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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Validation of the NOνA experiment 2023-tuning on simulated neutrino-matter interactions

NOνA is a long-baseline neutrino oscillation experiment that utilizes a two-detector design to study the oscillations of muon neutrinos into electron neutrinos over a baseline of 810 km. The Near Detector (ND) measures the neutrino beam spectrum and composition before oscillation, which is then compared to the oscillated neutrino energy spectrum observed in the Far Detector (FD). In the ND, the neutrinos are detected through their interactions with the heavy target nuclei within the detector. NOνA employs the GENIE neutrino event generator for simulating these neutrino-nucleus interactions. However, the default GENIE prediction does not adequately reproduce the ND data. To address this, NOνA developed a tune of the neutrino interaction models within GENIE version 3:0:6 to minimize discrepancies between the simulated predictions and the observed data in the ND. This dissertation tests the NOνA’s 2023 tune of the GENIE neutrino cross-section simulations by performing a data/simulations comparison for the ND. The analysis employed datasets comprising $2.55\times10^{21}$ protons-on-target (POT) in neutrino beam mode and $1.14\times10^{21}$ POT in antineutrino beam mode. The NOνA tuning of neutrino-matter interaction simulations matches with ND data within the $1\sigma$ error band, overestimating muon neutrino and antineutrino charged current interactions by approximately 6 % and 9 %, respectively. Discrepancies were observed in the energy region dominated by Quasi-Elastic-like interactions. Systematic uncertainties associated with the modeling of the neutrino cross-section, particularly those pertaining Quasi-Elastic like interactions, contributed considerably to the overall error in the simulations. Furthermore, the reconstruction algorithm used in NOνA for particle classification demonstrated significant misidentifications between charged pions and protons, as well as a tendency to overlook additional pions or protons in multi-particle simulated events.

Cortés Parra, Camilo Andrés↗
DOE OSTI2015

Elucidation of Peptide-Directed Palladium Surface Structure for Biologically Tunable Nanocatalysts

Peptide-enabled synthesis of inorganic nanostructures represents an avenue to access catalytic materials with tunable and optimized properties. This is achieved via peptide complexity and programmability that is missing in traditional ligands for catalytic nanomaterials. Unfortunately, there is limited information available to correlate peptide sequence to particle structure and catalytic activity to date. As such, the application of peptide-enabled nanocatalysts remains limited to trial and error approaches. In this paper, a hybrid experimental and computational approach is introduced to systematically elucidate biomolecule-dependent structure/function relationships for peptide-capped Pd nanocatalysts. Synchrotron X-ray techniques were used to uncover substantial particle surface structural disorder, which was dependent upon the amino acid sequence of the peptide capping ligand. Nanocatalyst configurations were then determined directly from experimental data using reverse Monte Carlo methods and further refined using molecular dynamics simulation, obtaining thermodynamically stable peptide-Pd nanoparticle configurations. Sequence-dependent catalytic property differences for C-C coupling and olefin hydrogenation were then eluddated by identification of the catalytic active sites at the atomic level and quantitative prediction of relative reaction rates. This hybrid methodology provides a clear route to determine peptide-dependent structure/function relationships, enabling the generation of guidelines for catalyst design through rational tailoring of peptide sequences

atomic pair distribution function↗
DOE OSTI2013

A TWO-YEAR TIME DELAY FOR THE LENSED QUASAR SDSS J1029+2623

We present 279 epochs of optical monitoring data spanning 5.4 years from 2007 January to 2012 June for the largest image separation (22.''6) gravitationally lensed quasar, SDSS J1029+2623. We find that image A leads the images B and C by {Delta} t {sub AB} = (744 {+-} 10) days (90% confidence); the uncertainty includes both statistical uncertainties and systematic differences due to the choice of models. With only a {approx}1% fractional error, the interpretation of the delay is limited primarily by cosmic variance due to fluctuations in the mean line-of-sight density. We cannot separate the fainter image C from image B, but since image C trails image B by only 2-3 days in all models, the estimate of the time delay between images A and B is little affected by combining the fluxes of images B and C. There is weak evidence for a low level of microlensing, perhaps created by the small galaxy responsible for the flux ratio anomaly in this system. Interpreting the delay depends on better constraining the shape of the gravitational potential using the lensed host galaxy, other lensed arcs, and the structure of the X-ray emission.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Local position-space two-nucleon potentials from leading to fourth order of chiral effective field theory

We present local, position-space chiral NN potentials through four orders of chiral effective field theory ranging from leading order (LO) to next-to-next-to-next-to-leading order (N 3 LO, fourth order) of the Δ-less version of the theory. The long-range parts of these potentials are fixed by the very accurate πN LECs as determined in the Roy-Steiner equations analysis. At the highest order (N 3 LO), the NN data below 190 MeV laboratory energy are reproduced with the respectable χ 2 /datum of 1.45. A comparison of the N 3 LO potential with the phenomenological Argonne v 18 (AV18) potential reveals substantial agreement between the two potentials in the intermediate range ruled by chiral symmetry, thus, providing a chiral underpinning for the phenomenological AV18 potential. Our chiral NN potentials may serve as a solid basis for systematic ab initio calculations of nuclear structure and reactions that allow for a comprehensive error analysis. In particular, the order by order development of the potentials will make possible a reliable determination of the truncation error at each order. Our new family of local position-space potentials differs from existing potentials of this kind by a weaker tensor force as reflected in relatively low D-state probabilities of the deuteron (P D ≲ 4.0 % for our N 3 LO potentials) and predictions for the triton binding energy above 8.00 MeV (from two-body forces alone). As a consequence, our potentials may lead to different predictions when applied to light and intermediate-mass nuclei in ab initio calculations and, potentially, help solve some of the outstanding problems in microscopic nuclear structure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Evaluating transition metal oxides within DFT-SCAN and SCAN + U frameworks for solar thermochemical applications

Using the strongly constrained and appropriately normed (SCAN) and SCAN+U approximations for describing electron exchange-correlation (XC) within density functional theory, we investigate the oxidation energetics, lattice constants, and electronic structure of binary Ce-, Mn-, and Fe-oxides, which are crucial ingredients for generating renewable fuels using two-step, oxide-based, solar thermochemical reactors. Unlike other common XC functionals, we find that SCAN does not over-bind the O 2 molecule, based on direct calculations of its bond energy and robust agreement between calculated formation enthalpies of main group oxides versus experiments. However, in the case of transition-metal oxides (TMOs), SCAN systematically overestimates (i.e., yields too negative) oxidation enthalpies due to remaining self-interaction errors in the description of their ground-state electronic structure. Adding a Hubbard U term to the transition-metal centers, where the magnitude of U is determined from experimental oxidation enthalpies, significantly improves the qualitative agreement and marginally improves the quantitative agreement of SCAN+U-calculated electronic structure and lattice parameters, respectively, with experiments. Importantly, SCAN predicts the wrong ground-state structure for a few oxides, namely, Ce 2 O 3 , Mn 2 O 3 , and Fe 3 O 4 , while SCAN+U predicts the right polymorph for all systems considered in this work. Furthermore, the SCAN+U framework, with an appropriately determined U, will be required to accurately describe ground-state properties and yield qualitatively consistent electronic properties for most transition-metal and rare earth oxides.

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

Constraints on neutrino physics from DESI DR2 BAO and DR1 full shape

The Dark Energy Spectroscopic Instrument (DESI) Collaboration has obtained robust measurements of baryon acoustic oscillations in the redshift range 0.1 < 𝑧 < 4.2, based on the Lyman-𝛼 forest and galaxies from data release 2. We combine these measurements with cosmic microwave background (CMB) data from Planck and the Atacama Cosmology Telescope to place our tightest constraints yet on the sum of neutrino masses. Assuming the cosmological Λ⁢ CDM model and three degenerate neutrino states, we find ∑𝑚 𝜈 < 0.0642 eV (95%) with a marginalized error of 𝜎⁡(∑𝑚 𝜈 ) = 0.020 eV. We also constrain the effective number of neutrino species, finding 𝑁 eff = 3.2⁢3$^{+0.35}_{−0.34}$ (95%), in line with the Standard Model prediction. When accounting for neutrino oscillation constraints, we find a preference for the normal mass ordering and an upper limit on the lightest neutrino mass of 𝑚 𝑙 < 0.023 eV (95%). However, we determine using frequentist and Bayesian methods that our constraints are in tension with the lower limits derived from neutrino oscillations. Correcting for the physical boundary at zero mass, we report a 95% Feldman-Cousins upper limit of ∑𝑚 𝜈 < 0.053 eV, breaching the lower limit from neutrino oscillations. Considering a more general Bayesian analysis with an effective cosmological neutrino mass parameter, ∑𝑚 𝜈,eff , that allows for negative energy densities and removes unsatisfactory prior weight effects, we derive constraints that are in 3⁢𝜎 tension with the same oscillation limit, while the error rises to 𝜎⁡(∑𝑚 𝜈,eff ) = 0.053 eV. In the absence of unknown systematics, this finding could be interpreted as a hint of new physics not necessarily related to neutrinos. The preference of DESI and CMB data for an evolving dark energy model offers one possible solution. In the 𝑤 0 ⁢𝑤 𝑎 ⁢CDM model, we find ∑𝑚 𝜈 < 0.163 eV (95%), relaxing the neutrino tension. These constraints all rely on the effects of neutrinos on the cosmic expansion history. Using full-shape power spectrum measurements of data release 1 galaxies, we place complementary constraints that rely on neutrino free streaming. Our strongest such limit in Λ ⁢CDM, using selected CMB priors, is ∑𝑚 𝜈 < 0.193 eV (95%).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Cross-correlation of CMB Polarization Lensing with High-$z$ Submillimeter $Herschel$-ATLAS Galaxies

Herein we report a 4.8σ measurement of the cross-correlation signal between the cosmic microwave background (CMB) lensing convergence reconstructed from measurements of the CMB polarization made by the P OLARBEAR experiment and the infrared-selected galaxies of the $Herschel$-ATLAS survey. This is the first measurement of its kind. We infer a best-fit galaxy bias of $b$ = 5.76 ± 1.25, corresponding to a host halo mass of log 10 (M h /M ⊙ ). =13.5$^{+0.2}_{-0.3}$ at an effective redshift of $z$ ~ 2 from the cross-correlation power spectrum. Residual uncertainties in the redshift distribution of the submillimeter galaxies are subdominant with respect to the statistical precision. We perform a suite of systematic tests, finding that instrumental and astrophysical contaminations are small compared to the statistical error. This cross-correlation measurement only relies on CMB polarization information that, differently from CMB temperature maps, is less contaminated by galactic and extragalactic foregrounds, providing a clearer view of the projected matter distribution. This result demonstrates the feasibility and robustness of this approach for future high-sensitivity CMB polarization experiments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Planck 2013 results. VII. HFI time response and beams

This paper characterizes the effective beams, the effective beam window functions and the associated errors for the Planck High Frequency Instrument (HFI) detectors. The effective beam is the angular response including the effect of the optics, detectors, data processing and the scan strategy. The window function is the representation of this beam in the harmonic domain which is required to recover an unbiased measurement of the cosmic microwave background angular power spectrum. The HFI is a scanning instrument and its effective beams are the convolution of: a) the optical response of the telescope and feeds; b) the processing of the time-ordered data and deconvolution of the bolometric and electronic transfer function; and c) the merging of several surveys to produce maps. The time response transfer functions are measured using observations of Jupiter and Saturn and by minimizing survey difference residuals. The scanning beam is the post-deconvolution angular response of the instrument, and is characterized with observations of Mars. The main beam solid angles are determined to better than 0.5% at each HFI frequency band. Observations of Jupiter and Saturn limit near sidelobes (within 5°) to about 0.1% of the total solid angle. Time response residuals remain as long tails in the scanning beams, but contribute less than 0.1% of the total solid angle. The bias and uncertainty in the beam products are estimated using ensembles of simulated planet observations that include the impact of instrumental noise and known systematic effects. Here, the correlation structure of these ensembles is well-described by five error eigenmodes that are sub-dominant to sample variance and instrumental noise in the harmonic domain. A suite of consistency tests provide confidence that the error model represents a sufficient description of the data. The total error in the effective beam window functions is below 1% at 100 GHz up to multipole &ell; ~ 1500, and below 0.5% at 143 and 217 GHz up to &ell; ~ 2000.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control

Herein, we present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional sub-spaces whose basis functions are realizations of a sequence of neural networks. Here, the finite-dimensional subspaces are then used to define a standard Galerkin approximation of the variational equation. This approach enjoys a number of advantages, including: the sequential nature of the algorithm offers a systematic approach to enhancing the accuracy of a given approximation; the sequential enhancements provide a useful indicator for the error that can be used as a criterion for terminating the sequential updates; the basic approach is largely oblivious to the nature of the partial differential equation under consideration; and, some basic theoretical results are presented regarding the convergence (or otherwise) of the method which are used to formulate basic guidelines for applying the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

A posteriori error analysis for a cut cell finite volume method

We study the solution of a diffusive process in a domain where the diffusion coefficient changes discontinuously across a curved interface. We consider discretizations that use regularly-shaped meshes, so that the interface “cuts” through the cells (elements or volumes) without respecting the regular geometry of the mesh. Consequently, the discontinuity in the diffusion coefficients has a strong impact on the accuracy and convergence of the numerical method. This motivates the derivation of computational error estimates that yield accurate estimates for specified quantities of interest. For this purpose, we adapt the well-known adjoint based a posteriori error analysis technique used for finite element methods. In order to employ this method, we describe a systematic approach to discretizing a cut-cell problem that handles complex geometry in the interface in a natural fashion yet reduces to the well-known Ghost Fluid Method in simple cases. We test the accuracy of the estimates in a series of examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Sloan Digital Sky Survey III photometric quasar clustering: Probing the initial conditions of the Universe

Here, the Sloan Digital Sky Survey has surveyed 14,555 square degrees of the sky, and delivered over a trillion pixels of imaging data. We present the large-scale clustering of 1.6 million quasars between z=0.5 and z=2.5 that have been classified from this imaging, representing the highest density of quasars ever studied for clustering measurements. This data set spans 0~ 11,00 square degrees and probes a volume of 80 h –3 Gpc 3 . In principle, such a large volume and medium density of tracers should facilitate high-precision cosmological constraints. We measure the angular clustering of photometrically classified quasars using an optimal quadratic estimator in four redshift slices with an accuracy of ~ 25% over a bin width of δ l ~ 10–15 on scales corresponding to matter-radiation equality and larger (0ℓ ~ 2–3).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

BAO from angular clustering: optimization and mitigation of theoretical systematics

Here, we study the methodology and potential theoretical systematics of measuring Baryon Acoustic Oscillations (BAO) using the angular correlation functions in tomographic bins. We calibrate and optimize the pipeline for the Dark Energy Survey Year 1 dataset using 1800 mocks. We compare the BAO fitting results obtained with three estimators: the Maximum Likelihood Estimator (MLE), Profile Likelihood, and Markov Chain Monte Carlo. The fit results from the MLE are the least biased and their derived 1-$\sigma$ error bar are closest to the Gaussian distribution value after removing the extreme mocks with non-detected BAO signal. We show that incorrect assumptions in constructing the template, such as mismatches from the cosmology of the mocks or the underlying photo-$z$ errors, can lead to BAO angular shifts. We find that MLE is the method that best traces this systematic biases, allowing to recover the true angular distance values. In a real survey analysis, it may happen that the final data sample properties are slightly different from those of the mock catalog. We show that the effect on the mock covariance due to the sample differences can be corrected with the help of the Gaussian covariance matrix or more effectively using the eigenmode expansion of the mock covariance. In the eigenmode expansion, the eigenmodes are provided by some proxy covariance matrix. The eigenmode expansion is significantly less susceptible to statistical fluctuations relative to the direct measurements of the covariance matrix because of the number of free parameters is substantially reduced

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Development of the Delphi display concept for alternative explanations decision making support - 120

Human operators of advanced technology systems, such as nuclear power, command and control, and deepwater oil drilling, must be able to evaluate and respond to a wide array of operational anomalies. Unfortunately, these circumstances are often complex and ambiguous, complicating decision making tasks. One common decision making error, called confirmation bias, occurs when decision makers prematurely focus on one explanation instead of systematically considering all plausible alternative explanations that could equally well account for an operational anomaly (Nickerson, 1998). The Delphi display is designed to counteract decision makers' tendencies towards confirmation bias and to encourage them to consider all plausible explanations, including high risk explanations, they might otherwise overlook. An initial Delphi display prototype was designed to help identify the underlying cause of operational anomalies in the complex, high-consequence technology of deepwater drilling. This prototype decision aid incorporates major indicators related to operational anomalies and presents corresponding plausible explanations for each indicator, ranging from high-risk system-critical explanations to lower-risk but still significant events. The Delphi display incorporates several innovative features to help decision makers detect and monitor operational anomalies and view the relationships among indicators and their associated plausible explanations. Preliminary evaluations of an early prototype Delphi display for detecting kicks in deepwater oil drilling operations have been promising. Moreover, the methodology used to design and develop the Delphi display can be readily generalized to numerous other operational contexts that require humans to make system-critical decisions. To illustrate, an initial Delphi display design for nuclear power plant control is described. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2012

Impact of electron density on the fixed-node errors in Quantum Monte Carlo of atomic systems

We analyze the effect of increasing charge density on the fixed-node errors in diffusion Monte Carlo (FNDMC). We compare FNDMC ground state energies of 4-electron atomic systems with nuclear charge using Hartree–Fock and restricted Configuration Interaction trial wave functions. We perform these calculations for several different values of the nuclear charge, and we analyze the systematic trends of the recovered correlation energies as a function of . For this testing system we demonstrate that the fixed-node error of the Hartree–Fock trial wave functions increases linearly with increasing the nuclear charge.

Chemistry↗
DOE OSTI2017

Homogenizing Advanced Alloys: Thermodynamic and Kinetic Simulations Followed by Experimental Results

Segregation of solute elements occurs in nearly all metal alloys during solidification. The resultant elemental partitioning can severely degrade as-cast material properties and lead to difficulties during post-processing (e.g., hot shorts and incipient melting). Many cast articles are subjected to a homogenization heat treatment in order to minimize segregation and improve their performance. Traditionally, homogenization heat treatments are based upon past practice or time-consuming trial and error experiments. Through the use of thermodynamic and kinetic modeling software, NETL has designed a systematic method to optimize homogenization heat treatments. Use of the method allows engineers and researchers to homogenize casting chemistries to levels appropriate for a given application. The method also allows for the adjustment of heat treatment schedules to fit limitations on in-house equipment (capability, reliability, etc.) while maintaining clear numeric targets for segregation reduction. In this approach, the Scheil module within Thermo-Calc is used to predict the as-cast segregation present within an alloy, and then diffusion controlled transformations is used to model homogenization kinetics as a function of time and temperature. Examples of computationally designed heat treatments and verification of their effects on segregation and properties of real castings are presented.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Line confusion in spectroscopic surveys and its possible effects: shifts in Baryon Acoustic Oscillations position

ABSTRACT Roman Space Telescope will survey about 17 million emission-line galaxies over a range of redshifts. Its main targets are Hα emission-line galaxies at low redshifts (z < 2) and [O iii] emission-line galaxies at high redshifts (z > 2). The Roman Space Telescope will estimate the redshift of these galaxies with single-line identification. This suggests that other emission-line galaxies may be misidentified as the main targets. In particular, it is hard to distinguish between the H β and [O iii] lines as the two lines are close in wavelength and hence the photometric information may not be sufficient to separate them reliably. Misidentifying H β emitter as [O iii] emitter will cause a shift in the inferred radial position of the galaxy by approximately 90 Mpc h−1. This length-scale is similar to the Baryon Acoustic Oscillation (BAO) scale and could shift and broaden the BAO peak, possibly introduce errors in determining the BAO peak position. We qualitatively describe the effect of this new systematic and further quantify it with a light-cone simulation with emission-line galaxies. Our results show a systematic shift in the recovered isotropic BAO positions that depends on the percentage of interlopers (percentage of ${\rm H}\,\beta$) in the sample. The systematic shift can be as large as $0.1{-}0.3\,\mathrm{ per}\,\mathrm{ cent} \, {\rm x}\, {{\%}}{\rm H}\,\beta$ for analysis performed at redshifts z = 1.3−1.9.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Data-driven approach to parameterize SCAN + U for an accurate description of 3 d transition metal oxide thermochemistry

Semilocal density-functional theory (DFT) methods exhibit significant errors for the phase diagrams of transition-metal oxides that are caused by an incorrect description of molecular oxygen and the large self-interaction error in materials with strongly localized electronic orbitals. Empirical and semiempirical corrections based on the DFT + U method can reduce these errors, but the parameterization and validation of the correction terms remains an on-going challenge. Here we develop a systematic methodology to determine the parameters and to statistically assess the results by considering interlinked thermochemical data across a set of transition metal compounds. We consider three interconnected levels of correction terms: (1) a constant oxygen binding correction, (2) Hubbard-U correction, and (3) DFT/DFT + U compatibility correction. The parameterization is expressed as a unified optimization problem. We demonstrate this approach for 3d transition metal oxides, considering a target set of binary and ternary oxides. With a total of 37 measured formation enthalpies taken from the literature, the dataset is augmented by the reaction energies of 1710 unique reactions that were derived from the formation energies by systematic enumeration. To ensure a balanced dataset across the available data, the reactions were grouped by their similarity using clustering and suitably weighted. The parameterization is validated using leave-one-out cross validation (CV), a standard technique for the validation of statistical models. We apply the methodology to the strongly constrained and appropriately normed (SCAN) density functional. Based on the CV score, the error of binary (ternary) oxide formation energies is reduced by 40% (75%) to 0.10 (0.03) eV/atom. A simplified correction scheme that does not involve SCAN/SCAN + U compatibility terms still achieves an error reduction of 30% (25%). The method and tools demonstrated here can be applied to other classes of materials or to parameterize the corrections to optimize DFT + U performance for other target physical properties.

36 MATERIALS SCIENCE↗
DOE OSTI2012

THE DISTANCE TO M101 HOSTING TYPE Ia SUPERNOVA 2011fe BASED ON THE TIP OF THE RED GIANT BRANCH

We present a new determination of the distance to M101, host of the Type Ia supernova (SN Ia) 2011fe, based on the tip of the red giant branch (TRGB) method. Our determination is based on Hubble Space Telescope archival F555W and F814W images of nine fields within the galaxy. Color-magnitude diagrams of arm-free regions in all fields show a prominent red giant branch. We measure the I-band magnitudes of the TRGB, obtaining a mean value of I{sub TRGB} = 25.28 {+-} 0.01 (where the error is a standard error), using an edge-detection method. We derive a weighted mean value of distance modulus (m - M){sub 0} = 29.30 {+-} 0.01(random) {+-} 0.12(systematic), corresponding to a linear distance of 7.24 {+-} 0.03 {+-} 0.40 Mpc. While previous estimates for M101 show a large range (TRGB distances of (m - M){sub 0} = 29.05-29.42 and Cepheid distances of (m - M){sub 0} = 29.04-29.71), our measurements of the TRGB distances for nine fields show a small dispersion of only 0.02. We combine our distance estimate and photometry in the literature to derive absolute peak magnitudes in optical and near-infrared bands of SN 2011fe. Absolute maximum magnitudes of SN 2011fe are {approx}0.2 mag brighter in the optical band and much more in the NIR than the current calibrations of SNe Ia in the literature. From the optical maximum magnitudes of SN 2011fe we obtain a value of the Hubble constant, H{sub 0} = 65.0 {+-} 0.5(random) {+-} 5.7(systematic) km s{sup -1} Mpc{sup -1}, slightly smaller than other recent determinations of H{sub 0}.

79 ASTRONOMY AND ASTROPHYSICS↗