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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Accelerating resonant spectroscopy simulations using multishifted biconjugate gradient

Resonant spectroscopies, which involve intermediate states with finite lifetimes, provide important insights into collective excitations in quantum materials that are otherwise inaccessible. However, theoretical understanding in this area is often limited by the numerical challenges of solving Kramers-Heisenberg-type response functions for large-scale systems. To address this, we introduce a multishifted biconjugate gradient algorithm that exploits the shared structure of Krylov subspaces across spectra with varying incident energies, effectively reducing the computational complexity to that of linear spectroscopies. Both mathematical proofs and numerical benchmarks confirm that this algorithm substantially accelerates spectral simulations, achieving constant complexity independent of the number of incident energies, while ensuring accuracy and stability. This development provides a scalable, versatile framework for simulating advanced spectroscopies in quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Revealing Local Structures through Machine-Learning-Fused Multimodal Spectroscopy

Atomistic structures of materials offer valuable insights into their functionality. Determining these structures remains a fundamental challenge in materials science, especially for systems with defects. While both experimental and computational methods exist, each has limitations in resolving nanoscale structures. Core-level spectroscopies, such as X-ray absorption (XAS) or electron energy-loss spectroscopies (EELS), have been used to determine the local bonding environment and structure of materials. Recently, machine learning (ML) methods have been applied to extract structural and bonding information from XAS/EELS data. However, frameworks relying solely on a single data stream, defined as characterization data derived from a single element using one technique, are often insufficient because multiple local environments can yield similar spectral features, making it challenging to differentiate between competing structural hypotheses. Here, in this work, we address this challenge by integrating multimodal ab initio simulations, experimental data acquisition, and ML techniques for structure characterization. Our goal is to determine local structures and properties using EELS and XAS data from multiple elements and edges. To showcase our approach, we use various lithium nickel manganese cobalt (NMC) oxide compounds which are used for lithium ion batteries, including those with oxygen vacancies and antisite defects, as the sample material system. We successfully inferred local element content, ranging from lithium to transition metals, with quantitative agreement with experimental data. Beyond local element inference, we find that ML model based on multimodal spectroscopic data is able to determine whether local defects such as oxygen vacancy and antisites are present, a task which is impossible for single mode spectra or other experimental techniques. Furthermore, our framework is able to provide physical interpretability, bridging spectroscopy with the local atomic and electronic structures.

battery↗
DOE OSTI2026

4-Electron Oxygen Reduction Reaction (ORR) with Iron Phthalocyanine (FePc) Functionalized Nanowire Templated-3D Fuzzy Graphene (NT-3DFG)

Iron phthalocyanine (FePc) is a promising alternative to platinum-based catalysts for sustainable energy devices; however, the plane-symmetry of Fe-N 4 sites, random aggregation, and poor conductivity of FePc present major barriers for their application as oxygen reduction reaction (ORR) electrocatalysts. Here, we report the synergistic effects of FePc electrocatalysts supported by a nanowire-templated three-dimensional fuzzy graphene (FePc@NT-3DFG) substrate. The in situ functionalized oxygen groups (iFOGs) at the edge of NT-3DFG localize Fe active sites in FePc under alkaline ORR conditions. With a uniform FePc distribution through many single layers of graphene, the NT-3DFG substrates improve O 2 adsorption and catalytic activity while stabilizing the electrochemical activity during reactions. The FePc@NT-3DFG catalyst exhibits fast ORR kinetics with an extremely low Tafel slope of 28.3 ± 2.7 mV dec −1 , a higher half-wave potential of 0.911 ± 0.004 V (vs RHE), and notable long-term stability at 0.5 V (vs RHE) of 96.0 ± 0.4% retention after 30 h. Surface chemistry spectra validate electronic configuration modification of Fe at the iFOGs. Density functional theory calculations indicate that the extra layers of graphene improve oxygen adsorption. Moreover, additional exploration of other transition metal phthalocyanines supports the effects of iFOGs through the transition toward 4e − ORR. This work offers an expanded strategy for active site modification through edge-based graphene substrates for 4e − ORR.

X-ray absorption spectroscopy↗
DOE OSTI2025

The XPS of pyridine: A combined theoretical and experimental analysis

A detailed analysis of the N(1s) and C(1s) X-Ray Photoelectron Spectroscopy (XPS) is made, where the measured XPS is compared with theoretical Sudden Approximation (SA) intensities and theoretical XPS Binding Energies (BEs). There is remarkably good agreement between the theoretical predictions and the measured XPS; in particular, the different full width at half maximum values for the C(1s) and N(1s) BEs are explained in terms of unresolved C(1s) BEs for the different C atoms in pyridine. Here, this work demonstrates that the combination of theory and XPS measurements can extract analysis of the XPS relevant to the molecular electronic structure. The theory used is based on fully relativistic self-consistent field solutions of the Dirac–Coulomb Hamiltonian, and the SA is used to determine relative XPS intensities.

Binding Energies (BEs)↗
DOE OSTI2025

Measurement of 𝐷-line energies in sodiumlike Ir

We report measurements of the 𝐷 1 and 𝐷 2 transition energies in Na-like Ir (Ir 66+ ). The 𝐷 1 3⁢𝑠−3⁢𝑝 1/2 transition energy, measured in the extreme ultraviolet (EUV) region at 169.977 ± 0.005 eV with a relative uncertainty of 29 ppm, represents one of the most precise 𝐷-line energy measurements to date for high atomic numbers 𝑍 ≥ 30. The 𝐷 2 3⁢𝑠−3⁢𝑝 3/2 transition energy, measured in the x-ray region, is 621.11 ± 0.06 eV. Therefore, there is a fine-structure separation of 451.13 ± 0.06 eV for the Na-like Ir 3⁢𝑝 levels. We present theoretical calculations of these energies using quantum electrodynamic-extended relativistic many-body perturbation theory and multiple-configuration Dirac-Hartree-Fock methods, and discuss the discrepancies between experimental and theoretical values. The prospect of determining the absolute nuclear charge radii of heavy elements, including rare isotopes, from these measurements is explored.

Atomic spectra↗
DOE OSTI2025

Data for: Climatic Imprint on Interfacially-Controlled Platinum-Palladium Resources

Data package for manuscript "Climatic Imprint on Interfacially-Controlled Platinum-Palladium Resources" by Emily G. Wright, Ivey Wang, Yihang Fang, Elaine D. Flynn, and Jeffrey G. Catalano. This dataset contains adsorption results from experiments designed to investigate the effect of chloride on Pd(II) adsorption to goethite and Pt(II) adsorption to hematite and goethite, including lab experiments, X-ray absorption fine structure spectroscopy, and models of retention within a laterite. See the associated manuscript for full methods information. The file "Wright2025_PtAds_data.csv" contains the target starting Pt concentration (uM), final aqueous Pt and associated error (in uM), calculated adsorbed Pt and associated error (in umol/m2), target and measured aqueous chloride (mM), target aqueous nitrate (mM), final pH, and mineral concentration/loading (g/L). Associated mineral-free controls (mineral loading = 0 g/L) are included; the aqueous Pd error was not calculated and chloride was not measured in every sample. These data appear in Figures 1, S3, S4, S5, S20, and S22 in the associated manuscript. The file "Wright2025_PdAds_data.csv" contains the target starting Pd concentration (uM), final aqueous Pd and associated error (in uM), calculated adsorbed Pd and associated error (in umol/m2), target and measured aqueous chloride (mM), and mineral concentration/loading (g/L). Associated mineral-free controls (mineral loading = 0 g/L) are included; the aqueous Pd error was not calculated and chloride was not measured in every sample. These data appear in Figures 1, S3, S4, S5, and S20 in the associated manuscript. The file "Wright2025_MineralBatches_data.csv" contains the mineral identity and BET specific surface area (m2/g) for every mineral batch synthesized and used in experiments. The annealing time used is listed for hydrothermally annealed goethite. These data appear in Table S2 in the associated manuscript. The file "Wright2025_XRD_data.csv" contains the XRD patterns for every mineral batch synthesized as the counts as a function of two theta (in degrees). See "Wright2025_MineralBatches_data.csv" for more details on specific mineral batches. These data appear in Figure S2 in the associated manuscript. The file "Wright 2025_ZetaPotential_data.csv" contains the measured zeta potentials for samples of goethite (batch G2) at pH 4 the presence of varying amounts of sodium chloride. These data appear in Table S3 in the associated manuscript. The file "Wright2025_XAFSSamples_data.csv" contains the specific mineral batch, measured final aqueous Pd or Pt (uM), measured final aqueous chloride (mM), and estimated adsorbed Pd or Pt (umol/m2) of all XAFS samples. These data appear in Tables S4, S7, S8, and S10 in the associated manuscript. The files "Wright2025_PdXAFS_data.csv" and "Wright2025_PtXAFS_data.csv" contain the normalized spectra of Pd and Pt, respectively, adsorbed to minerals at varying chloride concentrations. See "Wright2025_XAFSSamples_data.csv" for a guide to sample names. Note that "05" in a sample name is equivalent to "0.5". These data appear in Figures 2, S6, S7, S8, S12, S13, and S14 in the associated manuscript. The file "Wright2025_LateriteProfileProfileModelParameters_data.csv" include the ratio of hematite to hematite and goethite in two synthetic, modeled profiles, as well as the modeled surface areas of goethite and hematite as a function of relative depth within the modeled weathering zone. These data were used, in conjunction with equations presented in the paper, to calculate the theoretical concentrations of Pd and Pt (and the resulting Pt/Pd ratio) within the profiles. These data appear in Figure 3 in the associated manuscript. The file "Wright2025_Imagery_data.zip" is a zipped folder containing the TEM and STEM images appear in Figures S18 and S19. Individual files are labeled as either STEM (Fig. S18) or TEM (Fig. S19) with a letter representing the part of the multipart figure.

58 GEOSCIENCES↗
DOE OSTI2025

Gold L-shell emission spectroscopy as a temperature diagnostic in laser-driven experiments

Measurements of plasma conditions within gold hohlraums are challenging but provide important information about hohlraum energy transport. To date, there are no reliable passive diagnostic approaches that produce information about the hohlraum plasma conditions. Gold L-shell emission spectroscopy is a promising method to measure the electron temperature in multi-keV gold hohlraum plasmas. In this study, we compare time-resolved measurements of gold L-shell spectra against a more conventional electron temperature-sensitive diagnostic, K-shell emission from zinc, a mid-Z dopant. The Au L-shell and Zn K-shell spectra are taken simultaneously. The analysis of both sets of data exhibits good agreement with a singular rad-hydro model, suggesting a similar evolution in the mean electron temperature of the hohlraum plasma. These findings support the use of L-shell spectroscopy of gold as a method to study gold plasma conditions.

Emission spectroscopy↗
DOE OSTI2025

First Measurement of Z Opacity Sample Evolution near Solar Interior Conditions Using Time-Resolved Spectroscopy

Opacity model differences with Fe opacity measurements at high temperature (T>1⁢8⁢0 eV ) and high electron density (𝑛 𝑒 >3×10 22 cm −3 ) at nearly solar interior conditions have remained unresolved [Bailey et al., Nature 517, 56 (2015) and Nagayama et al., Phys. Rev. Lett. 122, 235001 (2019)]. Systematic errors from temporal gradients are one hypothesis for the discrepancy. Past data recorded on x-ray film provided spectral measurements over a time determined by the 2.8-ns backlighter duration. Here, we present the first measurements of opacity sample temporal evolution using novel hCMOS ultrafast x-ray camera technology. The measured conditions, measured backlighter time history, and modeled opacities are used to show that temporal gradients do not resolve the model-data discrepancy. The methods demonstrated provide potential advantages, including opacities at more extreme conditions, spectral line shift measurements, and improved measurements at other facilities.

atomic spectra↗
DOE OSTI2025

Epitaxial strain tuning of Er 3+ in ferroelectric thin films

Er 3+ color centers are promising candidates for quantum science and technology due to their long electron and nuclear spin coherence times, as well as their desirable emission wavelength. By selecting host materials with suitable, controllable properties, we introduce new parameters that can be used to tailor the Er 3+ emission spectrum. PbTiO 3 is a well-studied ferroelectric material with known methods of engineering different domain configurations through epitaxial strain. By distorting the structure of Er 3+ -doped PbTiO 3 thin films, we can manipulate the crystal fields around the Er 3+ dopant. This is resolved through changes in the Er 3+ resonant fluorescence spectra, tying the optical properties of the defect directly to the domain configurations of the ferroelectic matrix. Additionally, we are able to resolve a second set of peaks for films with in-plane ferroelectric polarization. We hypothesize these results to be due to either the Er 3+ substituting different sites of the PbTiO 3 crystal, differences in charges between the Er 3+ dopant and the original substituent ion, or selection rules. Systematically studying the relationship between the Er 3+ emission and the epitaxial strain of the ferroelectric matrix lays the pathway for future optical studies of spin manipulation by altering ferroelectric order parameters.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Impact of external screening on the valence and core level photoelectron spectra of monolayer W⁢S 2

Transition metal dichalcogenides (TMDs) represent an emerging class of layered materials with applications in microelectronics, optoelectronics, photonics, and catalysis. The confinement of charge carriers within the highly anisotropic, quasi-two-dimensional geometry of one-layer (1L) TMDs leads to reduced, variable dielectric screening, giving rise to a quasiparticle band gap that is highly susceptible to the surrounding dielectric environment. Here, exploiting the contrasting external dielectric environments of gold-supported and suspended 1L W⁢S 2 , we show how the electronic states of W⁢S 2 under the effective and ineffective screening environments align at a junction made within the same sheet of material. Photoelectron spectra point to the close alignment of the charge neutrality levels of W⁢S 2 in both environments, and the breakdown of rigid shifts between the valence states and core levels with the core levels shifting more than twice as much as the valence states. Furthermore, the effectively screened W⁢S 2 exhibits a valence state with the photoemission linewidth twice as large as the ineffectively screened suspended W⁢S 2 , presumably originated from the locally varying W⁢S 2 -Au distance and substrate disorders. Collectively, these findings provide key insights into the electronic behavior of W⁢S 2 and its photoemission process with the electronic states renormalized according to the external screening environments.

Dielectric properties↗
DOE OSTI2025

Layer-dependent spin-resolved electronic structure of ferromagnetic triple-layered ruthenate Sr4Ru3O10

High-resolution angle- and spin-resolved photoemission spectroscopy (ARPES) of the triple-layered ruthenate Sr4Ru3O10 reveals features of the electronic structure that extend our understanding of the layered strontium ruthenates. The spectra near the Fermi energy are very different from the nonmagnetic analogues Sr2RuO4 and Sr3Ru2O7 with distinct Fermi surfaces for wide electronlike minority spin bands around the zone center and narrow holelike majority spin Fermi surface contours around the zone corners. The most dramatic results are two narrow spectral peaks ∼30 meV below the Fermi level, a spin-minority holelike band at the Brillouin zone center, and a spin-majority saddle-band van Hove singularity at the zone edge, which exhibits almost 100% spin polarization at low temperature, and a strong temperature dependent coherence-incoherence crossover attributed to Hund metal correlations. Quantitative comparison of the ARPES to spin-polarized density functional theory (DFT) calculations identify the specific antibonding and nonbonding orbital origins of the narrow bands, with a prediction of different spatial localization in the central and outer layers. This is shown to be consistent with experimental ARPES multizone matrix element intensity variations, and implicates outer-layer-specific control of the in-plane metamagnetism. The renormalization of the bands relative to the mean-field DFT, the demonstration of spin-polarized oxygen bands, and of spin-minority and spin-majority band-crossing hybridization provide a more complete picture of the magnetism which displays aspects of both delocalized and local moment behavior.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Scattering-based structural inversion of soft materials via Kolmogorov–Arnold networks

Small-angle scattering techniques are indispensable tools for probing the structure of soft materials. However, traditional analytical models often face limitations in structural inversion for complex systems, primarily due to the absence of closed-form expressions of scattering functions. To address these challenges, we present a machine learning framework based on the Kolmogorov–Arnold Network (KAN) for directly extracting real-space structural information from scattering spectra in reciprocal space. This model-independent, data-driven approach provides a versatile solution for analyzing intricate configurations in soft matter. By applying the KAN to lyotropic lamellar phases and colloidal suspensions—two representative soft matter systems—we demonstrate its ability to accurately and efficiently resolve structural collectivity and complexity. Here, our findings highlight the transformative potential of machine learning in enhancing the quantitative analysis of soft materials, paving the way for robust structural inversion across diverse systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Structural, magnetic, optical, dielectric and electronic properties of R 2 NiIrO 6 (R = Pr and Nd): A comprehensive experimental and theoretical investigation

Double perovskites are highly promising materials capable of exhibiting a wide variety of phenomena. In this work, we perform a comprehensive experimental and theoretical study of polycrystalline R 2 NiIrO 6 (R = Pr and Nd) compounds. Both compounds were synthesised using the solid-state reaction method. Rietveld refinement confirmed a monoclinic structure with the P2 1 /n space group for both compounds. The scanning electron images showed the average grain sizes of 0.55 μm for R = Pr and 0.46 μm for R = Nd. Fourier transform infrared ra- diation spectra of the two compounds presented two intense bands at 470 cm -1 and 540 cm -1 . The optical measurements revealed that the band gaps of the compounds were in the visible absorption range. The field- cooled magnetisation - field hysteresis measurements indicated exchange bias properties in the synthesised compounds at low temperatures. Both temperature and frequency variation of dielectric constant and loss tangent measurements were conducted. The frequency-dependent ac conductivity measurements indicated that the conductivity increases with the increase of frequency as well as temperature. The Nd 2 NiIrO 6 compound showed lower ac conductivities compared to its isostructural Pr 2 NiIrO 6 compound. The atomic and electronic structures of Nd 2 NiIrO 6 and Pr 2 NiIrO 6 were explored using the spin-polarised calculations performed within the DFT+U method. Our results suggested that the inclusion of on-site correlations and repulsions for the d-states of atoms was necessary in order to obtain finite band gaps of Nd 2 NiIrO 6 and Pr 2 NiIrO 6 systems.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Mapping the three-dimensional fermiology of the triangular lattice magnet EuAg 4 Sb 2

In this paper, we report the temperature-field phase diagram as well as present a comprehensive study of the electronic structure and three-dimensional fermiology of the triangular-lattice magnet EuAg 4 ⁢Sb 2 , utilizing quantum oscillation measurements, angle-resolved photoemission spectroscopy, and first-principles calculations. The complex magnetic phase diagram of EuAg 4 ⁢Sb 2 highlights many transitions through nontrivial AFM states. Shubnikov-de Haas and de Haas-van Alphen oscillations were observed in the polarized ferromagnetic state of EuAg 4 ⁢Sb 2 , revealing three pairs of distinct spin-split frequency branches with small effective masses. A comparison of the angle-dependent oscillation data with first-principles calculations in the ferromagnetic state and angle-resolved photoemission spectra shows good agreement, identifying tubular hole pockets and hourglass-shaped hole pockets at the Brillouin zone center, as well as diamond-shaped electron pockets at the zone boundary. As the temperature increases, the frequency branches of the tiny hourglass pockets evolve into a more cylindrical shape, while the larger pockets remain unchanged. This highlights that variations in exchange splitting, driven by changes in the magnetic moment, primarily impact the small Fermi pockets without significantly altering the overall band structure. As a result, this is consistent with first-principles calculations, which show minimal changes near the Fermi level across ferromagnetic and simple antiferromagnetic states or under varying on-site Coulomb repulsion.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Sequential spectral line analysis for accurate density and temperature diagnosis of laboratory opacity measurements

The accuracy of iron opacity calculated in stellar interiors has been questioned since the discovery of the “solar problem” and the discrepancies between the measured and modeled iron opacity reported in 2015. Experimental opacity benchmarks require accurate temperature and density measurements, which were inferred by analyzing tracer magnesium spectra in those experiments. Could the observed discrepancy be explained by insufficient accuracy in the inferred temperature, density, and their uncertainties? Previous analyses may have yielded biased results due to three limitations: (1) simultaneous multi-line fitting, (2) approximations in line-shape models, and (3) exclusion of certain spectral lines due to insufficient background characterization. Notably, the first issue is a common concern for many inversion methods, including Bayesian inferences. We present a refined analysis method that overcomes these limitations, applied to three categories of iron opacity experiments (Anchor 1, 2, and 3). In particular, the sequential fitting method yields unbiased results with more realistic uncertainties by accounting for line inconsistencies in the parameter uncertainties. The average electron temperature and density values are 162 ± 6 eV and (7.0 ± 1.9) × 10 21 cm −3 for six Anchor 1 experiments, 189 ± 7 eV and (3.4 ± 0.3) × 10 22 cm −3 for 21 Anchor 2 experiments, and 201 ± 6 eV and (4.8 ± 1.1) × 10 22 cm −3 for nine Anchor 3 experiments. These results show ∼4% temperature and ∼20% density reproducibility over a decade, which also aligns with the inferred parameter uncertainties. In conclusion, the resulting temperature and density uncertainties lead to a quasi-continuum iron opacity variation of ±4%–7% for wavelengths below 9.5 Å, which is insufficient to explain the significant model-data discrepancies reported in 2015.

Absorption spectroscopy↗
DOE OSTI2026

Electron–Ion Covariance Reveals Geometry-Resolved Inner-Shell Spectra in CS 2 Photodissociation

The chemical shifts of inner-shell atomic orbitals are highly sensitive to chemical bonding and molecular structure. In evolving systems, however, the spectra of distinct molecular species and geometries overlap, obscuring the underlying chemical dynamics. Here we demonstrate the use of electron–ion covariance analysis to combine the structural sensitivity of Coulomb explosion imaging with inner-shell spectroscopy, yielding geometry-specific spectra of transient and product species. We apply this approach to the excited state dynamics of CS 2 probed by ionization above the S 2p edge. Electron–ion covariance with time- and momentum-selected S + and S 2+ ions isolates distinct S 2p photoelectron spectra for ground-state CS 2 , bent photoexcited CS 2 , the CS photoproduct, and bare atomic sulfur ─ species whose spectra overlap strongly in the channel-averaged measurement. Clear chemical shifts are observed in the covariance photoelectron spectrum for each of these species, all of which are consistent with high-level calculations. Here, by extracting the atomic S contribution to the photoelectron spectrum in a finely time-resolved manner we can disentangle this contribution to the overall time-resolved photoelectron spectrum as the photodissociation proceeds. These results demonstrate the promise of electron–ion covariance as a general approach to geometry-resolved inner-shell spectroscopy, opening a route to tracking structural evolution through chemical shifts in complex photoexcited molecules.

Ionization↗
DOE OSTI2025

Subnanometer Thick Native sp 2 Carbon on Oxidized Diamond Surfaces

Oxygen-terminated diamond has a wide breadth of applications, which include stabilizing near-surface color centers, semiconductor devices, and biological sensors. Despite the vast literature on characterizing functionalization groups on diamond, the chemical composition of the shallowest portion of the surface (<1 nm) is challenging to probe with conventional techniques like XPS and FTIR. In this work, we demonstrate the use of angleresolved XPS to probe the first ten nanometers of both oxygen and hydrogen terminated (100) single-crystalline diamond grown via chemical vapor deposition (CVD). With the use of consistent peakfitting methods, the peak identities and relative peak binding energies were identified for sp 2 carbon, ether, hydroxyl, carbonyl, and C−H groups for both of these diamond surface terminations. For the oxygen-terminated sample, we also quantified the thickness of the sp 2 carbon layer situated on top of the bulk sp 3 diamond bonded carbon to be 0.3 ± 0.1 nm, based on the analysis of the Auger electron spectra and D-parameter calculations. These results indicate that the majority of the oxygen is bonded to the sp 2 carbon layer on the diamond, and not directly to the sp 3 diamond bonded carbon.

Carbon↗
DOE OSTI2026

Search for a heavy neutral lepton with the MAGNETO-𝜈 experiment using 241 Pu 𝛽 − decays

The MAGNETO-𝜈 experiment searches for keV-scale heavy neutral leptons (HNLs) through precise measurements of the 𝛽 − -decay spectrum of 241 Pu. We present spectra comprising a total of 194 million 𝛽 − decays recorded using decay energy spectrometry with metallic magnetic calorimeters, representing the most statistically precise measurement of 241 Pu 𝛽 − decay to date. The 𝛽-endpoint energy was determined using 𝛾 rays and x-rays from an external 133 Ba calibration source, yielding 𝑄 𝛽 = 22.273⁢ (33) ⁢keV. The measured spectrum shows no statistically significant deviation from the allowed 𝛽-decay model. From a subset of the high-statistics data, we set an upper limit on the mixing of an 11.5-keV HNL with the electron neutrino, |𝑈 𝑒⁢4 | 2 < 1.31 × 10 −3 at the 95% confidence level.

A ≥ 220↗