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At least 145 records · Page 8

Collins asymmetries for pion-in-jet production in polarized ℓp collisions at the EIC

We study Collins azimuthal asymmetries for pion-in-jet production in polarized lepton-proton collisions, extending previous analyses of polarized pp scattering to a complementary and theoretically simpler process. We keep adopting a simplified transverse momentum dependent (TMD) approach, with a collinear configuration for the initial state, and employ the transversity and Collins fragmentation functions as extracted from semi-inclusive deep inelastic scattering and $e^{+}e^{-}$ annihilation processes. We then compute azimuthal asymmetries for the Electron-Ion Collider (EIC) kinematics, both within a leading order (LO) approach and by including quasireal photon exchange in the Weizsäcker-Williams approximation. Although this contribution is relevant in the whole kinematical range explored, it does not spoil the dominance of quark-initiated channels, leaving only a marginal role to their gluon counterparts. In this respect, Collins asymmetries in lepton-proton processes allow for a much clearer access to the transversity distribution, including its sea-quark component. As we will argue, a comparison with future EIC data could represent a further step in testing the hypothesis of the universality of the Collins function as well as of the TMD factorization for this class of processes.

Azimuthal asymmetries↗

A New Modeling Approach for a Priori Uncertainties of Laser Tracker Angle Measurements

Methods for modeling the uncertainty in laser tracker angle measurements vary within the metrology industry, leading to confusion and questionable stochastic modeling for survey network adjustments and error propagation analysis. Interpreting the published laser tracker manufacturer performance specifications to determine an a priori sigma value for weighting azimuth and zenith angle measurements can be confusing and has led to differing implementations. Furthermore, this paper proposes a unique way to model survey network a priori laser tracker angular uncertainties based on laser tracker manufacturers’ published maximum permissible error (MPE) values referenced to current standards for weighting survey network measurements. This paper’s proposed model takes into account the disparate effects that pointing errors, target centering errors, and leveling errors have on azimuth and zenith angular uncertainties for measurements with steep sightings and at near ranges.

42 ENGINEERING↗

Measurement of elliptic flow of 𝐽/𝜓 in $\sqrt{s_{NN}}$ = 200 GeV ⁢Au + Au collisions at forward rapidity

Here, we report the first measurement of the azimuthal anisotropy of 𝐽/𝜓 at forward rapidity (1.2 < |𝜂| < 2.2) in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV at the BNL Relativistic Heavy Ion Collider. The data were collected by the PHENIX experiment in 2014 and 2016 with integrated luminosity of 14.5 nb −1 . The second Fourier coefficient (𝑣 2 ) of the azimuthal distribution of 𝐽/𝜓 is determined as a function of the transverse momentum (𝑝𝑇) using the event-plane method. The measurements were performed for several selections of collision centrality: 0%–50%, 10%–60%, and 10%–40%. We find that in all cases the values of 𝑣 2 ⁡(𝑝 𝑇 ), which quantify the elliptic flow of 𝐽/𝜓, are consistent with zero. Within uncertainties, the results are consistent with measurements at midrapidity, indicating no significant elliptic flow of the 𝐽/𝜓 within the quark-gluon-plasma medium at collision energies of $\sqrt{s_{NN}}$ = 200 GeV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A Full-length Quench Antenna for MQXFA Production Series Quadrupole Magnet Testing

The MQXFA production series quadrupoles being built for the Hi-Lumi (HL) LHC upgrade by the US Accelerator Upgrade Project (US-HL-LHC AUP) will have very limited instrumentation for characterizing quench events that occur during magnet training and performance validation testing. In order to understand the origin of the quenches, and whether they have some implication for ongoing magnet fabrication, it was decided to build a full-length Quench Antenna (QA) with axial resolution of 50mm to be employed during cold testing in the anticryostat used for magnetic measurements. The goal is to have fineresolution, full-length coverage detection of quench events axially, as well as to have azimuthal resolution on the order of the cable width (about 1 degree for the cross-section), in a device that can be used both for vertical and horizontal testing. To achieve this, a 5m long QA with 128 channels of high-speed data acquisition has been designed and fabricated. The cylindrical antenna features an array of 12 full-length, dipole- and quadrupole-bucked coils positioned radially in the QA interior for azimuthal localization, and over 100 individual channels of short, high-sensitivity, antennas etched as flexible PCB circuits (which also buck dipole and quadrupole fields) wrapped circumferentially on the cylinder exterior in steps of 50mm along the magnet length for axial detection. This report discusses the design, construction and analysis of the MQXFA QA, and first results from using the antenna during quench testing in the production magnets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

CROCUS Urban Canyons - Space Science and Engineering Center (SPARC) Doppler lidar data

This is the netCDF format output from the Halo Photonics Streamline XR Doppler lidar that was deployed next to the Space Science and Engineering Center (SPARC) trailer at the University of Illnois-Chicago greenhouse parking lot during CROCUS Urban Canyons. The purpose of collecting this dataset is to provide vertical and horizontal wind profiles for studying the characteristics of turbulence over the urban canyon of Chicago. This data contains the radial velocity, intensity, and backscatter from the vertical profile, range height indicator, and sector scans that were performed over both Intensive Operating Period 1 and 2 of CROCUS Urban Canyons. There are four different types of files: * The Range Height Indicator (RHI) files contain scans that are along a constant azimuth, spanning the entire hemisphere of elevation values above the surface. * The Velocity Azimuth Display (VAD) files contain the raw radial velocity data from the 6-beam, 60 degree scans. * The User1 files contain stacked Plan Position Indicator scans over a 45 degree quadrant over downtown Chicago. * The Stare files contain vertically pointing scans. These are standard netCDF files that can be opened using xarray. The VAD scans can be processed from their raw radial velocities to horizontal wind speeds with the Atmospheric data Community Toolkit (https://arm-doe.github.io/ACT/).

EARTH SCIENCE > ATMOSPHERE > ATMOSPHERIC WINDS↗

Charged-particle production as a function of the relative transverse activity classifier in pp, p–Pb, and Pb–Pb collisions at the LHC

Measurements of charged-particle production in pp, p–Pb, and Pb–Pb collisions in the toward, away, and transverse regions with the ALICE detector are discussed. These regions are defined event-by-event relative to the azimuthal direction of the charged trigger particle, which is the reconstructed particle with the largest transverse momentum $(p^{trig}_T)$ in the range 8 < $p^{trig}_T$< 15 GeV/c. The toward and away regions contain the primary and recoil jets, respectively; both regions are accompanied by the underlying event (UE). In contrast, the transverse region perpendicular to the direction of the trigger particle is dominated by the so-called UE dynamics, and includes also contributions from initial- and final-state radiation. The relative transverse activity classifier, $R_T = N^T_{ch}/\langle N^T_{ch}\rangle$, is used to group events according to their UE activity, where $N^T_{ch}$ is the charged-particle multiplicity per event in the transverse region and $\langle N^T_{ch}\rangle$ is the mean value over the whole analysed sample. The energy dependence of the R T distributions in pp collisions at $\sqrt{s_{NN}}$ = 2.76, 5.02, 7, and 13 TeV is reported, exploring the Koba-Nielsen-Olesen (KNO) scaling properties of the multiplicity distributions. The first measurements of charged-particle p T spectra as a function of R T in the three azimuthal regions in pp, p–Pb, and Pb–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV are also reported. Data are compared with predictions obtained from the event generators PYTHIA 8 and EPOS LHC. This set of measurements is expected to contribute to the understanding of the origin of collective-like effects in small collision systems (pp and p–Pb).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Investigating strangeness enhancement with multiplicity in pp collisions using angular correlations

A study of strange hadron production associated with hard scattering processes and with the underlying event is conducted to investigate the origin of the enhanced production of strange hadrons in small collision systems characterised by large charged-particle multiplicities. For this purpose, the production of the single-strange meson ${\textrm{K}}_{\textrm{S}}^0$ and the double-strange baryon Ξ ± is measured, in each event, in the azimuthal direction of the highest-p T particle (“trigger” particle), related to hard scattering processes, and in the direction transverse to it in azimuth, associated with the underlying event, in pp collisions at $\sqrt{s}$ = 5.02 TeV and $\sqrt{s}$ = 13 TeV using the ALICE detector at the LHC. The per-trigger yields of ${\textrm{K}}_{\textrm{S}}^0$ and Ξ ± are dominated by the transverse-to-leading production (i.e., in the direction transverse to the trigger particle), whose contribution relative to the toward-leading production is observed to increase with the event charged-particle multiplicity. The transverse-to-leading and the toward-leading Ξ ± /${\textrm{K}}_{\textrm{S}}^0$ yield ratios increase with the multiplicity of charged particles, suggesting that strangeness enhancement with multiplicity is associated with both hard scattering processes and the underlying event. The relative production of Ξ ± with respect to ${\textrm{K}}_{\textrm{S}}^0$ is higher in transverse-to-leading processes over the whole multiplicity interval covered by the measurement. The ${\textrm{K}}_{\textrm{S}}^0$ and Ξ ± per-trigger yields and yield ratios are compared with predictions of three different phenomenological models, namely Pythia8.2 with the Monash tune, Pythia8.2 with ropes and EPOS LHC. The comparison shows that none of them can quantitatively describe either the transverse-to-leading or the toward-leading yields of ${\textrm{K}}_{\textrm{S}}^0$ and Ξ ± .

hadron-hadron scattering↗

GPU-accelerated kinetic Hall thruster simulations in WarpX

Abstract Two-dimensional (axial-azimuthal) simulations of a Hall thruster are performed using the open-source particle-in-cell code WarpX. The simulation conditions are chosen to match those of the axial-azimuthal benchmark first reported by Charoy et al. in 2019. A range of numerical and solver parameters is investigated in order to find those which yield the best performance. It is found that WarpX completes the benchmark case in 3.8 days on an Nvidia V100 GPU, and in as low as 1.5 days on a more recent Nvidia H100 GPU. Of the numerical parameters investigated, it is determined that the field-solve tolerance and particle resampling thresholds have the largest effect on the simulation wall time and that particle resampling may artificially widen electron velocity distribution functions, leading to unphysical heating. A semi-implicit scheme for the electrostatic field solve is tested and is found to produce results consistent to within 10% of the benchmark in less than twelve hours. The scaling properties of the electrostatic solver to multiple GPUs are also assessed on a uniform plasma test problem. The results of this work are discussed in the context of advancements in GPU hardware and the suitability of kinetic Hall thruster simulations for engineering applications.

Marks, Thomas A.↗

On the effects of reactant stratification and wall curvature in non-premixed rotating detonation combustors

The optimization of non-premixed rotating detonation combustors (RDCs) requires improved understanding of the coupled effects of reactant stratification, fluid property gradients, and complex shock-wave interactions on the detonation wave structure within annular geometries. In the current work, simultaneous orthogonal views of chemiluminescence and hydroxyl planar laser-induced fluorescence (PLIF) are utilized to establish the existence of a dual-wave system characterized by leading and trailing detonation waves that are closely coupled by the local flow physics. These features are persistent over a wide range of mass flow rates and are consistent with prior observations of non-premixed rotating detonations in annular geometries. The detailed instantaneous time sequences are compared with a 3D reactive unsteady Reynolds averaged Navier-Stokes (URANS) simulation to more clearly elucidate the in-situ combustion dynamics and the sensitivity to reactant inlet conditions. It is found that the dual-wave system results from unburned reactants that survive the leading detonation wave in the injector near field and are consumed within a trailing azimuthal reflected-shock combustion (ARSC) zone. By contrast, the injector far field is characterized by rapid mixing due to a sudden drop to subsonic conditions, and the bifurcated detonation wave structure collapses into a stronger, single-wave detonation front with higher overall pressure ratio as compared with the dual-wave system. While each RDC will have different inflow, mixing, and combustion characteristics, the underlying interactions between the stratified reactants and azimuthal wave dynamics identified through the combination of advanced MHz-rate diagnostics and 3D numerical simulations have important implications for the study of detonation wave stability, mode transition, and combustion efficiency in non-premixed annular RDCs.

3D URANS↗

Implementation of a Mesh refinement algorithm into the quasi-static PIC code QuickPIC

Plasma-based acceleration (PBA) has emerged as a promising candidate for the accelerator technology used to build a future linear collider and/or an advanced light source. In PBA, a trailing or witness particle beam is accelerated in the plasma wave wakefield (WF) created by a laser or particle beam driver. The WF is often nonlinear and involves the crossing of plasma particle trajectories in real space and thus particle-in-cell methods are used. The distance over which the drive beam evolves is several orders of magnitude larger than the wake wavelength. This large disparity in length scales is amenable to the quasi-static approach. Three-dimensional (3D), quasi-static (QS), particle-in-cell (PIC) codes, e.g., QuickPIC, have been shown to provide high fidelity simulation capability with 2-4 orders of magnitude speedup over 3D fully explicit PIC codes. In PBA, the witness beam needs to be matched to the focusing forces of the WF to reduce the emittance growth. In some linear collider designs, the matched spot size of the witness beam can be 2 to 3 orders of magnitude smaller than the spot size (and wavelength) of the wakefield. Such an additional disparity in length scales is ideal for mesh refinement where the WF within the witness beam is described on a finer mesh than the rest of the WF. A mesh refinement scheme is described that has been implemented into the 3D QS PIC code, QuickPIC. Very fine (high) resolution is used in a small spatial region that includes the witness beam and progressively coarser resolutions in the rest of the simulation domain. A fast multigrid Poisson solver has been implemented for the field solve on the refined meshes and a Fast Fourier Transform (FFT) based Poisson solver is used for the coarse mesh. The code has been parallelized with both MPI and OpenMP, and the parallel scalability has also been improved by using pipelining. A preliminary adaptive mesh refinement technique is described to optimize the computational time for simulations with an evolving witness beam size. Several test problems are used to verify that the mesh refinement algorithm provides accurate results. Additionally, the results are benchmarked against highly resolved simulations exhibiting near-azimuthal symmetry, performed using QPAD—a novel hybrid QS PIC code that uses a PIC description in the coordinates (r, ct – z) and a gridless description in the azimuthal angle, Φ.

Linear collider↗

ECCE sensitivity studies for single hadron transverse single spin asymmetry measurements

Here, we performed feasibility studies for various single transverse spin measurements that are related to the Sivers effect, transversity and the tensor charge, and the Collins fragmentation function. The processes studied include semi-inclusive deep inelastic scattering (SIDIS) where single hadrons (pions and kaons) were detected in addition to the scattered DIS lepton. The data were obtained in pythia6 and geant4 simulated e+p collisions at 18 GeV on 275 GeV, 18 on 100, 10 on 100, and 5 on 41 that use the ECCE detector configuration. Typical DIS kinematics were selected, most notably Q 2 >1 GeV 2 , and cover the x range from 10 -4 to 1. The single spin asymmetries were extracted as a function of x and Q 2 , as well as the semi-inclusive variables z, which corresponds to the momentum fraction the detected hadron carries relative to the struck parton, and P T , which corresponds to the transverse momentum of the detected hadron relative to the virtual photon. They are obtained in azimuthal moments in combinations of the azimuthal angles of the hadron transverse momentum and transverse spin of the nucleon relative to the lepton scattering plane. In order to extract asymmetries, the initially unpolarized MonteCarlo was re-weighted in the true kinematic variables, hadron types and parton flavors based on global fits of fixed target SIDIS experiments and e + e – annihilation data. The expected statistical precision of such measurements is extrapolated to 10 fb –1 and potential systematic uncertainties are approximated given the deviations between true and reconstructed yields. Similar neutron information is obtained by comparing the ECCE e+p pseudo-data with the same from the EIC Yellow Report and scaling the corresponding Yellow Report e+ 3 He pseudo-data uncertainties accordingly. The impact on the knowledge of the Sivers functions, transversity and tensor charges, and the Collins function has then been evaluated in the same phenomenological extractions as in the Yellow Report. Finally, the impact is found to be comparable to that obtained with the parametrized Yellow Report detector and shows that the ECCE detector configuration can fulfill the physics goals on these quantities.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A tutorial on the micro-trench technique for incident ion angle, material erosion, and impurity deposition measurements at plasma-facing surfaces

The micro-trench method is a new technique to measure polar and azimuthal incident ion angles, material erosion, and impurity deposition at plasma-facing surfaces, and has been applied in the DIII-D divertor. This article gives a tutorial of the micro-trench technique consisting of six steps: (1) micro-trench fabrication, (2) pre-exposure measurement of the fabricated micro-trench geometry, (3) tracer material deposition, (4) plasma exposure, (5) post-exposure observation of the tracer material, and (6) post-exposure measurement of the micro-trench geometry. Two criteria need to be satisfied to apply the micro-trench method successfully: (i) uniform impurity deposition on the micro-trench floor, and (ii) erosion dominated by the physical sputtering induced by the impinging ions. Furthermore, when those two criteria are satisfied, post-exposure analysis of the impurity deposition patterns on the micro-trench floor may be used to determine the polar and azimuthal incident ion directions (mean values of the ion angle directions), erosion rate, and impurity deposition rate during plasma exposure without computational interpretation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

General balance functions of identified charged hadron pairs of (π, Κ, ρ) in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

First measurements of balance functions (BFs) of all combinations of identified charged hadron (π, Κ, ρ) pairs in Pb–Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV recorded by the ALICE detector are presented. The BF measurements are carried out as two-dimensional differential correlators versus the relative rapidity (Δy) and azimuthal angle (Δφ) of hadron pairs, and studied as a function of collision centrality. The Δφ dependence of BFs is expected to be sensitive to the light quark diffusivity in the quark–gluon plasma. While the BF azimuthal widths of all pairs substantially decrease from peripheral to central collisions, the longitudinal widths exhibit mixed behaviors: BFs of ππ and cross-species pairs narrow significantly in more central collisions, whereas those of KK and pp are found to be independent of collision centrality. This dichotomy is qualitatively consistent with the presence of strong radial flow effects and the existence of two stages of quark production in relativistic heavy-ion collisions. Finally, the first measurements of the collision centrality evolution of BF integrals are presented, with the observation that charge balancing fractions are nearly independent of collision centrality in Pb–Pb collisions. Overall, the results presented provide new and challenging constraints for theoretical models of hadron production and transport in relativistic heavy-ion collisions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Spatial imaging of polarized deuterons at the Electron-Ion Collider

We study diffractive vector meson production at small-x in the collision of electrons and polarized deuterons e + d $\uparrow$ . We consider the polarization dependence of the nuclear wave function of the deuteron, which results in an azimuthal angular dependence of the produced vector meson when the deuteron is transversely polarized. The Fourier coefficients extracted from the azimuthal angular dependence of the vector meson differential cross-section exhibit notable differences between longitudinally and transversely polarized deuterons. The angular dependence of the extracted effective deuteron radius provides direct insight into the structure of the polarized deuteron wave function. Furthermore, we observe slightly increased gluon saturation effects when the deuteron is longitudinally polarized compared to the transversely polarized case. The small-x observables studied in this work will be accessible at the future Electron-Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Optimizing the Orientation of Solar Photovoltaic Systems Considering the Effects of Irradiation and Cell Temperature Models with Dust Accumulation

To cope with the growing installation capacities of solar photovoltaic (PV) systems in desert areas, it is necessary to revisit the energy production models and the optimal angles of PV panels given the significant impacts of ambient temperature, wind speed, dust accumulation, and cleaning frequency. In this study, these four factors are examined for four PV technologies (polycrystalline, microcrystalline, monocrystalline, and thin-film) at three cities in Jordan, Egypt, and Tunisia using precise ground-level meteo-solar measurements. Different models are compared to estimate the diffuse irradiance, as well as account for the effects of operating temperature, wind speed, and dust accumulation on energy production and optimal tilt and azimuth angles of the panels. The results reveal 1.5 % higher energy production estimates using the isotropic model, compared to the anisotropic model in the summer months. Considering the cooling effect of wind speed decreases the operating cell temperature drops by up to 7.05 % for thin film panels. The annually produced energy decreases by 24 % when the panels are cleaned bi-monthly. When the dust accumulation rate doubles, the energy production decreases by ~10 % for all studied cases. Also, the variations in optimal tilt and azimuth angles with dust accumulation rate are within ~3.0 degrees .

14 SOLAR ENERGY↗

Stable and unstable supersonic stagnation of an axisymmetric rotating magnetized plasma

The Naval Research Laboratory ‘Mag Noh problem’, described in this paper, is a self-similar magnetized implosion flow, which contains a fast magnetohydrodynamic (MHD) outward propagating shock of constant velocity. We generalize the classic Noh ( OSTI Tech. Rep. 577058, 1983) problem to include azimuthal and axial magnetic fields as well as rotation. Our family of ideal MHD solutions is five parametric, each solution having its own self-similarity index, gas gamma, magnetization, the ratio of axial to the azimuthal field and rotation. While the classic Noh problem must have a supersonic implosion velocity to create a shock, our solutions have an interesting three-parametric special case with zero initial velocity in which magnetic tension, instead of implosion flow, creates the shock at $t=0+$ . Our self-similar solutions are indeed realized when we solve the initial value MHD problem with the finite volume MHD code Athena. We numerically investigated the stability of these solutions and found both stable and unstable regions in parameter space. Stable solutions can be used to test the accuracy of numerical codes. Unstable solutions have also been widely used to test how codes reproduce linear growth, transition to turbulence and the practically important effects of mixing. Now we offer a family of unstable solutions featuring all three elements relevant to magnetically driven implosions: convergent flow, magnetic field and a shock wave.

Mechanics↗

Evidence of Alfvenic Poynting Flux as the Primary Driver of Auroral Motion During a Geomagnetic Substorm

Geomagnetic substorms are major energy transfer events where energy stored in the Earth's magnetotail is released into the ionosphere. Substorm phenomena, including auroral activities, earthward Poynting flux, magnetic field dipolarization, etc, have been extensively studied. However, the complex interplay among them is not fully understood. In a fortuitous event on June 7, 2013, the twin Van Allen Probes (separated by 0.4 h in local time) observed bursts of earthward Alfvenic Poynting flux in the vicinity of the plasma sheet boundary layer (PSBL). The Poynting flux bursts correlate with enhancements of auroral brightness around the footpoints of both spacecraft. This indicates a temporal and spatial correlation between the auroral brightening and Poynting flux bursts, and that the auroral motion is directly linked to the perpendicular expansion of the Alfven wave. These observations suggest that the Alfvenic Poynting flux is a primary driver for the auroral electron acceleration. Furthermore, around the time of auroral brightening, a dipolarization was seen to propagate more than 4 h in local time during a 20 min period. The azimuthal phase speed of this dipolarization (2 deg/min) is too small to explain the azimuthal motion of the aurora (13.6 deg/min), but the dipolarization could be related to the generation of the Alfvenic Poynting flux through phase mixing at strong density gradients like those in the PSBL.

58 GEOSCIENCES↗

Modeling the Contribution of Precipitation Loss to a Radiation Belt Electron Dropout Observed by Van Allen Probes

A drift-diffusion model is used to simulate the low-altitude electron distribution, accounting for azimuthal drift, pitch angle diffusion, and atmospheric backscattering effects during a rapid electron dropout event on 21st August 2013, at L = 4.5. Additional external loss effects are introduced during times when the low-altitude electron distribution cannot be reproduced by diffusion alone. Here, the model utilizes low-altitude electron count rate data from five POES/MetOp satellites to quantify pitch angle diffusion rates. Low-altitude data provides critical constraint on the model because it includes the drift loss cone region where the electron distribution in longitude is highly dependent on the balance between azimuthal drift and pitch angle diffusion. Furthermore, a newly derived angular response function for the detectors onboard POES/MetOp is employed to accurately incorporate the bounce loss cone measurements, which have been previously contaminated by electrons from outside the nominal field-of-view. While constrained by low-altitude data, the model also shows reasonable agreement with high-altitude data. Pitch angle diffusion rates during the event are quantified and are faster at lower energies. Precipitation is determined to account for all of the total loss observed for 450 keV electrons, 88% for 600 keV and 38% for 900 keV. Predictions made in the MeV range are deemed unreliable as the integral energy channels E3 and P6 fail to provide the necessary constraint at relativistic energies.

79 ASTRONOMY AND ASTROPHYSICS↗