic field model. Our simulation results show that the prediction of ion loss based on a single–value cutoff of the κ parameter or maximum of δμ/μ of a single FLC scattering is not accurate. Instead, the e–folding lifetime (τ) for the loss of ring current ions due to cumulative FLC scattering has been calculated for different initial ion energies, equatorial pitch angles, and L shells under different geomagnetic conditions. The results show that in general the FLC scattering loss is faster for ions of higher energy, higher mass, smaller pitch angle, higher L, and at high Kp level. Specifically, we find that at Kp = 6 the lifetime can be <10 h at L > 5 for 100 s keV protons and at L > 4 for 100 s keV O + , which demonstrates that FLC scattering can be an important mechanism for the observed fast loss (τ < 10 h) of ring current ions during geomagnetic storms. Furthermore, we formulate an empirical formula for τ as a function of ion energy, pitch angle, position, species, and Kp. The empirical formula can be directly included in ring current models to account for the FLC scattering effects.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Topographically Scattered Infrasound Waves Observed on Microbarometer Arrays in the Lower Stratosphere

When an acoustic wave strikes a topographic feature, some of its energy is scattered. Sensors on the ground cannot capture these scattered signals when they propagate at high angles. We report observations of upwardly-scattered acoustic waves prior to refraction back to the ground, intercepting them with a set of balloon-borne infrasound microbarometers in the lower stratosphere over northern Sweden. We show that these scattered waves generate a coda whose presence can be related to topography beneath balloons and low-altitude acoustic ducts. The inclination of the coda signals changes systematically with time, as expected from waves arriving from scatterers successively closer to receivers. The codas are present when a temperature inversion channels infrasound from a set of ground chemical explosions along the ground, but are absent following the inversion's dissipation. Since scattering partitions energy away from the main arrival, these observations imply a mechanism of amplitude loss that had previously been inaccessible to measurement. As such, these data and results allow for a better comprehension of interactions between atmospheric infrasound propagation and the solid earth

58 GEOSCIENCES↗

DOE OSTI2023

Measurement of the axial vector form factor from antineutrino–proton scattering

Scattering of high energy particles from nucleons probes their structure, as was done in the experiments that established the non-zero size of the proton using electron beams. The use of charged leptons as scattering probes enables measuring the distribution of electric charges, which is encoded in the vector form factors of the nucleon. Scattering weakly interacting neutrinos gives the opportunity to measure both vector and axial vector form factors of the nucleon, providing an additional, complementary probe of their structure. The nucleon transition axial form factor, F A , can be measured from neutrino scattering from free nucleons, ν μ n → μ – p and ν¯ μ p → μ + n , as a function of the negative four-momentum transfer squared (Q 2 ). Up to now, FA(Q 2 ) has been extracted from the bound nucleons in neutrino–deuterium scattering, which requires uncertain nuclear corrections. Here we report the first high-statistics measurement, to our knowledge, of the ν¯ μ p → μ + n cross-section from the hydrogen atom, using the plastic scintillator target of the MINERvA experiment, extracting F A from free proton targets and measuring the nucleon axial charge radius, r A , to be 0.73 ± 0.17 fm. The antineutrino–hydrogen scattering presented here can access the axial form factor without the need for nuclear theory corrections, and enables direct comparisons with the increasingly precise lattice quantum chromodynamics computations. Finally, the tools developed for this analysis and the result presented are substantial advancements in our capabilities to understand the nucleon structure in the weak sector, and also help the current and future neutrino oscillation experiments to better constrain neutrino interaction models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Exploring 3D elastic-wave scattering at interfaces using high-resolution phased-array system

The elastic-wave scattering at interfaces, such as cracks, is essential for nondestructive inspections, and hence, understanding the phenomenon is crucial. However, the elastic-wave scattering at cracks is very complex in three dimensions since microscopic asperities of crack faces can be multiple scattering sources. We propose a method for exploring 3D elastic-wave scattering based on our previously developed high-resolution 3D phased-array system, the piezoelectric and laser ultrasonic system (PLUS). We describe the principle of PLUS, which combines a piezoelectric transmitter and a 2D mechanical scan of a laser Doppler vibrometer, enabling us to resolve a crack into a collection of scattring sources. Subsequently, we show how the 3D elastic-wave scattering in the vicinity of each response can be extracted. Here, we experimentally applied PLUS to a fatigue-crack specimen. We found that diverse 3D elastic-wave scattering occurred in a manner depending on the responses within the fatigue crack. This is significant because access to such information will be useful for optimizing inspection conditions, designing ultrasonic measurement systems, and characterizing cracks. More importantly, the described methodology is very general and can be applied to not only metals but also other materials such as composites, concrete, and rocks, leading to progress in many fields.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Stable and tunable MeV $$\gamma$$-ray generation via dual-laser inverse Thomson scattering from a laser-plasma accelerator

Abstract Inverse Thomson scattering from laser-plasma accelerators offers a pathway to compact, tunable MeV $$\gamma$$ -ray sources for reduced-dose radiography and enhanced performance in nuclear resonance fluorescence (NRF)-based isotope identification. However, photon yield and spectral quality are often limited by constraints on interaction geometry and scatter-laser tunability. Here we demonstrate a MeV $$\gamma$$ -ray source based on a dual-laser inverse Thomson scattering configuration driven by a 100-TW laser-plasma accelerator. Electron beams tunable from 122 to 204 MeV with $$<5$$ mrad divergence and $$<1$$ mrad pointing stability generate $$\gamma$$ rays with peak energies from 276 keV to 1.2 MeV and yields up to $$2\times 10^{7}$$ photons per shot. By independently controlling the interaction position and the scatter-pulse duration, we experimentally match the scatter pulse to the walk-off-limited interaction length. Extending the scatter pulse to 200 fs increases photon production by approximately $$15\%$$ while maintaining operation in the linear Thomson regime, thereby preserving narrow spectral bandwidth and controlled radiation divergence. Radiographic characterization demonstrates MeV-level penetration and $$\approx 0.1$$ mm spatial resolution, while stable operation is sustained over multi-hour timescales across multiple days. These results show that interaction-length optimization provides a scalable strategy for improving photon yield, spectral control, and operational stability in compact laser-plasma-accelerator-driven $$\gamma$$ -ray sources.

Tsai, Hai-En↗

DOE OSTI2025

Harnessing emergent multiple scattering resonances in a photonic glass structure for photoelectrochemical energy conversion

Light trapping nanostructures are often necessary to improve carrier collection yields in semiconductor photoelectrodes with intrinsically poor electron transport. Photonic crystal templates can generate tailorable light trapping via periodic and precise nanostructure, though this is not a scalable strategy for photoelectrochemical (PEC) applications. It is therefore critical to identify alternative mechanisms for light trapping that tolerate disorder. Light trapping in disordered media is generated by the diffusive transport caused by multiple scattering. In some cases, multiple scattering can generate resonances that resemble those observed in photonic crystals. While resonant multiple scattering is a disorder tolerant light trapping mechanism, it is unclear if the effect is sufficiently adaptable, or even useful, for PEC applications. Here, we describe a photonic omission glass, a nanostructure that can controllably induce resonances in multiple scattering transport. We characterized the emergence of these resonances after coating a disordered SiO 2 colloidal structure with a layer of TiO 2 , which functions both as dielectric contrast and as a light absorbing semiconductor. We show in finite element simulations and spectroscopic characterization that the resonant multiple scattering effect improves light trapping near the interface between the structure and the bulk electrolyte. This effect, coupled with the increased electrochemically active surface area, results in a hierarchically structured TiO 2 photoanode with orders of magnitude higher photocurrents compared to an equivalent planar photoanode for PEC reactions such as alkaline water oxidation. We show that controlling this resonant multiple scattering effect can be advantageous for improving PEC energy conversion in disordered photoelectrodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Machine learning on neutron and x-ray scattering and spectroscopies

Neutron and x-ray scattering represent two classes of state-of-the-art materials characterization techniques that measure materials structural and dynamical properties with high precision. These techniques play critical roles in understanding a wide variety of materials systems from catalysts to polymers, nanomaterials to macromolecules, and energy materials to quantum materials. In recent years, neutron and x-ray scattering have received a significant boost due to the development and increased application of machine learning to materials problems. This article reviews the recent progress in applying machine learning techniques to augment various neutron and x-ray techniques, including neutron scattering, x-ray absorption, x-ray scattering, and photoemission. We highlight the integration of machine learning methods into the typical workflow of scattering experiments, focusing on problems that challenge traditional analysis approaches but are addressable through machine learning, including leveraging the knowledge of simple materials to model more complicated systems, learning with limited data or incomplete labels, identifying meaningful spectra and materials representations, mitigating spectral noise, and others. We present an outlook on a few emerging roles machine learning may play in broad types of scattering and spectroscopic problems in the foreseeable future.

Chen, Zhantao↗

DOE OSTI2022

Simulated effect of edge plasma density parameters on lower hybrid wave scattering in EAST

The incorporation of lower hybrid (LH) wave spectrum broadening in the poloidal wavenumber (⁠k θ ) space at the last close field surface (LCFS) is reported to lead to better agreement of the modeled LH wave current profile with the experimental results [Baek et al., Nucl. Fusion 61, 106034 (2021)]. To further understand its underlying mechanism and find the possible influence factors, effects of wave scattering caused by drift-wave type density fluctuation on the probability distribution of the LH wave polar refractive index (⁠N θ ) at the LCFS are studied under density parameters in the scrape-off-layer. According to a scattering model [P. T. Bonoli and E. Ott, Phys Fluids 25(2), 359–375 (1982)], scattering probability and scattering angle distribution are two main factors that determine the degree of spectral broadening. Studies presented here show that the total scattering probability increases first and then decreases as the wave propagates toward a smaller normalized radius of poloidal magnetic flux (⁠ρ⁠). The degree of spectral broadening is found to depend on the density and density fluctuation together by changing the intensity and a proportion of the geometrical optics approximation term and the E×B drift term in the scattering model. Additionally, the fluctuation correlation length can significantly modify the probability distribution of N θ at the LCFS, which is found to significantly change the LH wave current profile.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

The contribution of Compton ionization to ultrafast x-ray scattering

We investigate the role of Compton ionization in ultrafast non-resonant x-ray scattering using a molecular model system, which includes the ionization continuum via an orthonormalized plane wave ansatz. Elastic and inelastic components of the scattering signal, as well as coherent-mixed scattering that arises from electron dynamics, are calculated. By virtue of a near-quantitative distinction between scattering related to electronic transitions into bound and continuum states, we demonstrate how Compton ionization contributes to the coherent-mixed component. Analogous to inelastic scattering, the contribution to the coherent-mixed signal is significant and particularly manifests at intermediate and high-momentum transfers. Strikingly, for molecules with inversion symmetry, the exclusion of bound or continuum transitions may lead to the prediction of spurious coherent-mixed signals. We conclude that qualitative and quantitative accuracies of predicted scattering signals on detectors without energy resolution require that elements of the two-electron density operator are used. This approach inherently accounts for all accessible electronic transitions, including ionization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Enhancing Thomson scattering polychromator performance with multi-pass spectral filters

In photon-deficient, noncollective Thomson scattering diagnostics, filter polychromators are typically employed in the spectral analysis of Thomson-scattered signals to achieve acceptable signal-to-noise performance. Currently, the most common polychromator filter configuration employs a set of single-passband optical filters that define individual spectral channels. Here, we introduce a new spectral analysis method for Thomson scattering based on spectral filters with multiple passbands, referred to as Thomson scattering spectral multiplexing. Implementing multi-bandpass spectral filters on polychromators increases the achievable range of electron temperature measurement for a given number of filters employed. In addition, Thomson scattering spectral multiplexing reduces systematic measurement uncertainty, with fewer required spectral channels, thereby decreasing light loss from reduced optical element interactions. A multi-bandpass filter set, optimized by a genetic algorithm, has been successfully installed and tested on the Helically Symmetric eXperiment (HSX), demonstrating the benefits of the Thomson scattering spectral multiplexing method.

Instruments & Instrumentation↗

DOE OSTI2021

Humidified single-scattering albedometer (H-CAPS-PM SSA ): Design, data analysis, and validation

In this work, we report the development and validation of a new humidified aerosol single-scattering albedometer to quantify the effects of water uptake on submicrometer particle optical properties. The instrument simultaneously measures in situ aerosol light extinction ( σ ep ) and scattering ( σ sp ) using a cavity-attenuated phase shift-single scattering albedo particulate matter (PM) monitor (CAPS-PM SSA , Aerodyne Research, Inc., Billerica, MA, USA). It retrieves by difference aerosol light absorption ( σ ap ) and directly quantifies aerosol single-scattering albedo (SSA), the aerosol “brightness.” We custom built a relative humidity (RH) control system using a water vapor-permeable membrane humidifier and coupled it to the CAPS-PM SSA to enable humidified aerosol observations. Our humidified instrument (H-CAPS-PM SSA ) overcomes problems with noise caused by mirror purge-flow humidification, heating, and characterizing cell RH. Careful angular truncation corrections in scattering, particularly for larger particles, were combined with empirical observations. Results show that the optimal operational size to be D p < 400 nm. The H-CAPS-PM SSA was evaluated with several pure single-component aerosols including ammonium sulfate ((NH 4 ) 2 SO 4 ), absorbing nigrosin, and levoglucosan, an organic biomass smoke tracer. The measured σ ep , σ sp , and the derived optical hygroscopicity parameter ( κ ) for size-selected ammonium sulfate are in good agreement with literature values. For dry size-selected nigrosin in the 100 < D p < 400 nm range, SSA values increased from ~0.3 to 0.65 with increasing D p . The enhancement in nigrosin σ ap at RH = 80% was a factor of 1.05–1.20 relative to dry conditions, with the larger particles showing greater enhancement. SSA increased with RH with the largest fractional enhancement measured for the smallest particles. For polydisperse levoglucosan, we measured an optical κ of 0.26 for both light extinction and scattering and negligible absorption. Our new instrument enables reliable observations of the effects of ambient humidity on mixed aerosol optical properties, particularly for light-absorbing aerosols whose climate forcing is uncertain due to measurement gaps.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Estimating the impact of foregrounds on the future detection of Rayleigh scattering

Rayleigh scattering of the cosmic microwave background (CMB) by neutral hydrogen shortly after recombination leaves frequency-dependent imprints on intensity and polarization fluctuations. High signal-to-noise observations of CMB Rayleigh scattering would provide additional insight into the physics of recombination, including greater constraining power for parameters like the primordial helium fraction, the light relic density, and the sum of neutrino masses. However, such a measurement of CMB Rayleigh scattering is challenging due to the presence of astrophysical foregrounds, which are more intense at the high frequencies, where the effects of Rayleigh scattering are most prominent. Here we forecast the detectability of CMB Rayleigh scattering including foreground removal using blind internal linear combination methods for a set of near-future surveys. Furthermore, we show that atmospheric effects for ground-based observatories and astrophysical foregrounds pose a significant hindrance to detecting CMB Rayleigh scattering with experiments planned for this decade, though a high-significance measurement should be possible with a future CMB satellite.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Constraining the scatter in the galaxy–halo connection at Milky Way masses

In this work, we develop and implement two new methods for constraining the scatter in the relationship between galaxies and dark matter haloes. These new techniques are sensitive to the scatter at low halo masses, making them complementary to previous constraints that are dependent on clustering amplitudes or rich galaxy groups, both of which are only sensitive to more massive haloes. In both of our methods, we use a galaxy group finder to locate central galaxies in the Sloan Digital Sky Survey main galaxy sample. Our first technique uses the small-scale cross-correlation of central galaxies with all lower mass galaxies. This quantity is sensitive to the satellite fraction of low-mass galaxies, which is in turn driven by the scatter between haloes and galaxies. The second technique uses the kurtosis of the distribution of line-of-sight velocities between central galaxies and neighbouring galaxies. This quantity is sensitive to the distribution of halo masses that contain the central galaxies at fixed stellar mass. Theoretical models are constructed using peak halo circular velocity, Vpeak, as our property to connect galaxies to haloes, and all comparisons between theory and observation are made after first passing the model through the group-finding algorithm. We parametrize scatter as a lognormal distribution in M* at fixed Vpeak, σ[M*|Vpeak]. The cross-correlation technique yields a constraint of σ[M*|Vpeak] = 0.27 ± 0.05 dex at a mean Vpeak of 168 km s-1, corresponding to a scatter in log M* at fixed Mh of σ[M*|Mh] = 0.38 ± 0.06 dex at $M_\text{h}=10^{11.8}\, \text{M}_\odot$. The kurtosis technique yields σ[M*|Vpeak] = 0.30 ± 0.03 at Vpeak = 209 km s-1, corresponding to σ[M*|Mh] = 0.34 ± 0.04 at $M_\text{h}=10^{12.2}\, \text{M}_\odot$. The values of σ[M*|Mh] are significantly larger than the constraints at higher masses, in agreement with the results of hydrodynamic simulations. This increase is only partly due to the scatter between Vpeak and Mh, and it represents an increase of nearly a factor of 2 relative to the values inferred from clustering and group studies at high masses.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Quantum Interference in Two-Atom Resonant X-ray Scattering of an Intense Attosecond Pulse

We theoretically investigate resonant x-ray scattering from two noninteracting Ne+ ions driven by an intense attosecond pulse using a nonrelativistic, QED-based time-dependent framework. Our model includes Rabi oscillations, photoionization, Auger decay, and quantum interference among elastic scattering and resonance fluorescence pathways. We analyze how the total scattering signal depends on pulse intensity, atomic configuration, and initial electronic state. We find that the total resonant scattering yield exceeds its nonresonant counterpart; the angular dependence of the signal qualitatively resembles a two-atom structure factor; and the visibility of interference fringes is sensitive to pulse area and the initial electronic state. Only a subset of final states reached via resonance fluorescence exhibits interference, determined by the indistinguishability of photon emission pathways. Fringe visibility is maximized in the linear scattering regime, where ionization is minimal and resonance fluorescence pathways can be largely indistinguishable. These results highlight optimal conditions for applying ultrafast resonant x-ray scattering to single-particle imaging.

Venkatesh, Akilesh↗