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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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Protein3D: Enabling analysis and extraction of metal‐containing sites from the Protein Data Bank with molSimplify

Abstract Metalloenzymes catalyze a wide range of chemical transformations, with the active site residues playing a key role in modulating chemical reactivity and selectivity. Unlike smaller synthetic catalysts, a metalloenzyme active site is embedded in a larger protein, which makes interrogation of electronic properties and geometric features with quantum mechanical calculations challenging. Here we implement the ability to fetch crystallographic structures from the Protein Data Bank and analyze the metal binding sites in the program molSimplify. We show the usefulness of the newly created protein3D class to extract the local environment around non‐heme iron enzymes containing a two histidine motif and prepare 372 structures for quantum mechanical calculations. Our implementation of protein3D serves to expand the range of systems molSimplify can be used to analyze and will enable high‐throughput study of metal‐containing active sites in proteins.

Edholm, Freya↗
NASA NTRS1992

Higher-order quantum entanglement

In quantum mechanics, the general state describing two or more particles is a linear superposition of product states. Such a superposition is called entangled if it cannot be factored into just one product. When only two particles are entangled, the stage is set for Einstein-Podolsky-Rosen (EPR) discussions and Bell's proof that the EPR viewpoint contradicts quantum mechanics. If more than two particles are involved, new possibilities and phenomena arise. For example, the Greenberger, Horne, and Zeilinger (GHZ) disproof of EPR applies. Furthermore, as we point out, with three or more particles even entanglement itself can be an entangled property.

Zeilinger, Anton↗
NASA NTRS1992

Algorithmic information theory and the hidden variable question

The admissibility of certain nonlocal hidden-variable theories are explained via information theory. Consider a pair of Stern-Gerlach devices with fixed nonparallel orientations that periodically perform spin measurements on identically prepared pairs of electrons in the singlet spin state. Suppose the outcomes are recorded as binary strings l and r (with l sub n and r sub n denoting their n-length prefixes). The hidden-variable theories considered here require that there exists a recursive function which may be used to transform l sub n into r sub n for any n. This note demonstrates that such a theory cannot reproduce all the statistical predictions of quantum mechanics. Specifically, consider an ensemble of outcome pairs (l,r). From the associated probability measure, the Shannon entropies H sub n and H bar sub n for strings l sub n and pairs (l sub n, r sub n) may be formed. It is shown that such a theory requires that the absolute value of H bar sub n - H sub n be bounded - contrasting the quantum mechanical prediction that it grow with n.

Fuchs, Christopher↗
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↗
NASA NTRS1994

Computed potential energy surfaces for chemical reactions

Quantum mechanical methods have been used to compute potential energy surfaces for chemical reactions. The reactions studied were among those believed to be important to the NASP and HSR programs and included the recombination of two H atoms with several different third bodies; the reactions in the thermal Zeldovich mechanism; the reactions of H atom with O2, N2, and NO; reactions involved in the thermal De-NO(x) process; and the reaction of CH(squared Pi) with N2 (leading to 'prompt NO'). These potential energy surfaces have been used to compute reaction rate constants and rates of unimolecular decomposition. An additional application was the calculation of transport properties of gases using a semiclassical approximation (and in the case of interactions involving hydrogen inclusion of quantum mechanical effects).

Walch, Stephen P.↗
NASA NTRS2003

Threshold Laws for Two-Electron Ejection Processes: A Still Controversial Problem in Atomic Physics

This talk deals with collision processes of the following kind: (a) an ionizing collision of an electron with a neutral atom, (b) a photon incident of a negative ion resulting in two-electron ejection. In both cases the final state is a positive ion and two outgoing electrons, and in principle both processes should be governed by the same form of threshold law. It is generally conceded that this is one of the most difficult basic problems in nonrelativistic quantum mechanics. The standard treatment (due to Wannier) will be briefly reviewed in terms of the derivation of his well- known threshold law for the yield (Q) of positive ions vs. the excess energy (E): Q(sub w) varies as E(exp 1.127...). The derivation is a brilliant analysis based on Newton's equations, leading to the dominance of events in which the two electrons emerge on opposite sides of the residual ion with similar energies. In contrast, I will argue on the basis of quantum mechanical ideas that in the threshold limit the more likely outcome are events in which the electrons emerge with decidedly different energies, leading to a formally different (Coulomb-dipole) threshold law Q(sub CD) varies as E(1 + C sin(alpha ln(E)+mu)]/[ln(E)](exp 2). Additional aspects of that approach will be discussed . Some: experimental results will be presented, and more incisive predictions involving polarized projectiles and targets will be given.

Temkin, Aaron↗
NASA NTRS1975

Role of magnetic fields in physics and astrophysics; Proceedings of the Conference, Copenhagen, Denmark, June 5-7, 1974

The papers deal with the role of magnetism in astrophysics and the properties of matter in the presence of unusually large magnetic fields. Topics include a quantum-mechanical treatment of high-energy charged particles radiating in a homogeneous magnetic field, the solution and properties of the Dirac equation for magnetic fields of any strength up to 10 to the 13th power gauss, experimental difficulties encountered and overcome in generating megagauss fields, the effect of strong radiation damping for an ultrarelativistic charge in an external electromagnetic field, magnetic susceptibilities of nuclei and elementary particles, and Compton scattering in strong external electromagnetic fields. Other papers examine static uniform electric and magnetic polarizabilities of the vacuum in arbitrarily strong magnetic fields, quantum-mechanical processes in neutron stars, basic ideas of mean-field magnetohydrodynamics, helical MHD turbulence, relations between cosmic and laboratory plasma physics, and insights into the nature of magnetism provided by relativity and cosmology. Individual items are announced in this issue.

Canuto, V.↗
DOE OSTI2023

Graph-based quantum response theory and shadow Born–Oppenheimer molecular dynamics

Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born–Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. Further, the proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems

Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light–matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials).

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Geometrical picture of the electron–electron correlation at the large- D limit

In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schrödinger equation. Such an error in the different calculations is not directly observable as there is no simple quantum mechanical operator, apart from correlation functions, that correspond to such quantity. Here, we use the dimensional scaling approach, in which the electrons are localized at the large-dimensional scaled space, to describe a geometric picture of the electronic correlation. Both, the mean field, and the exact solutions at the large-D limit have distinct geometries. Thus, the difference might be used to describe the correlation effect. Moreover, correlations can be also described and quantified by the entanglement between the electrons, which is a strong correlation without a classical analog. Entanglement is directly observable and it is one of the most striking properties of quantum mechanics and bounded by the area law for local gapped Hamiltonians of interacting many-body systems. This study opens up the possibility of presenting a geometrical picture of the electron–electron correlations and might give a bound on the correlation energy. Furthermore, the results at the large-D limit and at D = 3 indicate the feasibility of using the geometrical picture to get a bound on the electron–electron correlations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRSDate not supplied

Resolving Wave-Particle Duality Could Accelerate the Mass Production of Quantum Computers

Quantum computers, hypothesized in 1980s, use concepts of superposition and entanglement phenomena. Although theoretical propositions and associated search algorithms for accurate measurements are being generated, the development of practical quantum computers themselves are advancing very slowly requiring enormous time and investments. The underlying concepts of a quantum computer are not new to the optical domain. However, the crucial enabling concepts of Entanglement and Superposition Principle are remaining clouded under the unresolved postulates, Wave-Particle Duality (WPD), and Wave Packet Reduction (WPR), implicating incompleteness in the interpretations of the mathematical formalism behind Quantum Mechanics. The WPD debate started during late1600 between Newton and Huygens. Young’s resolution of WPD through his double-slit experiment in 1802 was effectively overturned by Einstein’s interpretation of photoelectric effect as due to “indivisible light quanta”. However, Einstein disowned his “light quanta” postulate shortly before his death in1955, even though it had earned him the Nobel Prize. We resolve WPD by synthesizing Newton’s and Maxwell’s concepts and assume atoms do emit quanta but propagate as time-finite exponential pulses. This assumption also resolves WPR for light-matter interaction with the assumption that Schrodinger’s ψ represents atom’s internal dipolar amplitude stimulations. This over-turns Born’s interpretation that ψ only represents the abstract mathematical probability amplitude, rather than the physical “internal amplitude stimulation” of the quantum entity. However, our concept of atomic pulse emission forces us to re-derive the expression for the N-slit grating-spectrometer response since the classical derivation uses CW light, which does not exist. This pulsespectrometric response function strengthens our postulate since the grating response to the exponential pulse appears to be the convolution of a Lorentzian spectrum with the classical CW response function of the grating. The Fourier Transform of an exponential function is Lorentzian and QM predicts spontaneous emission line width to be Lorentzian. Then, conceptually one can extend the grating-expression (with N=2) to get the double-slit pattern. This approach preserves the classical causality that each of the two slits, like the N-signals out of a grating, are physically real and jointly stimulate the quantum detector array at the far field to generate the “Local” cosine fringes. The detector array executes the square modulus operation on its imposed dipolar amplitude stimulation and absorbs the necessary energy to fill up their quantum cups. Hence the double-slit pattern must also be “Local”, just as the N-slit grating spectrum is generated locally at the exit spectral-plane of the spectrometer. This removes the need to believe that “single photons” mysteriously generate the double slit pattern. Quantum computers, hypothesized in 1980s, use concepts of superposition and entanglement phenomena. Although theoretical propositions and associated search algorithms for accurate measurements are being generated, the development of practical quantum computers themselves are advancing very slowly requiring enormous time and investments. The underlying concepts of a quantum computer are not new to the optical domain. However, the crucial enabling concepts of Entanglement and Superposition Principle are remaining clouded under the unresolved postulates, Wave-Particle Duality (WPD), and Wave Packet Reduction (WPR), implicating incompleteness in the interpretations of the mathematical formalism behind Quantum Mechanics. The WPD debate started during late1600 between Newton and Huygens. Young’s resolution of WPD through his double-slit experiment in 1802 was effectively overturned by Einstein’s interpretation of photoelectric effect as due to “indivisible light quanta”. However, Einstein disowned his “light quanta” postulate shortly before his death in1955, even though it had earned him the Nobel Prize. We resolve WPD by synthesizing Newton’s and Maxwell’s concepts and assume atoms do emit quanta but propagate as time-finite exponential pulses. This assumption also resolves WPR for light-matter interaction with the assumption that Schrodinger’s ψ represents atom’s internal dipolar amplitude stimulations. This over-turns Born’s interpretation that ψ only represents the abstract mathematical probability amplitude, rather than the physical “internal amplitude stimulation” of the quantum entity. However, our concept of atomic pulse emission forces us to re-derive the expression for the N-slit grating-spectrometer response since the classical derivation uses CW light, which does not exist. This pulsespectrometric response function strengthens our postulate since the grating response to the exponential pulse appears to be the convolution of a Lorentzian spectrum with the classical CW response function of the grating. The Fourier Transform of an exponential function is Lorentzian and QM predicts spontaneous emission line width to be Lorentzian. Then, conceptually one can extend the grating-expression (with N=2) to get the double-slit pattern. This approach preserves the classical causality that each of the two slits, like the N-signals out of a grating, are physically real and jointly stimulate the quantum detector array at the far field to generate the “Local” cosine fringes. The detector array executes the square modulus operation on its imposed dipolar amplitude stimulation and absorbs the necessary energy to fill up their quantum cups. Hence the double-slit pattern must also be “Local”, just as the N-slit grating spectrum is generated locally at the exit spectral-plane of the spectrometer. This removes the need to believe that “single photons” mysteriously generate the double slit pattern.

Quantum Computer↗
DOE OSTI2023

Suppression of Midinfrared Plasma Resonance Due to Quantum Confinement in δ-Doped Silicon

The classical Drude model provides an accurate description of the plasma resonance of three-dimensional materials, but only partially explains two-dimensional systems where quantum mechanical effects dominate such as P:δ layers—atomically thin sheets of phosphorus dopants in silicon that induce electronic properties beyond traditional doping. Previously it was shown that P:δ layers produce a distinct Drude tail feature in ellipsometry measurements. However, the ellipsometric spectra could not be properly fit by modeling the δ layer as a discrete layer of classical Drude metal. In particular, even for large broadening corresponding to extremely short relaxation times, a plasma resonance feature was anticipated but not evident in the experimental data. In this work, we develop a physically accurate description of this system, which reveals a general approach to designing thin films with intentionally suppressed plasma resonances. Our model takes into account the strong charge-density confinement and resulting quantum mechanical description of a P:δ layer. Here, we show that the absence of a plasma resonance feature results from a combination of two factors: (i) the sharply varying charge-density profile due to strong confinement in the direction of growth; and (ii) the effective mass and relaxation time anisotropy due to valley degeneracy. The plasma resonance reappears when the atoms composing the δ layer are allowed to diffuse out from the plane of the layer, destroying its well-confined two-dimensional character that is critical to its distinctive electronic properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Time-Resolved Observation of Hole Tunneling in van der Waals Multilayer Heterostructures

We reported a time-resolved study of quantum-mechanical tunneling of holes between two MoSe 2 monolayers that are separated by a monolayer WS 2 energy barrier. Four-layer heterostructures of MoSe 2 /WS 2 /MoSe 2 /graphene, as well as control samples, were fabricated by mechanical exfoliation and dry transfer techniques. To time-resolve the hole tunneling process, an ultrashort laser pulse was used to excite electrons and holes in both MoSe 2 layers. Here, by utilization of the graphene layer to eliminate carriers in the third MoSe 2 layer, the first MoSe 2 layer is selectively populated with the holes, which then tunnel to the third MoSe 2 layer. By monitoring decay of the hole population with an ultrashort probe pulse, we measure a hole tunneling time of about 20 ps, which is found to slightly increase with the injected carrier density. Besides the fundamental interests of real-time observation of the quantum-mechanical tunneling effect across a nanometer barrier, these results provide quantitative understanding on tunneling mechanisms of charge transfer in van der Waals heterostructures, which is useful for designing sophisticated van der Waals multilayer heterostructures.

36 MATERIALS SCIENCE↗
DOE OSTI2021

PYSEQM

PYSEQM is a package for performing semi-empirical quantum mechanical (SEQM) simulations on molecular systems utilizing PyTorch. SEQM simulations determine molecular properties (energy, electron density, dipole moment, ect.) by solving an approximate Schrödinger equation for the motions of electrons in a molecule. The use of PyTorch provides three specific advantages. First, it allows the calculations to be offloaded to GPU accelerators, giving an order of magnitude increase in speed. Second, back propagation is used to get atomic forces (derivative of the total energy with respect to atomic position) at the same computational cost as the energy calculation itself. Finally, the use of PyTorch makes for a natural interface to modern machine learning methods, which can be used to adjust the semi-empirical parameters build into SEQM methods. Additionally, PYSEQM implements various other optimizations for performing quantum mechanics based molecular dynamics, including SP2 for rapid GPU based solution of the self-consistent field algorithm, and the extended Lagrangian method for rapid QM-MD.

Nebgen, Benjamin↗
DOE OSTI2021

Solitons in lattice field theories via tight-binding supersymmetry

Reflectionless potentials play an important role in constructing exact solutions to classical dynamical systems (such as the Korteweg-de Vries equation), non-perturbative solutions of various large-N field theories (such as the Gross-Neveu model), and closely related solitonic solutions to the Bogoliubov-de Gennes equations in the theory of superconductivity. These solutions rely on the inverse scattering method, which reduces these seemingly unrelated problems to identifying reflectionless potentials of an auxiliary one-dimensional quantum scattering problem. There are several ways of constructing these potentials, one of which is quantum mechanical supersymmetry (SUSY). In this paper, motivated by recent experimental platforms, we generalize this framework to develop a theory of lattice solitons. We first briefly review the classical inverse scattering method in the continuum limit, focusing on the Korteweg-de Vries (KdV) equation and SU(N) Gross-Neveu model in the large N limit. We then generalize this methodology to lattice versions of interacting field theories. Our analysis hinges on the use of trace identities, which are relations connecting the potential of an equation of motion to the scattering data. For a discrete Schrödinger operator, such trace identities had been known as far back as Toda; however, we derive a new set of identities for the discrete Dirac operator. We then use these identities in a lattice Gross-Neveu and chiral Gross-Neveu (Nambu-Jona-Lasinio) model to show that lattice solitons correspond to reflectionless potentials associated with the discrete scattering problem. These models are of significance as they are equivalent to a mean-field theory of a lattice superconductor. To explicitly construct these solitons, we generalize supersymmetric quantum mechanics to tight-binding models. We show that a matrix transformation exists that maps a tight-binding model to an isospectral one which shares the same structure and scattering properties. The corresponding soliton solutions have both modulated hopping and onsite potential, the former of which has no analogue in the continuum limit. We explicitly compute both topological and non-topological soliton solutions as well as bound state spectra in the aforementioned models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

An experimental and chemical kinetic modeling study of 4-butoxyheptane combustion

Here, the combustion kinetics of a novel oxygenated bioblendstock for diesel, 4-butoxyheptane (4-BH), was investigated experimentally using a flow reactor and a heated, high-pressure shock tube. The flow reactor experiments employed oxygen as the oxidizer and helium as the diluent with oxidation conducted at atmospheric pressure and 10 bar for temperatures from 400 to 1000 K at 20-K intervals. The fuel, oxidizer, and diluent flow rates were varied at different temperatures to maintain a constant initial fuel mole fraction of 1000 ppm, with stoichiometric equivalence ratio, and a residence time of 2.0 s. The reacted gas was fed to two separate GC systems that could qualitatively and quantitatively detect product species. Additionally, real fuel-air ignition delay time (IDT) data were collected using a heated, high-pressure shock-tube facility. Fuel lean (φ = 0.5) and stoichiometric (φ = 1.0) mixtures were investigated at 10 atm as well as at 30 atm for the fuel lean case for temperatures between 847 and 1259 K. A detailed chemical kinetics mechanism was developed to model the product distribution from the flow reactor and IDTs from the shock tube. The proposed model was able to predict the double NTC behavior in flow reactor experiments reasonably well. Model predictions at low temperatures were observed to be highly sensitive to the rate constants of ketohydroperoxide (KHP) decomposition in the case of the OOH group in α position which were modeled based on existing literature studies on ethers. It was noted that in the absence of theoretical or experimental studies, the rate constants for KHP decomposition used in the literature were empirically set. Additional studies are required to address the gap in model prediction obtained in this study and to reduce the uncertainty in kinetics models for ether oxidation. Predicted product concentrations and IDTs showed some quantitative agreement with experimental data, but the overall reactivity of the IDTs is underpredicted. Additionally, significant deviation is observed for the IDT results at 10 atm for the stoichiometric case with minor deviations for the other cases. The reaction pathways to the missing products were then further analyzed theoretically through quantum-mechanical calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1998

Molecular Processes in Comets

The research focused on molecular hydrogen and its response to ultraviolet radiation, photoelectron impact excitation and X-ray radiation and on the interpretation of the ultraviolet spectra of the Jupiter dayglow and auroras. A systematic effort was made to obtain reliable rate coefficients for rovibrational energy transfer of H2, particularly in collisions with hydrogen atoms. We carried out elaborate quantum-mechanical calculations of the scattering of H and H2 on what had been characterized as a reliable potential energy surface of the H3 molecular system. These calculations took into account reactive channels and rate coefficients for ortho-para transitions were obtained. Quantal calculations are too complex to be applied to all the possible rovibrational transitions and we turned to a semi-classical method. With it we calculated rate coefficients for transitions, reactive and non-reactive, for all the rovibrational levels. We carried out the calculations for three of the available H3 potential energy surfaces. We discovered an unexpected sensitivity of the rate coefficients for the non-reactive channels to the potential energy surface. This discovery stimulated more thorough investigations of the potential energy surface elsewhere and to the construction of a new surface. We have used it in further semi-classical calculations in work that will shortly be 2 completed and which, together with new quantum-mechanical calculations should comprise a set of reliable rate coefficients that can be used in discussions of H2 on the Jovian planets. We carried out a detailed study of the Jovian ultraviolet dayglow. There has been a long-running argument about the dayglow on Jupiter. There are two sources of excitation: fluorescence and photoelectron impact excitation. It had been argued that a third source "the electron glow" was needed to bring theory and observation into agreement. We believe we have shown conclusively that the third source is unnecessary. We have achieved a close quantitative agreement between the predicted spectrum arising from fluorescence and photoelectrons and the measured spectrum. We also demonstrated a method by which the presence of HD could be established observationary. Similar calculations were carried out of the ultraviolet spectra of the Jovian auroras. We again found close agreement. Indeed, the agreement was so detailed we were able to derive the temperature of the atmosphere. We found, contrary to the standard model of the time, a high temperature between 400 K and 600 K and established the presence of a significant temperature gradient. A large temperature gradient was indeed found by direct sampling with the Jupiter probe.

Dalgarno, A.↗