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All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Some analytical results for radiative transfer in thick atmospheres

Singular eigenmode expansions are a convenient analytical tool with which to study problems of monochromatic radiative transfer in thick or semi-infinite atmospheres. Some closed-form solutions are presented for anisotropic scattering, with the neglect of polarization effects. A basic ingredient for applications to the semi-infinite medium is Chandrasekhar's H-function, which is best defined through the Wiener-Hopf factorization. The solutions of the Milne and albedo problems are discussed in order that the method of matched asymptotic approximations may be used to describe the solution for a thick atmosphere adjacent to a diffusely reflecting ground. Expressions for the emerging distributions are quoted. A possible extension of the general scheme to problems involving polarization is indicated.

Kuscer, I.↗
NASA NTRS1995

Interpretation of Extinction in Gaussian-Beam Scattering

The extinction efficiency for the interaction of a plane wave with a large nonabsorbing spherical particle is approximately 2.0. When a Gaussian beam of half-width w(sub 0) is incident upon a spherical particle of radius a with w(sub 0)/a less than 1, the extinction efficiency attains unexpectedly high or low values, contrary to intuitive expectations. The reason for this is associated with the so-called compensating term in the scattered field, which cancels the field of the Gaussian beam behind the particle, thereby producing the particle's shadow. I introduce a decomposition of the total exterior field into incoming and outgoing portions that are free of compensating terms. It is then shown that a suitably defined interaction efficiency has the intuitively expected asymptotic values of 2.0 for w(sub 0)/a much greater than 1 and 1.0 for w(sub 0)/a much less than 1.

Lock, James A.↗
DOE OSTI2024

First simultaneous global QCD analysis of dihadron fragmentation functions and transversity parton distribution functions

We perform a comprehensive study within quantum chromodynamics (QCD) of dihadron observables in electron-positron annihilation, semi-inclusive deep-inelastic scattering, and proton-proton collisions, including recent cross section data from Belle and azimuthal asymmetries from STAR. We extract simultaneously for the first time π + π − dihadron fragmentation functions (DiFFs) and the nucleon transversity distributions for up and down quarks as well as antiquarks. For the transversity distributions we impose their small- x asymptotic behavior and the Soffer bound. In addition, we utilize a new definition of DiFFs that has a number density interpretation to then calculate expectation values for the dihadron invariant mass and momentum fraction. Furthermore, we investigate the compatibility of our transversity results with those from single-hadron fragmentation (from a transverse momentum dependent/collinear twist-3 framework) and the nucleon tensor charges computed in lattice QCD. We find a universal nature to all of this available information. Future measurements of dihadron production can significantly further this research, especially, as we show, those that are sensitive to the region of large parton momentum fractions. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Determination of asymptotic normalization coefficients for the channel 16 O→ α+ 12 C: excited state 16 O(0 + ; 6.05 MeV)

Asymptotic normalization coefficients (ANC) determine the overall normalization of cross sections of peripheral radiative capture reactions. In the present paper, we treat the ANC C for the virtual decay 16 O(0 + ; 6.05 MeV)→ α+ 12 C(g.s.), the known values of which are characterized by a large spread (0.29 - 1.65) × 10 3 fm -1/2 . The ANC C is found by analytic continuation in energy of the α 12 C s-wave scattering amplitude, known from the phase-shift analysis of experimental data, to the pole corresponding to the 16O bound state and lying in the unphysical region of negative energies. To determine C, two different methods of analytic continuation are used. In the first method, the scattering data are approximated by the sum of polynomials in energy in the physical region and then extrapolated to the pole. The best way of extrapolation is chosen on the basis of the exactly solvable model. Within the second approach, the ANC C is found by solving the Schrödinger equation for the two-body α 12 C potential, the parameters of which are selected from the requirement of the best description of the phase-shift analysis data at a fixed experimental binding energy of 16 O(0 + ; 6.05 MeV) in the α+ 12 C channel. The values of the ANC C obtained within these two methods lie in the interval (886–1139) fm -1/2 .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Celestial IR divergences and the effective action of supertranslation modes

Infrared divergences in perturbative gravitational scattering amplitudes have been recently argued to be governed by the two-point function of the supertranslation Goldstone mode on the celestial sphere. We show that the form of this celestial two-point function simply derives from an effective action that also controls infrared divergences in the symplectic structure of General Relativity with asymptotically flat boundary conditions. This effective action finds its natural place in a path integral formulation of a celestial conformal field theory, as we illustrate by re-deriving the infrared soft factors in terms of celestial correlators. Our analysis relies on a well-posed action principle close to spatial infinity introduced by Compère and Dehouck.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2018

Implementation of J-A Methodology Elastic-Plastic Crack Instability Analysis Capability into the WARP-3D Code

Characterization of the near crack-tip stress/strain fields is the foundation of fracture mechanics. The description of the near tip stress field and the prediction of when fracture occurs is well established for brittle materials that exhibit linear elastic behavior. However, in ductile materials or conditions that violate linear elastic assumptions (Aluminum alloys, Al 2024-T3, Al 2024- T351 etc.), the elastic-plastic crack-tip stress fields are characterized by the Hutchison-Rice-Rosengren (HRR) field. The J-integral is commonly used to characterize amplitude of the HRR field under elastic-plastic conditions. The J-integral has been demonstrated for crack-tip fields that are under high constraint conditions (i.e., small-scale plasticity where the J-dominance is maintained). However, as the external load increases, yielding changes from small- to largescale plasticity and usually a loss of constraint (i.e., reduction in the triaxial stress field along the crack front). The loss of constraint leads to the deviation of the crack-tip stress fields from that given by the HRR field. Hence, the J-dominance will be gradually lost and additional parameter(s) are required to quantify the crack-tip stress fields and predict fracture behavior. The assessment objectives were to: 1) implement a two-parameter (i.e., J-A) fracture criterion into an elastic-plastic three-dimensional (3D) finite element analysis (FEA), 2) validate the implementation by comparison with the A parameter from literature data, 3) conduct material characterization tests to quantify the material behavior and provide fracture data for validation of the J-A fracture criteria, and (4) perform evaluations to establish if the J-A criteria can be used to predict fracture in a ductile metallic material (e.g., aluminum alloys). The A parameter in these criteria is the second parameter in a three-term elastic-plastic asymptotic expansion of the neartip stress behavior. A series of extensive FEAs were performed using WARP3D software package to obtain solutions for the A parameter for different specimen configurations. The methodology needed for the estimation of the A parameter in the asymptotic expansion was developed and implemented using Matlab®. A user material (UMAT) routine was used to model the material stress-strain response using a Ramberg-Osgood power law with a hardening exponent (n) and a material coefficient (alpha). This UMAT routine was successfully implemented in WARP3D software and validated through comparison with the experimental data. Three configurations were extracted from published results: 1) center cracked plate (CCP), 2) single edge-cracked plate (SECP), and 3) double edge-cracked plate (DECP). These configurations and four other configurations (three-hole tension (THT)), three-point bend (3PTB), three-hole compact tension (3PCT), and compact tension (CT)) were analyzed to verify the methodology that was developed and implemented into WARP3D. Solutions of the A parameter were obtained for remote tension loading conditions that started with small-scale yielding and continued into the large-scale plasticity regime. The results indicate that the methodology developed can be used to calculate the elastic-plastic J-A parameters for test specimens with a range of crack geometries, material strain hardening behaviors, and loading conditions. The J-A parameters were implemented as fracture criteria and used to predict the test results. For comparison, other fracture criteria were used to predict the same test results. Major findings include: The A constraint parameter A varies with specimen type and applied load thus accurate determination is crucial in predicting the failure load, and the A parameter is asymptotic as the failure load is approached, making an accurate determination difficult (i.e., small differences in the A parameter can cause large variations in failure load) for materials exhibiting elastic-plastic behavior. The failure predictions from J-A methodology were more accurate than the traditionally used KC and J methods, and have comparable scatter to that observed when using the crack-tip opening angle (CTOA) method. However, the J-A methodology requires considerable effort (expertise level and labor) to implement and to evaluate the A parameter for different specimen types and materials, or to apply this methodology to part-through crack (e.g., 3D problems) structural applications.

Hamm, Kenneth R., Jr.↗
NASA NTRS1991

High frequency scattering by a smooth coated cylinder simulated with generalized impedance boundary conditions

Rigorous uniform geometrical theory of diffraction (UGTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock-type integrals, characteristic to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. As usual, the diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.

Syed, Hasnain H.↗
NASA NTRS1998

Re-examination of a Classic Experiment to Measure the Positronium-Helium Cross Section

In 1975, before the advent of positronium beams, a clever experiment was carried out in an attempt to measure low-energy Ps-atom scattering cross-sections, especially that of Ps-He. A series of parallel thin plates was placed in the vessel containing the sample of gas, and positrons were allowed to enter the chamber from a radioactive source. The time spectrum of annihilation radiation was observed in the traditional way, and the pickoff annihilation due to thermalized Ps striking one of the plates was to be the special feature of the experiment. Using a diffusion analysis the authors derived cross- sections for several gases, and for helium the value obtained was sigma = 0.0166 pi(alpha)(sub o, sup 2). Even then this value was thought to be very much too small, while recent measurements and some calculations suggest a more reasonable value would be sigma = 3 to 13 pi(alpha)(sub o,sup 2). It has always been puzzling that an apparently well-designed experiment should give such an unsatisfactory result. We have now re-examined the analysis of the data with some interesting consequences which may explain the discrepancy. Two main observations support our re-analysis. First, we note that the mean free path for Ps-He scattering would be quite long if the cross-section were as small as that quoted above; the diffusion method itself would seem to be questionable. For the larger values, however, there would be no such problem. Second, it was assumed that when the annihilation rate had settled down and was following an exponential decay curve the asymptotic solution of the diffusion equation had been reached. We find, instead, that a superposition of exponentials can accurately represent the decay curve, consistent with the higher cross-section value.

Drachman, Richard J.↗
DOE OSTI2022

Size-Dependent Adsorption and Adhesion Energetics of Ag Nanoparticles on Graphene Films on Ni(111) by Calorimetry

Interest in the use of carbon supports for late transition metal nanoparticle catalysts has expanded rapidly due to the increasing importance of electrocatalysts for clean energy and environmental technologies and the use and storage of renewable electricity. Compared to oxide supports, almost nothing is known about the effect of metal nanoparticle size on the energies of the metal atoms within carbon-supported nanoparticles, yet these energies are crucial for understanding their surface reactivity and sintering kinetics. Here, the growth morphology and adsorption energetics of vapor-deposited Ag onto clean graphene/Ni(111) surfaces have been studied using a combination of single-crystal adsorption calorimetry (SCAC) and He + low-energy ion scattering (LEIS). The differential heat of Ag adsorption is 207 kJ/mol for making ~30 atom Ag particles on graphene terraces at 100 K and 16 kJ/mol higher for making ~9 atom Ag clusters at defect sites at the same temperature. The heat of adsorption increases rapidly with Ag coverage as 3D Ag nanoparticles nucleate and grow in size, asymptotically reaching within 5 kJ/mol of the bulk Ag sublimation enthalpy (285 kJ/mol) by 2 ML. The heats of adsorption and Ag nanoparticle densities from LEIS (~10 16 /m 2 ) were combined to provide the Ag/graphene adhesion energy (E adh = 1.8 J/m 2 in the large-particle limit) and the Ag chemical potential (μ) versus effective particle diameter (D). The Ag chemical potential was well-fitted by μ(D) = (3γ v /M – E adh )(1 + (1.5 nm)/D)(2V m /D), where γ v /M is the surface energy of bulk Ag and V m is its molar volume. The same equation is known to fit similar data for late transition metals on clean surfaces of metal oxide single crystals. The adhesion energy of Ag measured here on graphene falls within the wide range measured for Ag on those oxide surfaces and is almost as large as on the oxide that binds Ag particles most strongly, namely CeO 2 (111), which is well-known to be very effective at resisting catalyst deactivation by metal sintering. Furthermore, these results imply that carbon supports will be effective at resisting sintering and that Ag particles smaller than 6 nm on graphene will bind small adsorbed reaction intermediates more weakly than supports with weaker adhesion to Ag, like MgO(100).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Direct observation of the momentum distribution and renormalization factor in lithium

We have measured the momentum distribution and renormalization factor $Z_{k_F}$ in liquid and solid lithium by high-resolution Compton scattering. High-resolution data over a wide momentum range exhibit a clear feature of the renormalization and a sharp drop of momentum densities at the Fermi momentum $k_F$. In this work, these results are compared with those computed by quantum Monte Carlo simulation performed both on a disordered crystal and a liquid exhibiting very good agreement. Asymptotic behavior of the experimental and theoretical momentum distributions are examined to estimate $Z_{k_F}$. The experimentally obtained $Z_{k_F} = 0.43^{+0.11}_{–0.01}$ for liquid Li and $0.54^{+0.11}_{–0.02}$ for solid Li are in good agreement with theoretical results of 0.54 ± 0.01 and 0.64 ± 0.01, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Lorentz symmetry and IR structure of the BFSS matrix model

The BFSS matrix model relates flat space M-theory to a large N limit of matrix quantum mechanics describing N non-relativistic D0-branes. M-theory, being a theory of gravity in flat space, has a rich infrared structure that includes various soft theorems and an infinite set of conserved charges associated to asymptotic symmetries. In this work, we ask: to what extent is this infrared structure present in BFSS? We find that all the salient features concerning the infrared structure of M-theory carry over naturally to the quantum mechanics dual. Moreover, we demonstrate that the dual statement of the soft graviton theorem in the matrix model implies that D0-brane scattering amplitudes in BFSS enjoy the full 11d Lorentz symmetry of M-theory, a claim which has been long anticipated. We also offer several first-principle consistency checks for our findings, including a computation of the soft theorem which does not presuppose the BFSS duality and a non-trivial match between several known symmetries of M-theory and BFSS that appear naturally in this formalism. These calculations give non-perturbative evidence in support of the BFSS duality as a model of flat space holography.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

The hyperplane of early-type galaxies: using stellar population properties to increase the precision and accuracy of the fundamental plane as a distance indicator

ABSTRACT We use deep spectroscopy from the SAMI (Sydney-AAO Multi-object Integral) Galaxy Survey to explore the precision of the fundamental plane (FP) of early-type galaxies as a distance indicator for future single-fibre spectroscopy surveys. We study the optimal trade-off between sample size and signal-to-noise ratio (SNR), and investigate which additional observables can be used to construct hyperplanes with smaller intrinsic scatter than the FP. We add increasing levels of random noise (parametrized as effective exposure time) to the SAMI spectra to study the effect of increasing measurement uncertainties on the FP- and hyperplane-inferred distances. We find that, using direct-fit methods, the values of the FP and hyperplane best-fitting coefficients depend on the spectral SNR, and reach asymptotic values for a mean $\langle \mathrm{ SNR} \rangle =40\, \mathrm{\mathring{\rm A}}^{-1}$. As additional variables for the FP we consider three stellar-population observables: light-weighted age, stellar mass-to-light ratio, and a novel combination of Lick indices ($I_\mathrm{age}$). For an $\langle \mathrm{ SNR} \rangle =45~\mathrm{\mathring{\rm A}}^{-1}$ (equivalent to 1-h exposure on a 4-m telescope), all three hyperplanes outperform the FP as distance indicators. Being an empirical spectral index, $I_\mathrm{age}$ avoids the model-dependent uncertainties and bias underlying age and mass-to-light ratio measurements, yet yields a 10 per cent reduction of the median distance uncertainty compared to the FP. We also find that, as a by-product, the $I_\mathrm{age}$ hyperplane removes most of the reported environment bias of the FP. After accounting for the different SNR, these conclusions also apply to a 50 times larger sample from SDSS-III (Sloan Digital Sky Survey). However, in this case, only $\mathrm{ age}$ removes the environment bias.

D’Eugenio, Francesco (ORCID:0000000323888172)↗
NASA NTRS1985

Effect of Scattering on Instabilities in Line-driven Stellar Winds

Line driven O-B stellar winds are unstable to perturbations of short spatial wavelength and the growth rates for such instabilities are very rapid. The nature of the nonlinear development of this instability is unknown, but might possibly be one of blobs of gas driven through ambient gas or a quasiregular train of outward moving shocks. In either case the resulting dissipation of mechanical energy might explain the observed anomalous heating n O-B stars as evidenced by their X-ray emission and high ionization state. It also might explain the observed fine structure of the absorption lines and their time variability. The driving due to the absorption of the stellar continuum flux was considered and the effects of the diffuse, scattered radiation field were neglected. It was shown that under certain special conditions the effect of scattering could reduce the instability growth rate to zero. A stability analysis that includes scattering, but that uses the more physically realistic assumption of complete redistribution instead of coherent scattering, and that includes the effects of transverse velocity gradients, which become important as the flow moves away from the stellar surface is presented. It is found that the instability is eliminated right at the base of the wind, but that as the flow moves outward the instability rate rapidly becomes equal to a substantial fraction of the calculated value, the fraction asymptotically reaching 80% at large radii. Since this still implies many e folds in a characteristic outflow time, the primary conclusion that these winds are highly unstable is unchanged.

Owocki, S. P.↗
NASA NTRS2000

Radiative Properties of Cirrus Clouds in the Infrared (8-13 microns) Spectral Region

Atmospheric radiation in the infrared (IR) 8-13 microns spectral region contains a wealth of information that is very useful for the retrieval of ice cloud properties from aircraft or space-borne measurements. To provide the scattering and absorption properties of nonspherical ice crystals that are fundamental to the IR retrieval implementation, we use the finite-difference time domain (FDTD) method to solve for the extinction efficiency, single-scattering albedo, and the asymmetry parameter of the phase function for ice crystals smaller than 40 microns. For particles larger than this size, the improved geometric optics method (IGOM) can be employed to calculate the asymmetry parameter with an acceptable accuracy, provided that we properly account for the inhomogeneity of the refracted wave due to strong absorption inside the ice particle. A combination of the results computed from the two methods provides the asymmetry parameter for the entire practical range of particle sizes between 1 micron and 10000 microns over wavelengths ranging from 8 microns to 13 microns. For the extinction and absorption efficiency calculations, several methods including the IGOM, Mie solution for equivalent spheres (MSFES), and the anomalous diffraction theory (ADT) can lead to a substantial discontinuity in comparison with the FDTD solutions for particle sizes on the order of 40 microns. To overcome this difficulty, we have developed a novel approach called the stretched scattering potential method (SSPM). For the IR 8-13 microns spectral region, we show that SSPM is a more accurate approximation than ADT, MSFES, and IGOM. The SSPM solution can be further refined numerically. Through a combination of the FDTD and SSPM, we have computed the extinction and absorption efficiency for hexagonal ice crystals with sizes ranging from 1 to 10000 microns at 12 wavelengths between 8 and 13 microns Calculations of the cirrus bulk scattering and absorption properties are performed for 30 size distributions obtained from various field campaigns for midlatitude and tropical cirrus cloud systems. Parameterization of these bulk scattering properties is carried out by using second-order polynomial functions for the extinction efficiency and the single-scattering albedo and the power law expression for the asymmetry parameter. We note that the volume-normalized extinction coefficient can be separated into two parts: one is inversely proportional to effective size and is independent of wavelength, and the other is the wavelength-dependent effective extinction efficiency. Unlike conventional parameterization efforts, the present parameterization scheme is more accurate because only the latter part of the volume-normalized extinction coefficient is approximated in terms of an analytical expression. After averaging over size distribution, the single-scattering albedo is shown to decrease with an increase in effective size for wavelengths shorter than 10.0 microns whereas the opposite behavior is observed for longer wavelengths. The variation of the asymmetry parameter as a function of effective size is substantial when the effective size is smaller than 50 microns. For effective sizes larger than 100 microns, the asymmetry parameter approaches its asymptotic value. The results derived in this study can be useful to remote sensing applications involving IR window bands under cirrus cloud conditions.

Yang, Ping↗
DOE OSTI2025

Quantum magic and computational complexity in the neutrino sector

We consider the quantum magic in systems of dense neutrinos undergoing coherent flavor transformations, relevant for supernova and neutron-star binary mergers. Mapping the three-flavor-neutrino system to qutrits, the evolution of quantum magic is explored in the single scattering angle limit for a selection of initial tensor-product pure states for 𝑁 𝜈 ≤ 8 neutrinos. For |𝜈𝑒⟩ ⊗𝑁𝜈 initial states, the magic, as measured by the 𝛼 = 2 stabilizer Renyi entropy ℳ 2 , is found to decrease with radial distance from the neutrino sphere, reaching a value that lies below the maximum for tensor-product qutrit states. Further, the asymptotic magic per neutrino, ℳ 2 /𝑁 𝜈 , decreases with increasing 𝑁 𝜈 . In contrast, the magic evolving from states containing all three flavors reaches values only possible with entanglement, with the asymptotic ℳ 2 /𝑁 𝜈 increasing with 𝑁 𝜈 . These results highlight the connection between the complexity in simulating quantum physical systems and the parameters of the Standard Model.

computational complexity↗
DOE OSTI2026

A Proof of the Asymptotic Variance of Path Length Estimators for Single-Collision Monte Carlo Source Iteration in the Thick Diffusion Limit

Here, we prove a theorem relating the variance of path length estimators for single-collision Monte Carlo source iteration to a parameter that becomes infinitesimally small in an important physical regime arising in radiative transfer. In our usage, “single-collision Monte Carlo source iteration” refers to Monte Carlo Boltzmann transport methods in which each Monte Carlo particle history includes no more than a single collision, and the physics of multiple scattering is modeled by lagging the scattering source term and iterating until this term converges. Our theorem can be used to construct variance reduction techniques which improve the order of the estimator variance. This enables calculations that would otherwise require impractically large sample sizes to achieve practical estimator uncertainties. We believe this is the first postulation of a theorem relating estimator variance to a limiting case parameter for single-collision Monte Carlo source iteration, and the first proof of such a theorem. We illustrate the theorem’s value with an example in which the authors of a transport method used the theorem to design a variance reduction technique that improved the uncertainty of their solution by a factor of about 500 for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material.

Mathematics and Computing↗
DOE OSTI2020

Energetics and Structure of Nickel Atoms and Nanoparticles on MgO(100)

The growth morphology and interfacial energetics of vapor deposited Ni on the MgO(100) surface at 300 and 100 K have been studied using single crystal adsorption calorimetry (SCAC), He + low-energy ion scattering spectroscopy (LEIS), X-ray photoelectron spectroscopy (XPS), and low-energy electron diffraction (LEED). At 300 K, the Ni atoms grow as three-dimensional nanoparticles with a saturation number density of 5 × 10 16 particles/m 2 . The differential heat of adsorption at 300 K increases rapidly with coverage, from 276 (initially) to 311 kJ/mol by 0.4 ML. Thereafter, it slowly increases asymptotically to the sublimation enthalpy of bulk Ni (430 kJ/ml) by 9 ML. The Ni 2p 3/2 XPS peak binding energy at 300 K is initially (i.e., at 0.16 ML) 1.4 eV higher than that for bulk Ni(solid), but it decreases to that value at high coverage. The Ni atoms form a metastable phase at 300 K when in nanoparticles with diameter <2.5 nm, and the adhesion energy of such Ni nanoparticles to MgO(100) was found to be 3.05 J/m 2 . At 100 K, the Ni atoms form single adatoms and then 0.17 nm thick 2D islands at low coverage with fewer Ni-Ni bonds compared to the Ni nanoparticles formed at 300 K. Thus, the initial heat (i.e., for the first ~0.03 ML) is 148 kJ/mol at 100 K, 128 kJ/mol lower than at 300 K, and remains lower for the 2D islands. With increasing coverage at 100 K, the tiny 2D Ni islands grow in size to cover nearly the entire surface before thickening. Lastly, the XPS Ni 2p 3/2 peak binding energy for 0.21 ML Ni on MgO(100) at 100 K is 2.2 eV higher than that for bulk Ni(solid), suggesting charge transfer from Ni to MgO(100) and formation of Ni 2+ at very low coverage.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1993

Ab Initio Potential Energy Surface for H-H2

Ab initio calculations employing large basis sets are performed to determine an accurate potential energy surface for H-H2 interactions for a broad range of separation distances. At large distances, the spherically averaged potential determined from the calculated energies agrees well with the corresponding results determined from dispersion coefficients; the van der Waals well depth is predicted to be 75 +/- 3 micro E(h). Large basis sets have also been applied to reexamine the accuracy of theoretical repulsive potential energy surfaces (25-70 kcal/mol above the H-H2 asymptote) at small interatomic separations; the Boothroyd, Keogh, Martin, and Peterson (BKMP) potential energy surface is found to agree with results of the present calculations within the expected uncertainty (+/- 1 kcal/mol) of the fit. Multipolar expansions of the computed H-H2 potential energy surface are reported for four internuclear separation distances (1.2, 1.401, 1.449, and 1.7a(0)) of the hydrogen molecule. The differential elastic scattering cross section calculated from the present results is compared with the measurements from a crossed beam experiment.

Patridge, Harry↗