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ML-Based Pebble Power Reconstruction for Pebble Bed Reactor Analysis

Pebble power reconstruction has been explored to complement the conventional homogenized modeling approach in pebble bed reactor (PBR) analysis, as detailed heterogeneous geometry calculations are computationally expensive. The random distribution of pebble fuels within the core challenges the application of conventional pin power reconstruction methods. To address this, we introduce a machine learning approach based on the transformer model, composed of encoder and decoder layers, to estimate the flux and power form functions for reconstructing individual pebble neutron fluxes and powers. The homogeneous neutron flux distribution within each spectral zone (SZ) is obtained from finite element solutions of global diffusion or transport calculations. Verification tests demonstrate that the trained transformer model accurately predicts power form functions over a range of conditions, including variations in pebble enrichment, location, type, SZ size, and burnup. In particular, verification using a three-dimensional PBR benchmark with burned pebbles shows good agreement in heterogeneous pebble power distributions between Griffin and Serpent. These results highlight the potential of applying conventional pin power reconstruction approaches to PBR cores with randomly distributed pebbles.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Short-range spin freezing in the double trillium lattice spin-liquid candidate KSrFe 2 ⁢(PO 4 ) 3 revealed via 31 P NMR

A comprehensive 31 P nuclear magnetic resonance (NMR) study, combined with thermodynamic measurements and first-principles band-structure calculations, has been conducted to explore the ground state of the 𝑆=5/2 double trillium lattice antiferromagnet KSrFe 2 ⁢(PO 4 ) 3 . Our experimental results indicate that the magnetic ground state is neither a conventional three-dimensional (3D) long-range order (LRO) nor a pure gapless spin-liquid state, as conjectured previously [Boya et al., APL Mater. 10, 101103 (2022)]. Specifically, the observation of a nearly field-independent NMR linewidth below 𝑇* = (3.5 ± 0.4)⁢ K, and a significant enhancement of spin-spin relaxation rate 1/𝑇 2 below 2⁢𝑇* (where 𝑇* is the characteristic temperature identified from the magnetic susceptibility), indicate a complex magnetic ground state where spin freezing coexists with persistent dynamics. Furthermore, we argue that the lack of magnetic LRO and the persistence of strong magnetic fluctuations in KSrFe 2 ⁢(PO 4 ) 3 are unlikely to originate from intersite K/Sr disorder, rather they arise due to intrinsic magnetic frustration. In conclusion, our findings position KSrFe 2 ⁢(PO 4 ) 3 into a broader family of geometrically frustrated magnets characterized by coexisting spin freezing and pronounced antiferromagnetic fluctuations, marking it as a promising platform for investigating exotic phenomena in 3D frustrated magnets.

Exotic phases of matter↗

Efficient truncations of SU( N c ) lattice gauge theory for quantum simulation

Quantum simulations of lattice gauge theories offer the potential to directly study the nonperturbative dynamics of quantum chromodynamics, but naive analyses suggest that they require large computational resources. Large 𝑁 𝑐 expansions are performed to order 1/𝑁 𝑐 to simplify the Hamiltonian of pure SU⁡(𝑁𝑐) lattice gauge theories. A reformulation of the electric basis is introduced with a truncation strategy based on the construction of local Krylov subspaces with plaquette operators. Numerical simulations show that these truncated Hamiltonians are consistent with traditional lattice calculations at relatively small couplings. It is shown that the computational resources required for quantum simulation of time evolution generated by these Hamiltonians is 17–19 orders of magnitude smaller than previous approaches, provided that the truncations in this work can reach lattice spacings in three-dimensional simulations comparable to the two-dimensional simulations performed.

Lattice QCD↗

Three-dimensional lattice modulations in the charge density wave system Lu 2 Ir 3 Si 5

Using total and resonant x-ray scattering coupled to large-scale computer modeling, we study the lattice modulations in the complex charge density wave (CDW) material Lu 2 ⁢Ir 3 ⁢Si 5 . Here, we find that it is a unique quantum system where periodic lattice modulations related to emergent CDW order occur in three orthogonal atomic planes of the crystal lattice, leading to the emergence of an unusual three-dimensional (3D) pattern of short and long Ir-Ir and Lu-Lu bonds. The 3D character of observed lattice modulations explains the largely isotropic character of the changes in the electronic properties occurring when the CDW order sets in, demonstrating the strong electron-lattice coupling in Lu 2 ⁢Ir 3 ⁢Si 5 . The result is supported by DFT calculations based on the experimental structure data. Altogether, our work provides strong evidence for the presence of a relationship between the dimensionality of emergent lattice distortions and that of concurrent changes in the electronic properties of CDW materials. The relationship may need to be accounted for when these materials are explored for practical applications.

36 MATERIALS SCIENCE↗

Scalable Quantum Monte Carlo Method for Polariton Chemistry via Mixed Block Sparsity and Tensor Hypercontraction Method

We present a reduced-scaling auxiliary-field quantum Monte Carlo (AFQMC) framework designed for large molecular systems and ensembles, with or without coupling to optical cavities. Our approach leverages the natural block sparsity of the Cholesky decomposition (CD) of electron repulsion integrals in molecular ensembles and employs tensor hypercontraction (THC) to efficiently compress low-rank Cholesky blocks. By representing the Cholesky vectors in a mixed format, keeping high-rank blocks in block-sparse form and compressing low-rank blocks with THC, we reduce the scaling of exchange-energy evaluation from quartic to robust cubic in the number of molecular orbitals N, while lowering memory from cubic toward quadratic. Benchmark analyses on one-, two-, and three-dimensional molecular ensembles (up to ∼1,200 orbitals) show that (a) the number of nonzeros in Cholesky tensors grows linearly with system size across dimensions; (b) the average numerical rank increases sublinearly and does not saturate at these sizes; and (c) rank heterogeneity─some blocks nearly full rank and many low rank, naturally motivates the proposed mixed block sparsity and THC scheme for efficient calculation of exchange energy. In conclusion, we demonstrate that the mixed scheme yields cubic wall-time scaling with favorable prefactors and preserves AFQMC accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Using multimodal X-ray computed tomography to advance 3D petrography: A non-destructive investigation of olivine inside a carbonaceous chondrite

Rocks form in three dimensions through time and studying them provides information from inside dynamic systems we cannot otherwise observe. Yet how we typically access the interior of the rocks themselves to gain that information may limit our understanding and influence how we reconstruct the processes that formed them. Here, we demonstrate combined non-destructive 3D X-ray imaging techniques that produce quantitative densitometric and crystallographic maps of entire individual grains inside a rock. Olivine grains throughout a sample of the carbonaceous chondrite Northwest Africa (NWA) 11346 were each characterized by size, shape, composition, zoning intensity, and crystallographic orientation. The addition of 3D crystallographic mapping to calibrated 3D densitometric analysis—used to calculate chemical composition—demonstrates a fully non-destructive petrographic method and provides unique insight. For instance, in our case, using crystallographic data to delineate individual grains and then measuring the 3D size, shape, and composition of each distinguishes variably reset relict grains from those later crystallized after a melting event. Intersection in a 2D slice could not have led to this interpretation because the integration of three-dimensional size, rounding, composition, location, and crystallographic orientation measured from each grain forms the key patterns. Multimodal laboratory X-ray imaging has strong potential to advance 3D petrography.

36 MATERIALS SCIENCE↗

Spin qubit properties of the boron-vacancy/carbon defect in the two-dimensional hexagonal boron nitride

Spin qubit defects in two-dimensional materials have a number of advantages over those in three-dimensional hosts including simpler technologies for defect creation and control, as well as qubit accessibility. In this work, we select the V B C B defect in the hexagonal boron nitride (hBN) as a possible optically controllable spin qubit and explain its triplet ground state and neutrality. In this defect a boron vacancy is combined with a carbon dopant substituting the closest boron atom to the vacancy. Our density-functional-theory calculations confirmed that the system has dynamically stable spin triplet and singlet ground states. As revealed from our linear response GW calculations, the spin-sensitive electronic states are localized around the three undercoordinated N atoms and make local peaks in the density of electronic states within the bandgap. Using the triplet and singlet ground state energies, as well as the energies of the optically excited states, obtained from solution to the Bethe–Salpeter equation, we construct the spin-polarization cycle, which is found to be favorable for the spin qubit initialization. The calculated zero-field splitting parameters ensure that the splitting energy between the spin projections in the triplet ground state is comparable to that of the known spin qubits. We thus propose the V B C B defect in hBN as a promising spin qubit.

2D BN↗

Small Molecule Inhibitor-Modulated Al 2 O 3 Atomic Layer Deposition on Monolayer MoS 2 for Controlled Nucleation

The integration of ultrathin dielectrics on two-dimensional (2D) semiconductors is essential for advancing beyond-Si electronics. However, the intrinsic inertness of van der Waals 2D basal planes remains a primary bottleneck to achieving uniform dielectric nucleation and growth. Here, in this study, we introduce a small molecule inhibitor (SMI)-modulated thermal atomic layer deposition (ALD) strategy, exemplified by aluminum oxide (Al 2 O 3 ) ALD on monolayer molybdenum disulfide (1L MoS 2 ) with acetic acid (HAc) SMI. The ABC-type sequence comprises HAc inhibitor (A), trimethylaluminum (TMA) precursor (B), and deionized H 2 O coreactant (C). In situ quartz crystal microbalance (QCM) studies reveal robust HAc adsorption on Al 2 O 3 and suppression of subsequent oxide growth on HAc-passivated surfaces. When applied to 1L MoS 2 , this inhibitory pathway enables HAc to selectively passivate nascent Al 2 O 3 nuclei formed on the MoS 2 surface, limiting their three-dimensional (3D) island coarsening and redirecting precursor adsorption toward the uncovered basal plane. Consequently, nearly continuous ultrathin (∼1.5 nm) Al 2 O 3 films are achieved on 1L MoS 2 with markedly improved uniformity compared to standard Al 2 O 3 ALD using TMA and H 2 O, as validated by atomic force microscopy (AFM), cross-sectional scanning transmission electron microscopy (STEM), and energy-dispersive X-ray spectroscopy (EDS). Density functional theory (DFT) calculations further provide atomistic insight into HAc-modulated Al 2 O 3 nucleation, corroborating the energetic preference of HAc for Al 2 O 3 over MoS 2 and attenuated TMA adsorption on HAc-passivated surfaces. Spatially resolved Raman spectroscopy also confirms that the HAc-modulated process preserves the structural integrity of 1L MoS 2 , with only minimal strain and doping perturbations observed after dielectric deposition. This SMI-modulated approach offers a broadly applicable framework for controlling ALD nucleation across various inhibitors, ALD chemistries, and 2D materials, opening opportunities for reliable dielectric integration in next-generation nanoelectronics.

36 MATERIALS SCIENCE↗

Controlled gate networks: theory and application to eigenvalue estimation

We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed with the fewest number of gates. We present the general theory of controlled gate networks and show that, under quite general conditions, it can significantly reduce the number of two-qubit gates needed to produce linear combinations of unitary operators. The first example we consider is a variational subspace calculation for a two-qubit system. The second example is estimating the eigenvalues of a two-qubit Hamiltonian via the rodeo algorithm (Choi et al. in Phys Rev Lett 127(4):040505, 2021. https://doi.org/10.1103/PhysRevLett.127.040505) using operators that we call controlled reversal gates. We use the Quantinuum H1-2 and IBM Perth devices to realize the quantum circuits. The third example is the application of controlled gate networks to the controlled time evolution of a free nucleon on a three-dimensional lattice. For all of the examples, we show very substantial reductions in the number of two-qubit gates required. Our work demonstrates that controlled gate networks are a useful tool for reducing gate complexity in quantum algorithms for quantum many-body problems such as those relevant to nuclear physics.

Bee-Lindgren, Max [Georgia Institute of Technology↗

Aromatic Amide Foldamers Show Conformation‐Dependent Electronic Properties

Electron transport in organic molecules and biomolecules is governed by electronic structure and molecular conformations. Despite recent progress, key challenges remain in understanding the role of intramolecular interactions and three-dimensional (3D) conformations on the electron transport behavior of organic molecules. In this work, the electronic properties of aromatic amide foldamers are characterized that organize into distinct 3D structures, including an extended secondary amide that adopts a trans-conformation and a folded N-methylated tertiary amide that adopts a cis-conformation. Results from single-molecule electronic experiments show that the extended secondary amide exhibits a fourfold enhancement in molecular conductance compared to the folded N-methylated tertiary amide, despite a longer contour length. The results show that extended amide molecules are governed by a through-bond electron transport mechanism, whereas folded amide molecules are dominated by through-space transport. Bulk spectroscopic characterization and density functional theory calculations further reveal that extended amides have a smaller HOMO–LUMO gap and larger transmission values compared to folded amides, consistent with single-molecule electronic experiments. Overall, this work shows that 3D molecular conformations significantly influence the electronic properties of single-molecule junctions.

electron transport↗

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↗

Measurement of the longitudinal flow-plane decorrelation using multiplane cumulants in $\sqrt{s_{NN}}$ = 200 GeV Au+Au, Ru+Ru, and Zr+Zr collisions

Measurements of the variation of anisotropic flow-plane angles (𝛹 𝑛 ) with rapidity, commonly known as the flow-plane decorrelation, provide important insights into the initial conditions of the matter produced in heavy-ion collisions. Here, in this paper, using data collected by the STAR experiment, we report the first measurement of the four-plane correlator observable 𝑇 𝑛 ⁡{𝑏⁢𝑎;𝑑⁢𝑐}=⟨⟨sin⁡[𝑛⁢(𝛹$^𝑏_𝑛$ − 𝛹$^𝑎_𝑛$)]⁢sin⁡[𝑛⁢(𝛹$^𝑑_𝑛$ − 𝛹$^𝑐_𝑛$)]⟩⟩, where superscripts 𝑎, 𝑏, 𝑐, and 𝑑 denote sequential pseudorapidity (𝜂) regions with 𝑎 corresponding to the most backward region, 𝑏 and 𝑐 close to mid-rapidity with 𝜂 𝑏 < 0 and 𝜂 𝑐 > 0, and 𝑑 being the most forward. The measurement is performed for the elliptic and triangular flow (i.e.~𝑛 = 2 and 3) in Au+Au and isobar (Ru+Ru, Zr+Zr) collisions at $\sqrt{s_{NN}}$=200~GeV. The goal of calculating the correlation of the flow-plane angle variations from backward to mid-central, and from mid-central to forward regions, is to probe the systematic variation of flow angle over a wide 𝜂 range. In mid-central collisions (10−30% centrality), we find 𝑇 2 ⁡{𝑏⁢𝑎;𝑑⁢𝑐} =−0.004 ±0.001⁢(s⁢t⁢a⁢t) ±0.002⁢(s⁢y⁢s⁢t) independent of the collision system. Such a small value of 𝑇 2 favors a random-walk'' variation of the flow-plane angles, where the rapidity correlation length is smaller than the entire region under study. These measurements provide new information on the decorrelation patterns in the system and offer a quantitative estimate of possible systematic variations in anisotropic flow angles such astwist’’ between forward and backward regions. This opens new opportunities for understanding the three-dimensional structure and the time evolution of the quark-gluon plasma created in heavy-ion collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Breaking the Linear Scaling Relations for the Oxygen Reduction Reaction with a Dual‐Atom Catalyst Composed of a MnFe‐Porphyrrole Aerogel

Bimetallic catalysts offer enhanced catalytic performance through synergistic interactions between the two metals, allowing them to break the linear scaling relations and reach high electrocatalytic activity. This study presents bimetallic aerogel-based catalyst synthesized as a covalent, three-dimensional framework containing neighboring iron and manganese sites. The aerogel structure provides a high surface area and porosity, facilitating an ultra-high active site density and efficient mass transport. The MnFe porphyrrole's unique structure is obtained by alternately linking Mn-porphyrin and Fe-corrole complexes. It exhibited outstanding performance with an onset potential of 0.99 V RHE . Comparative studies with a free-base Fe porphyrrole catalyst (E onset 0.97 V RHE ) revealed that while Mn incorporation led to only a slight improvement in half-cell performance, it resulted in significantly enhanced performance in anion exchange membrane fuel cell. The MnFe catalyst achieved an OCV of 0.97 V and a peak power density of 0.27 W cm −2 , outperforming the free-base Fe counterpart. Using density functional theory calculations, we show that the higher ORR activity of MnFe-porphyrrole is due to charge transfer between Mn and Fe atoms, which is absent in the reference free-base Fe-porphyrrole. These findings underscore the advantages of bimetallic catalysts in improving ORR activity and fuel cell efficiency by leveraging synergistic effects.

Aerogel↗

Mesoscale atomic engineering in a crystal lattice

Controlling individual atoms using lasers, ion traps and scanning probe tips has transformed our understanding of matter and enabled breakthroughs in quantum science. Extending this control into three-dimensional (3D) solids and across mesoscopic scales, however, remains a foundational challenge. Electron irradiation in electron microscopes is known to induce atomic displacements, and atomic manipulation has been proposed and demonstrated. Yet repeated and deterministic control has remained elusive. Here, in this study, we demonstrate deterministic atomic engineering in a 3D crystal, creating ordered arrangements of more than 40,000 user-defined defects within minutes across a 150 nm × 100 nm × 13 nm volume. By steering individual Cr atoms in the magnetic semiconductor CrSBr into selected interstitial sites using an electron beam directed with sub-20-pm-scale accuracy, we create vacancy–interstitial complexes. The resulting impurity array forms a mesoscale crystal embedded within the host lattice, a new form of engineered artificial matter that remains stable at room temperature and outside the microscope. By tracking Cr atom displacements, we identify conditions under which the defect structures are predictable. Our calculations suggest that these defects form correlated impurity states with intra-defect optical transitions and inter-defect kinetic and Coulomb interactions. This establishes a generalizable platform for atomic defect engineering at mesoscopic, and potentially macroscopic, scales, opening opportunities for scalable quantum technologies, including deterministic colour-centre placement, quantum simulation of many-body lattice models and atomic-scale manufacturing.

74 ATOMIC AND MOLECULAR PHYSICS↗

Initial steady-state core simulation capability or thermal and pool-type molten salt reactors, coupling reactor physics, thermal-hydraulics, and evolving chemistry

This report presents the development and validation of an initial steady-state multiphysics capability for molten salt reactors (MSRs) under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in Fiscal Year 2025. The framework integrates neutronics, thermal-hydraulics, species transport, and thermochemistry to capture the coupled dynamics of liquid-fueled systems. Implementation and testing were performed on two representative designs: the Molten Salt Reactor Experiment (MSRE), a thermal-spectrum, channeled-flow reactor, and the Lotus Molten Salt Reactor (L-MSR), a fast-spectrum, pool-type reactor. The modeling suite employs Griffin for reactor physics and depletion, Pronghorn and SAM for thermal-hydraulics, Thermochimica for chemistry, and Saline for thermophysical properties, with benchmarking and validation carried out against historical MSRE data, experimental flow-loop measurements, and reference depletion calculations from Monte Carlo codes. The framework demonstrated the ability to reproduce key reactor behaviors including temperature feedback, reactivity losses, delayed neutron precursor transport, xenon poisoning, and redox potential evolution. The results confirm the feasibility and accuracy of the coupled models in predicting steady-state and selected transient MSR behaviors. This latter ones are used in this report as a proxy indicating that the steady-state models from which the transient starts are accurate. For MSRE, validation showed good agreement with pump start-up and natural circulation tests, while for the L-MSR, benchmarking confirmed hydraulic calibration and consistency of neutronics–thermal coupling. The tools also provided new insights into species transport, noble metal deposition, and salt solidification dynamics. On the Xenon transport front, the code is validated against the steady state Xenon poisoining measurement and showed good agreement with the experimental value. Identified areas for future work include advanced void transport modeling, three-dimensional simulations, improved alloy corrosion models, and tighter integration with high-fidelity Monte Carlo codes. These developments provide a foundation for high-fidelity MSR simulations that can support reactor design optimization, safety assessments, and long-term operational strategies.

42 - ENGINEERING↗

Integrated Molten Salt Reactor Modeling Capabilities in NEAMS Thermal Hydraulics Tools

The DOE neams program supports a full range of computational thermal fluids analysis capabilities and code developments for a broad range of advanced reactor concepts. The research and development approach under the thermal fluids technical area synergistically combines three length and time scales in a hierarchical multi-scale approach. To enable multi-scale thermal fluids capability using these codes, a key joint effort has been underway to develop an integrated system- and engineering-scale thermal fluids analysis capability, through integration of SAM and Pronghorn codes, both based on the MOOSE framework. This report summarizes recent advances in developing an integrated system- and engineering-scale modeling capability for the msr concept, which has gained significant interest in recent years. A consistent framework was established by coupling Pronghorn and SAM through the Saline interface, with thermophysical properties provided by the Molten Salt Thermal Property Database (MSTDB-TP). Further improvements were made to the coupling schemes and domain-overlapping strategies, enhancing the stability and robustness of multi-code simulations. Verification and validation efforts demonstrate the accuracy of this integration across a range of benchmark problems, including one-dimensional heated pipe flows, three-dimensional natural convection loops with evolving isotopic compositions, and \gls{msre} demonstration cases. Within Pronghorn, new capabilities were introduced to model corrosion and noble-metal plating phenomena, supported by an extended thermal-hydraulics framework and refined turbulence treatments. To capture two-phase flow behavior, a multiphase Euler–Euler model was implemented in Pronghorn, including advanced closure relations, high-resolution advection techniques, and capillary force reconstruction. Preliminary verification cases confirm the fidelity of the approach, while planned validation efforts target canonical multiphase benchmarks and application to msr components such as the msre pump bowl. Finally, updates to SAM’s msr mass transfer modeling were extended to consider noble gas migration into porous structures like graphite. The point kinetics model was updated to include reactivity feedback contributions from any defined species, such as xenon. The gas transport model was expanded for applicability to gas mixtures, bubble efflux phenomena, and species transport between liquid and gas phases. A selection of multi-scale Sherwood number correlations from MOSCATO/NekRS and multi-phase correlations from literature have been added for improved accuracy in calculating mass transfer coefficients. A companion effort on developing system-level redox corrosion has also been incorporated into SAM. Collectively, these enhancements strengthen the predictive capability of SAM and Pronghorn for simulating MSR thermal-hydraulics, corrosion, multiphase behavior, and fission-product transport, providing a more complete toolset for design, safety analysis, and licensing support of next-generation \gls{msr}s.

42 - ENGINEERING↗

Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized Transverse Momentum-Dependent Parton Distribution Functions at Physical Quark Masses

We present the first lattice QCD calculations of the isovector helicity transverse momentum-dependent parton distribution function (TMDPDF) and the flavor-dependent unpolarized TMDPDFs for up and down quarks in the proton. Our computations utilize domain-wall fermion discretization with physical quark masses. Employing Coulomb-gauge-fixed quark correlation functions within the large-momentum effective theory framework, we access nonperturbative transverse quark separations 𝑏 𝑇 up to approximately 1 fm, corresponding to transverse momenta as low as 200 MeV. Based on the quasi-TMD factorization theorem, we construct renormalization-group–invariant ratios that are equal to the corresponding light-cone TMDPDF ratios. At moderate 𝑥, our results reveal that the isovector helicity and unpolarized TMDPDFs exhibit nearly identical transverse structure up to a normalization factor, and the unpolarized distributions display only mild flavor dependence. These findings not only support key trends observed in recent global analyses but also provide robust, nonperturbative constraints that can distinguish between different parameterizations. This Letter establishes a first-principles benchmark for TMDPDFs, offering valuable input for ongoing and future experimental efforts to map the proton’s three-dimensional structure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Determining the Conformation of Supported Complexes Using an 17 O TEDOR-like NMR Experiment

Dynamic nuclear polarization surface-enhanced nuclear magnetic resonance (NMR) spectroscopy has enabled the determination of the three-dimensional configuration of surface sites, in particular supported metal complexes of relevance to single-site heterogeneous catalysis. These approaches have chiefly leveraged the application of NMR double-resonance experiments that either reveal the complex conformation via point-to-point intramolecular distances between spin-labeled atoms or the complex-surface orientation via distances between the spins and the surface plane. Either method typically requires expensive isotope labeling and each reports on different structural features. The application of an experiment that simultaneously reveals both types of distances with chemical resolution would be ideal. Here, in this article, we describe an 17 O{ 1 H} pseudo-3D correlation experiment that achieves this goal. Specifically, Si–O–Si and Si–O–M oxygens are well-resolved by 17 O NMR; therefore, distances can be simultaneously measured radially, between Si– 17 O–M and the 1 H’s of the ligands, and vertically to the Si– 17 O–Si linkages of the silica support. We demonstrate the experiment using supported yttrium and zirconium complexes. Good agreement is obtained when comparing the experimental results to theoretical predictions from density functional theory calculations, highlighting the reliability of this relatively simple experiment.

alkyls↗