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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Directed flow from parton spin-orbit coupling in $pp$ and $pA$ collisions

We point out a novel mechanism to generate cos φ two-particle azimuthal correlation (‘directed flow’) in unpolarized proton-proton and proton-nucleus collisions in the forward rapidity region of the projectile proton. This is a direct consequence of the recently discovered strong spin-orbit coupling in gluons at small-x. The observable simultaneously serves as a unique probe into the double helicity parton distribution functions of the proton.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Double-differential Measurements of Mesonless Charged-current Muon Neutrino Interactions on Argon with Final-State Protons using the MicroBooNE Detector

This note reports the first double-differential measurements of charged-current $ν_µ$ scattering on argon leading to final states containing zero mesons and one or more protons. This event topology (hereafter abbreviated as CC0$πNp$) is the most common at the neutrino energies typically produced by the Fermilab Booster Neutrino Beam. A detailed understanding of neutrino-argon scattering in the CC0$πNp$ channel is therefore crucial for the success of the precision neutrino oscillation analyses planned for the Short-Baseline Neutrino (SBN) program. This remains true for the upcoming Deep Underground Neutrino Experiment (DUNE), but the higher mean neutrino energy used there will ensure that more inelastic reaction modes, such as single pion production, will also play a major role. The analysis described in this note builds on a previous MicroBooNE study of the CC0$πNp$ channel which obtained the first single-differential cross-section measurements on an argon target. Since that foundational work, significant improvements have been made to MicroBooNE’s simulation software, event reconstruction algorithms, and procedure for calculating systematic uncertainties. When combined with a larger dataset (corresponding to a beam exposure of 6.79 × 10 20 protons-on-target versus 1.60 × 10 20 in Ref. [3]), these enhancements allow the important CC0$πNp$ channel to be studied in more detail. This note begins with a description of the data and simulation samples used as input to the analysis. Section 3 then defines the CC0$πNp$ signal event topology, and Section 4 describes a set of selection criteria designed to identify these events in MicroBooNE data. Binning schemes are then defined in Section 5 for two double-differential measurements of event rates. The first of these considers the momentum and scattering cosine of the outgoing muon, while the second reports the same observables for the leading proton, i.e., the final-state proton with the largest momentum. After a discussion of systematic uncertainties in Section 6, the note concludes by comparing the predictions of MicroBooNE Monte Carlo (MC) simulations to the measured double-differential distributions. These results will form the basis for a future extraction of flux-averaged double-differential CC0$πNp$ cross sections that will be immediately comparable to the theoretical predictions of multiple neutrino event generators. The selection described herein may also be used to study various other observables in CC0$πNp$ events, including those which are sensitive to correlations between leptonic and hadronic kinematics in the final state.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

The influence of δ-(Al,Fe)OOH on seismic heterogeneities in Earth’s lower mantle

The high-pressure phases of oxyhydroxides (δ-AlOOH, ε-FeOOH, and their solid solution), candidate components of subducted slabs, have wide stability fields, thus potentially influencing volatile circulation and dynamics in the Earth’s lower mantle. Here, we report the elastic wave velocities of δ-(Al,Fe)OOH (Fe/(Al + Fe) = 0.13, δ-Fe13) to 79 GPa, determined by nuclear resonant inelastic X-ray scattering. At pressures below 20 GPa, a softening of the phonon spectra is observed. With increasing pressure up to the Fe 3+ spin crossover (~ 45 GPa), the Debye sound velocity (vD) increases. At higher pressures, the low spin δ-Fe 13 is characterized by a pressure-invariant vD. Using the equation of state for the same sample, the shear-, compressional-, and bulk-velocities (v S , v P , and v Φ ) are calculated and extrapolated to deep mantle conditions. The obtained velocity data show that δ-(Al,Fe)OOH may cause low-v Φ and low-v P anomalies in the shallow lower mantle. At deeper depths, we find that this hydrous phase reproduces the anti-correlation between v S and v Φ reported for the large low seismic velocity provinces, thus serving as a potential seismic signature of hydrous circulation in the lower mantle.

58 GEOSCIENCES↗
DOE OSTI2023

Detailed study of quark-hadron duality in spin structure functions of the proton and neutron

Background: The response of hadrons, the bound states of the strong force (QCD), to external probes can be described in two different, complementary frameworks: as direct interactions with their fundamental constituents, quarks and gluons, or alternatively as elastic or inelastic coherent scattering that leaves the hadrons in their ground state or in one of their excited (resonance) states. The former picture emerges most clearly in hard processes with high momentum transfer, where the hadron response can be described by the perturbative expansion of QCD, while at lower energy and momentum transfers, the resonant excitations of the hadrons dominate the cross section. The overlap region between these two pictures, where both yield similar predictions, is referred to as quark-hadron duality and has been extensively studied in reactions involving unpolarized hadrons. Some limited information on this phenomenon also exists for polarized protons, deuterons, and 3 He nuclei, but not yet for neutrons. Purpose: In this paper, we present comprehensive and detailed results on the correspondence between the extrapolated deep inelastic structure function g 1 of both the proton and the neutron with the same quantity measured in the nucleon resonance region. Thanks to the fine binning and high precision of our data, and using a well-controlled perturbative QCD (pQCD) fit for the partonic prediction, we can make quantitative statements about the kinematic range of applicability of both local duality and global duality. Method: We use the most updated QCD global analysis results at high x from the Jefferson Lab Angular Momentum Collaboration to extrapolate the spin structure function g 1 into the nucleon resonance region and then integrate over various intervals in the scaling variable x. We compare the results with the large data set collected in the quark-hadron transition region by the CLAS Collaboration, including, for the first time, deconvoluted neutron data, integrated over the same intervals. We present this comparison as a function of the momentum transfer Q 2 . Results: We find that, depending on the integration interval and the minimum momentum transfer chosen, a clear transition to quark-hadron duality can be observed in both nucleon species. Furthermore, we show, for the first time, the approach to scaling behavior for g 1 measured in the resonance region at sufficiently high momentum transfer. Conclusions: Here, our results can be used to quantify the deviations from the applicability of pQCD for data taken at moderate energies and can help with extraction of quark distribution functions from such data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Spin-orbit entanglement in the Color Glass Condensate

We compute the spin-orbit correlations of quarks and gluons at small-x and show that the helicity and the orbital angular momentum of individual partons are strongly anti-aligned even in unpolarized or spinless hadrons and nuclei. Combined with the fact that gluons in the Color Glass Condensate are linearly polarized, our finding indicates that the helicity and the orbital angular momentum of single gluons are maximally entangled in a quantum mechanical sense.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Spin-dependent Pomeron and Odderon in elastic proton–proton scattering

We introduce a new model of near-forward elastic proton-(anti)proton scattering at high energy based on the modern formulation of Pomeron and Odderon in terms of Wilson lines and generalized TMDs (GTMDs). We compute the helicity-dependent elastic amplitudes $\phi$1,2,3,4,5 in this model and study their energy dependence from the nonlinear small-x evolution equations. While both Pomeron and Odderon contribute to helicity-flip processes in general, in the forward limit t = 0 only the double helicity-flip amplitude $\phi$2, dominated by the spin-dependent Odderon, survives. This may effect the extraction of the ρ parameter as well as the total cross section in the LHC energy domain and beyond

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Phonon-informed Neural Thermal Scattering (NeTS) Optimization for Crystalline Graphite and Beryllium Metal

Fast neutrons born from fission lose energy through scattering interactions in the process of slowing-down. As neutrons thermalize to the order of $k$ $b$ $T$ (where $k$ $b$ is the Boltzmann constant, and $T$ is the temperature of the medium), their de Broglie wavelength and energy approaches the order of inter-atomic spacing and quantized lattice vibrations, i.e., phonons. At thermal energies, the thermal scattering law (TSL), i.e., $S$($α, β$), captures crystal binding contributions to the total reaction rate, or cross section. This dimensionless material property describes the energy ($β$) and momentum ($α$) exchanges available in a medium. Currently, $S$($α, β$) is evaluated in the Full Law Analysis Scattering System Hub (FLASSH) code for discrete inputs and stored as ENDF/B File 7 for 0-phonon elastic (MT 2) and n-phonon inelastic (MT 4) processes. Further processing recasts $S$($α, β$) into cumulative distribution functions for sampling post-collision scattering kinematics. In practice, interpolation schemes are employed to access data between tabulated values. An improvement to this juncture of the nuclear data pipeline is supplying cross sections on-the-fly (OTF), as has been developed for the un-resolved resonance region to minimize non-physical interpolation errors. This capability may improve simulation accuracy for accident and transient analyses, where rapidly varying changes in temperature and pressure are difficult to predict beforehand. To do so, deep artificial neural networks (ANNs) can be employed which collapse non-linear, complex data into a lightweight dictionary of neural weights and biases. This has been successfully demonstrated for the hydrogen in light water $S$($α, β$) dataset in the form of a Neural Thermal Scattering (NeTS) module. In this work, the NeTS framework is extended to consider the impact of material-dependent dynamical features on optimal neural pre-processing and architecture design decisions, such as number of neurons per hidden layer, residual skip connections and neural depth. New NeTS modules for crystalline graphite and beryllium metal illuminate a novel correlation between dynamical nonlinearity and optimal neural parametrization when deploying $S$($α, β$) on-the-fly.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Interacting spin and charge density waves in the kagome metal FeGe

Unveiling the interplay between spin density wave (SDW) and charge density wave (CDW) orders in correlated electron materials is important in obtaining a comprehensive understanding of their electronic, structural, and magnetic properties. Kagome lattice materials are interesting because their flat electronic bands, Dirac points, and Van Hove singularities can enable a variety of exotic electronic and magnetic phenomena. The kagome metal FeGe (the B35 phase), which exhibits a CDW order deep within an A-type antiferromagnetic (AFM) phase, was found to respond dramatically to postgrowth annealing—with the ability to tune the CDW repeatedly from long-range order to negligible order. Additionally, neutron scattering studies suggest that incommensurate magnetic peaks that onset at 𝑇 Canting = 𝑇 SDW ≈ 60 K in the system arise from a SDW order instead of the AFM double-cone structure. Here, in this study, we use inelastic neutron scattering to show that two distinct spin excitations exist below 𝑇 Canting corresponding to two coexisting magnetic orders in the system in both sets of annealed samples with and without CDW. While CDW order or negligible order can dramatically affect the onset temperature of 𝑇 Canting and elastic incommensurate magnetic scattering, its impact on low-energy spin fluctuations is more limited. In both samples, a pair of gapless incommensurate spin excitations arising from the SDW order wave vector coexist with gapped commensurate spin waves from the A-type AFM order across 𝑇 Canting . The low-energy spin excitations for both samples couple dynamically to the lattice through enhanced magnetic scattering intensity on cooling below 𝑇 CDW , regardless of the status of the static long-range CDW order. The incommensurate SDW order in the long-range CDW ordered sample also induces a tiny in-plane lattice distortion of the kagome lattice that is absent in the negligible CDW ordered sample, in a way that is different from the previously known SDW and CDW ordering materials.

charge density waves↗
DOE OSTI2023

Isotopic Constraints on the Nature of Primary Precipitates in Archean–Early Paleoproterozoic Iron Formations from Determinations of the Iron Phonon Density of States of Greenalite and 2L- and 6L-Ferrihydrite

Iron formations (IFs) are chemical sedimentary rocks that were widely deposited before the Great Oxidation Event (GOE) around 2.4- 2.2 Ga. It is generally thought that IFs precipitated as hydrated Fe 3+ oxides (HFOs) such as ferrihydrite following surface oxidation of Fe 2+ -rich, anoxic deep waters. This model often implicates biological oxidation and underpins reconstructions of marine nutrient concentrations. However, nanoscale petrography indicates that an Fe 2+ silicate, greenalite, is a common primary mineral in well-preserved IFs, motivating an alternative depositional model of anoxic ferrous silicate precipitation. It is unclear, however, if Fe 2+ -rich silicates can produce the Fe isotopic variations in IFs that are well explained by Fe 2+ oxidation. To address this question, we constrain the equilibrium Fe isotopic ( 56 Fe/ 54 Fe) fractionation of greenalite and ferrihydrite by determining the iron phonon densities of states for those minerals. Here, we use ab initio density functional theory (DFT + U) calculations and nuclear resonant inelastic X-ray scattering spectroscopy to show that ferrous greenalite should be isotopically lighter than ferrihydrite by similar to 1-1.2 parts per thousand at equilibrium, and fractionation should scale linearly with increasing Fe 3+ content in greenalite. By anchoring ferrihydrite-greenalite mineral pair fractionations to published experimental Fe isotopic fractionations between HFOs and aqueous Fe 2+ , we show that ferrous greenalite may produce all but the heaviest pre-GOE Fe isotopic compositions and mixed valence greenalites can produce the entire record. Our results suggest that heavy Fe isotope enrichments alone are not diagnostic of primary IF mineralogies, and ferrihydrite and partially oxidized or even purely ferrous greenalite are all viable primary IF mineralogies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Water Migration and Swelling in Engineered Barrier Materials for Radioactive Waste Disposal

Deep, underground repositories are needed to isolate radioactive waste from the biosphere. Because bentonite is an integral component of many multibarrier repository systems, information on the hydraulic behavior of bentonite is crucial for modeling the long-term viability of such systems. In this paper the hydraulic behavior of bentonite samples was analyzed as a function of aggregate size, and samples were subjected to hydrothermal treatments involving contact with NaCl, KCl, and deionized water. Neutron and X-ray imaging were used to quantify water sorption into packed bentonite samples and bentonite swelling into the water column. The distance between the original clay-water interface and the wetting front was determined as a function of time. Average water uptake exhibited a square-root-of-time dependence in freshly prepared samples, but more variable rates were observed for samples previously in contact with water. The radiography was supported by small-angle neutron scattering analysis and ultra-small-angle neutron scattering analysis of aggregate size distributions and by inelastic neutron scattering to understand the physicochemical environment of the sorbed water. Results showed that hydrothermal treatment with KCl had the greatest effect of increased water transport in the bentonite, possibly as a result of the interaction of K + with smectite layers in the clay.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Phase and Morphology of Water-ice Grains Formed in a Cryogenic Laboratory Plasma

Abstract Grains of ice are formed spontaneously when water vapor is injected into a weakly ionized laboratory plasma in which the background gas has been cooled to cryogenic temperatures comparable to those of deep space. These ice grains are levitated indefinitely within the plasma so that their time evolution can be observed under free-floating conditions. Using microscope imaging, ice grains are shown to have a spindle-like fractal structure and grow over time. Both crystalline and amorphous phases of ice are observed using Fourier transform infrared spectroscopy. A mix of crystalline and amorphous grains coexists under certain thermal conditions, and a linear mixing model is used on the ice absorption band surrounding 3.2 μ m to examine the ice phase composition and its temporal stability. The extinction spectrum is also affected by inelastic scattering as grains grow, and characteristic grain radii are obtained from Mie scattering theory and compared to size measurements from direct imaging. Observations are used to compare possible ice nucleation mechanisms, and it is concluded that nucleation is likely catalyzed by ions, as ice does not nucleate in the absence of plasma and impurities are not detected. Ice grain properties and infrared extinction spectra show similarity to observations of some astrophysical ices observed in protoplanetary disks, implying that the fractal morphology of the ice and observed processes of homogeneous ice nucleation could occur as well in such astrophysical environments with weakly ionized conditions.

Astronomy & Astrophysics↗
DOE OSTI2026

Hadron-Argon Cross-Section Measurements at Protodune

The Deep Underground Neutrino Experiment (DUNE) is a next-generation experiment designed to measure neutrino oscillations with unprecedented precision, specifically seeking to identify CP violation in the lepton sector. DUNE utilizes the Liquid Argon Time Projection Chamber (LArTPC) as its core detecting technology, offering high-resolution imaging to reconstruct neutrino interactions on argon. A primary challenge in this reconstruction is the modeling of hadronic final-state interactions (FSI), where hadrons produced at the initial interaction vertex undergo further scattering before escaping the nucleus. In this thesis, I utilize the ProtoDUNE-SP detector and its 1~GeV/$c$ hadron beam at the CERN Neutrino Platform to present the first measurements of total inelastic $\pi^+$-argon and proton-argon cross sections in an energy regime critical to DUNE. I detail the development and validation of the ``slicing method'', which utilizes a kiloton-scale LArTPC to extract hadron-argon cross sections. These measurements provide an indispensable benchmark for informing DUNE's FSI modeling, and our results show no significant tension with current model predictions. Additionally, I study the impact of FSI modeling on DUNE’s sensitivity to oscillation parameters. This study demonstrates that variations in FSI models may be degenerate with oscillation features, highlighting the necessity of using direct experimental data to refine interaction models. Finally, I provide an outlook on related studies that will further contribute to this effort, supporting the ambitious physics goals of upcoming neutrino oscillation programs including DUNE.

Yin-Rui, Liu [U. Chicago (main)]↗
DOE OSTI2026

Impact of QCD energy evolution on observables in heavy-ion collisions

Here, we study how the inclusion of energy dependence as dictated by quantum chromodynamic (QCD) small-x evolution equations affects key observables in ultra-relativistic heavy-ion collisions. Specifically, we incorporate JIMWLK evolution into the IP-Glasma framework, which serves as the initial condition for a simulation pipeline that includes viscous relativistic hydrodynamics and a hadronic afterburner. This approach enables a consistent modeling of highly energetic nuclei across varying Bjorken-x values, which are relevant for different collision energies and rapidity regions. In comparison to the standard IP-Glasma setup without small-x evolution, we observe pronounced changes in particle multiplicities and spectral distributions, especially in smaller systems and at the highest available energies. We further explore effects on anisotropic flow observables and correlations between mean transverse momentum and elliptic flow. Our findings underscore the critical role of nonlinear QCD evolution in accurately modeling the early stages of heavy-ion collisions, as well as its implications for extracting transport properties of the quark-gluon plasma.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Small-x structure of oxygen and neon isotopes as seen by the Large Hadron Collider

Results on collisions of O-16 nuclei performed at the Relativistic Heavy Ion Collider (RHIC) have been presented for the first time at Quark Matter 2023 by the STAR collaboration. O-16+O-16 collisions are also expected to take place in the near future at the Large Hadron Collider (LHC) at much higher beam energies. We explore the potential of beam-energy-dependent studies for this system to probe small-x dynamics and QCD evolution. We perform 3+1D IP-Glasma simulations to predict the rapidity dependence of the initial geometry of light-ion collisions, focusing on O-16+O-16 and Ne-20+Ne-20 collisions at root s(NN) = 70 GeV and 7 TeV. The choice of Ne-20 is motivated by its strongly elongated geometry, which may respond differently to the effect of the high-energy evolution compared to the more spherical O-16. We find that smearing induced by soft gluon production at high energy causes mild variations in the initial-state eccentricities as a function of the collision energy. These effects could be resolved in future experiments and deserve further investigation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Results from the DUNE ND-LAr 2x2 Demonstrator Run 2

The Deep Underground Neutrino Experiment (DUNE) is a cutting-edge, long-baseline experiment under construction in the United States, based on large liquid-argon time projection chambers (LArTPCs). The DUNE Near Detector LArTPC (ND-LAr) will employ a novel modular architecture using a pixelated LArPix charge readout. To validate this design and characterize detector response, the 2×2 demonstrator—an array of eight optically isolated LArTPC modules—was deployed at Fermilab in 2024. During winter 2025, the 2x2 demonstrator was operated for a second data-taking campaign (Run 2) with the aim of studying the low-energy response of the detector. Run 2 focused on calibration and response studies using a suite of deployed radioactive sources. Gamma sources (²²Na, ⁶⁰Co, and ⁸⁸Y) were used to probe module-to-module performance variations, energy resolution, and calibrations. Neutron sources (AmBe and a pulsed neutron generator) enabled studies of neutron interactions in liquid argon, including inelastic scatters and neutron capture signals, relevant for low-energy backgrounds and detector modeling. In addition, the detector was doped with ²²⁰Rn, providing Bi–Po coincidence signals that allow precise calibration of the charge and scintillation response. This poster will present results from these calibration campaigns. These studies provide critical validation of the ND-LAr modular LArTPC concept and inform calibration and reconstruction strategies for the full DUNE near detector.

Mora-Lepin, Luis [Florida State U.] (ORCID:0000000↗
DOE OSTI2020

Warming nuclear pasta with dark matter: kinetic and annihilation heating of neutron star crusts

Neutron stars serve as excellent next-generation thermal detectors of dark matter, heated by the scattering and annihilation of dark matter accelerated to relativistic speeds in their deep gravitational wells. However, the dynamics of neutron star cores are uncertain, making it difficult at present to unequivocally compute dark matter scattering in this region. On the other hand, the physics of an outer layer of the neutron star, the crust, is more robustly understood. We show that dark matter scattering solely with the low-density crust still kinetically heats neutron stars to infrared temperatures detectable by forthcoming telescopes. We find that for both spin-independent and spin-dependent scattering on nucleons, the crust-only cross section sensitivity is 10 -43 - 10 -41 cm 2 for dark matter masses of 100 MeV - 1 PeV, with the best sensitivity arising from dark matter scattering with a crust constituent called nuclear pasta (including gnocchi, spaghetti, and lasagna phases). For dark matter masses from 10 eV to 1 MeV, the sensitivity is 10 -39 - 10 -34 cm 2 , arising from exciting collective phonon modes in a neutron superfluid in the inner crust. Furthermore, for any s-wave or p-wave annihilating dark matter, we show that dark matter will efficiently annihilate by thermalizing just with the neutron star crust, regardless of whether the dark matter ever scatters with the neutron star core. This implies efficient annihilation in neutron stars for any electroweakly interacting dark matter with inelastic mass splittings of up to 200 MeV, including Higgsinos. We conclude that neutron star crusts play a key role in dark matter scattering and annihilation in neutron stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Probing gluon saturation with forward di-hadron correlations in proton-nucleus collisions

We present a detailed numerical investigation of semi-inclusive forward di-hadron production in proton–nucleus collisions employing the Color Glass Condensate effective theory. We focus on the regime where di-hadrons are produced nearly back-to-back in the transverse plane, thereby justifying a transverse-momentum-dependent factorization approach in terms of small-x gluon distributions. Our computation integrates several key elements: i) non-linear rapidity evolution via the Balitsky–Kovchegov equation with running coupling, ii) both perturbative and non-perturbative Sudakov resummation, and iii) a phenomenologically constrained model for the initial conditions for small-x gluon distributions. We compare this phenomenological framework to experimental data from the STAR Collaboration on azimuthal correlations in forward di-pion production in both proton–proton and proton–gold collisions. We analyze the systematic theoretical uncertainties associated with the saturation scales of nuclei at the initial scale for rapidity evolution and with those associated with the hadronization process. Finally, we make predictions for the kinematics anticipated to be covered by the ALICE Forward Calorimeter (FoCal) upgrade at the Large Hadron Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Helicity at small x: oscillations generated by bringing back the quarks

We construct a numerical solution of the recently-derived large-N c &N f small-x helicity evolution equations with the aim to establish the small-x asymptotics of the quark helicity distribution beyond the large-N c limit explored previously in the same framework. (Here N c and N f are the numbers of quark colors and flavors.) While the large-N c helicity evolution involves gluons only, the large-N c &N f evolution includes contributions from quarks as well. We find that adding quarks to the evolution makes quark helicity distribution oscillate as a function of x. Our numerical results in the large-N c &N f limit lead to the x-dependence of the flavor-singlet quark helicity distribution which is well-approximated by $$ {\left.\Delta \Sigma \left(x,{Q}^2\right)\right|}_{\mathrm{large}\hbox{-} {N}_c\&{N}_f}\sim {\left(\frac{1}{x}\right)}^{\alpha_h^q}\cos \left[{\omega}_q\ln \left(\frac{1}{x}\right)+{\varphi}_q\right]. $$. The power $α^{q}_{h}$ exhibits a weak N f -dependence, and, for all Nf values considered, remains very close to $α^{q}_{h}$(N f =0)=$\left(4/\sqrt{3}\right)\sqrt{\alpha_s{N}_c/\left(2\pi \right)}$ obtained earlier in the large-N c limit. The novel oscillation frequency ω q and phase shift φ q depend more strongly on the number of flavors N f (with ω q = 0 in the pure-glue large-N c limit). The typical period of oscillations for ΔΣ is rather long, spanning many units of rapidity. We speculate whether the oscillations we find are related to the sign variation with x seen in the strange quark helicity distribution extracted from the data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗