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At least 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Observation of Flat Bands in Gated Semiconductor Artificial Graphene

Flat bands near M points in the Brillouin zone are key features of honeycomb symmetry in artificial graphene (AG) where electrons may condense into novel correlated phases. Here we report the observation of van Hove singularity doublet of AG in GaAs quantum well transistors, which presents the evidence of flat bands in semiconductor AG. Two emerging peaks in photoluminescence spectra tuned by backgate voltages probe the singularity doublet of AG flat bands and demonstrate their accessibility to the Fermi level. As the Fermi level crosses the doublet, the spectra display dramatic stability against electron density, indicating interplays between electron-electron interactions and honeycomb symmetry. Our results provide a new flexible platform to explore intriguing flat band physics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Spontaneous Gap Opening and Potential Excitonic States in an Ideal Dirac Semimetal Ta 2 Pd 3 Te 5

The opening of an energy gap in the electronic structure generally indicates the presence of interactions. In materials with low carrier density and short screening length, long-range Coulomb interaction favors the spontaneous formation of electron-hole pairs, so called excitons, opening an excitonic gap at the Fermi level. Excitonic materials host unique phenomena associated with pair excitations. However, there is still no generally recognized single-crystal material with excitonic order, which is, therefore, awaited in condensed matter physics. Here, we show that excitonic states may exist in the quasi-one-dimensional material Ta 2 Pd 3 Te 5 , which has an almost ideal Dirac-like band structure, with the Dirac point located exactly at the Fermi level. We find that an energy gap appears at 350 K, and it grows with decreasing temperature. The spontaneous gap opening is absent in a similar material Ta 2 Ni 3 Te 5 . Intriguingly, the gap is destroyed by the potassium deposition on the crystal, likely due to extra-doped carriers. Furthermore, we observe a pair of in-gap flat bands, which is an analog of the impurity states in a superconducting gap. All these observations can be properly explained by an excitonic order, providing Ta 2 Pd 3 Te 5 as a new and promising candidate realizing excitonic states. Published by the American Physical Society 2024

Zhang, Peng (ORCID:0000000225634670)↗
DOE OSTI2025

Diagrammatic Monte Carlo Approach to Real‐frequency Response Functions and the Spin‐Fermion Model of Hot Spots (Final Report)

This three‐year research project was focused on two outstanding condensed matter problems (i) Real‐frequency response functions in Coulomb systems at finite temperature, and Fermi surface (FS) reconstruction in the Spin-Fermion (SF) model. The uniform electron gas (jellium) model, describing electrons interacting via long‐range Coulomb forces on positive neutralizing background, is fundamentally important both for understanding the physics of correlated electrons and for formulation of the time‐dependent density functional theory (TDDFT). The spin-fermion model has found a wide range of applications in the physics of cuprates and iron‐based superconductors to explain the “strange metal" behavior and to suggest a possible pairing mechanism for high‐temperature superconductivity. The project’s goals were development and application of the Diagrammatic Monte Carlo (DiagMC) techniques for solving the above problems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Cross Section Results from the MicroBooNE Experiment

The MicroBooNE detector is currently the largest operating liquid argon neutrino experiment in the world. Located at the Fermi National Accelerator Laboratory (Fermilab), MicroBooNE has been collecting both electron neutrino (\(\nu _{e}\)) and muon neutrino (\(\nu _{\mu }\)) interactions from both the Booster Neutrino Beam (BNB) and the Neutrino Main Injector (NuMI) since late 2015. During this time, MicroBooNE has measured a wide-variety of interaction topologies including \(\nu _{\mu }\) charged current, \(\nu _{e}\) charged current, resonant \(\pi ^{0}\), and various high multiplicity interactions. To date, many of MicroBooNE’s measurements are either the first of their kind using liquid argon as a target material, or have the largest number of events collected using a liquid argon detector. All of these measurements combine to form a rich cross section programme, aiming to enhance understanding of GeV-range neutrino interaction on liquid argon for upcoming detectors such as SBND, ICARUS, and DUNE.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Temperature-Dependent Electron–Electron Interaction in Graphene on SrTiO 3

We present that the electron band structure of graphene on SrTiO 3 substrate has been investigated as a function of temperature. The high-resolution angle-resolved photoemission study reveals that the spectral width at Fermi energy and the Fermi velocity of graphene on SrTiO 3 are comparable to those of graphene on a BN substrate. Near the charge neutrality, the energy-momentum dispersion of graphene exhibits a strong deviation from the well-known linearity, which is magnified as temperature decreases. Such modification resembles the characteristics of enhanced electron-electron interaction. Lastly, our results not only suggest that SrTiO 3 can be a plausible candidate as a substrate material for applications in graphene-based electronics but also provide a possible route toward the realization of a new type of strongly correlated electron phases in the prototypical two-dimensional system via the manipulation of temperature and a proper choice of dielectric substrates.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Dynamic behavior of the quantum Zakharov-Kuznetsov equations in dense quantum magnetoplasmas

Quantum Zakharov-Kuznetsov (qZK) equation is found in a dense quantum magnetoplasma. Via the spectral analysis, we investigate the Hamiltonian and periodicity of the qZK equation. Using the Hirota method, we obtain the bilinear forms and N-soliton solutions. Asymptotic analysis on the two-soliton solutions shows that the soliton interaction is elastic. Figures are plotted to reveal the propagation characteristics and interaction between the two solitons. We find that the one soliton has a single peak and its amplitude is positively related to H{sub e}, while the two solitons are parallel when H{sub e} < 2, otherwise, the one soliton has two peaks and the two solitons interact with each other. Hereby, H{sub e} is proportional to the ratio of the strength of magnetic field to the electronic Fermi temperature. External periodic force on the qZK equation yields the chaotic motions. Through some phase projections, the process from a sequence of the quasi-period doubling to chaos can be observed. The chaotic behavior is observed since the power spectra are calculated, and the quasi-period doubling states of perturbed qZK equation are given. The final chaotic state of the perturbed qZK is obtained.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Nodal hybridization in a two-dimensional heavy-fermion material

Metals with partially filled core atomic shells can form quasiparticles at a low temperature arising from the hybridization of the core level and conduction electrons. The thermodynamic and spectroscopic properties of these metals can be understood as those of a simple metal, but with a significant mass enhancement over the free electron mass—commonly referred to as heavy fermions. In most heavy-fermion materials, the hybridization is approximately isotropic in position and momentum space. However, a combination of low dimensionality and symmetry properties of the core-level wavefunctions can give rise to highly anisotropic electronic interactions with the conduction electrons. Here, in this study, we demonstrate anisotropic hybridization that vanishes along specific directions in momentum space—referred to as nodes—in a lanthanide-based two-dimensional van der Waals heavy-fermion compound, CeSiI. Quasiparticle interference measurements reveal a set of discrete hotspots with high spectral intensity on the Fermi surface. Theoretical modelling and comparison with the quasiparticle interference pattern of the non-heavy-fermion isostructural analogue LaSiI suggest that these features arise from an unconventional electron interaction involving hybridization nodes unique to CeSiI. As a result, the effective mass of the quasiparticles varies by orders of magnitude depending on their direction in momentum space.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Nuclear enhancement of the photon yield in cosmic ray interactions

The concept of the nuclear enhancement factor has been used since the beginning of γ-ray astronomy. It provides a simple and convenient way to account for the contribution of nuclei (A > 1) in cosmic rays (CRs) and in the interstellar medium (ISM) to the diffuse γ-ray emission. An accurate treatment of the dominant emission process, such as hadronic interactions of CRs with the ISM, enables one to study CR acceleration processes and CR propagation in the ISM, and provides a reliable background model for searches of new phenomena. The Fermi Large Area Telescope launched in 2008 provides excellent quality data in a wide energy range 30 MeV-1 TeV where the diffuse emission accounts for the majority of photons. Exploiting its data to the fullest requires a new study of the processes of γ-ray production in hadronic interactions. In this paper we point out that several commonly used studies of the nuclear enhancement factor fail to account for the spectrally averaged energy loss fraction which ensures that the energy fraction transferred to photons is averaged properly with the spectra of CR species. We present a new calculation of the spectrally averaged energy loss fraction and the nuclear enhancement factor using the QGSJET-II-04 and EPOS-LHC interaction models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Entanglement entropy, single-particle occupation probabilities, and short-range correlations

For quantum many-body systems with short-range correlations (SRCs), the intimate relationship between their magnitude, the behavior of the single-particle occupation probabilities at momenta larger than the Fermi momentum, and the entanglement entropy is a new qualitative aspect not studied and exploited yet. A large body of recent condensed matter studies indicates that the time evolution of the entanglement entropy describes the nonequilibrium dynamics of isolated and strongly interacting many-body systems, in a manner similar to the Boltzmann entropy, which is strictly defined for dilute and weakly interacting many-body systems. Both theoretical and experimental studies in nuclei and cold atomic gases have shown that the fermion momentum distribution has a generic behavior n(k)=C/k 4 at momenta larger than the Fermi momentum, due to the presence of SRCs, with approximately 20% of the particles having momenta larger than the Fermi momentum. Further, the presence of the long momentum tails in the presence of SRCs changes the textbook relation between the single-particle kinetic energy and occupation probabilities, n mf ⁡(k) = 1/{1+ exp ⁡β[ϵ⁡(k)-μ]} for momenta very different form the Fermi momentum, particularly for dynamics processes. SRCs induced high-momentum tails of the single-particle occupation probabilities increase the entanglement entropy of fermionic systems, which in its turn affects the dynamics of many nuclear reactions, such as heavy-ion collisions and nuclear fission.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Investigating effects of relativistic kinematics, dimensionality, interactions, and short-range correlations on the ratio of quartic over quadratic nuclear symmetry energies

While ample evidence for the so-called empirical parabolic law of the Equation of State (EOS) of isospin asymmetric nuclear matter (ANM) has been obtained in many studies within both non-relativistic and relativistic nuclear many-body theories using various interactions, it has been unclear if there is any fundamental physics reason for the small quartic symmetry energy compared to the quadratic one even as the ANM approaches pure neutron matter. Within both relativistic and non-relativistic Free Fermi Gas (FFG) models in coordinate spaces of arbitrary dimension d with and without considering Short-Range Correlations (SRC) as well as non-linear Relativistic Mean Field (RMF) models, we study effects of relativistic kinematics, dimensionality, interactions and SRC on the ratio Ψ(ρ) of quartic over quadratic symmetry energies in ANM EOSs. We found that the ratio Ψ(ρ) in the FFG model depends strongly on the dimension d. While it is very small already in the normal 3D space, it could be even smaller in spaces with reduced dimensions for sub-systems of particles in heavy-ion reactions and/or whole neutron stars due to constraints, collectivities and/or symmetries. Here, we also found that the ratio Ψ(ρ) could theoretically become very large only at the ultra-relativistic limit far above the density reachable in neutron stars. On the other hand, nuclear interaction directly and/or indirectly through SRC-induced high-momentum nucleons affect significantly the density dependence of Ψ(ρ) compared to the relativistic FFG model prediction. The SRC affects significantly not only the kinetic energy of symmetric nuclear matter but also the ratio Ψ(ρ) while the relativistic corrections are found negligible. The results may help better understand the EOS of dense neutron-rich matter.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Measurement of $d^2 \sigma/d|\vec{q}|d E_{avail}$ and 2p2h contribution using charged current $\nu_\mu$ interactions in the NOvA Near Detector

This Thesis presents the analysis methods and measurement of the $d^2 \sigma/d|\vec{q}|d E_{avail}$-CC inclusive cross section that describes neutrino scattering in a predominantly hydrocarbon medium. Studies that are prerequisite for the analysis including, variable determinations, event selections, efficiency, purity determinations, and systematic uncertainty estimations, are summarized. Tests of the analysis are also detailed, and shown to reproduce the input distributions. The double-differential cross-section measurement provides the foundation for determination of the inclusive rate for the excess induced by 2p2h processes together with nuclear medium effects that are not described by the Fermi gas model. The methodology for the extraction of this rate, defined as the excess observed relative to the rate estimated for known single-nucleon interactions, is described in detail. The following new measurements are reported in this Thesis: (1) The $\nu_\mu-$CC inclusive double-differential cross section as a function of three-momentum transfer and available hadronic energy, for an average $E_\nu$ of 1.8 GeV, is obtained. The double-differential cross section value that obtains when the bin widths are taken to be the dimensions of the entire analysis domain, e.g. $0.2 \le |\vec{q}| \le 2.0 GeV/c$ and $0.0 \le E_{avail} \le 2.0$ GeV, is inclusive cross section is $(6.05 \pm 0.75)\times10^{-39}$ cm$^2$/GeV/GeV/$c$/nucleon. An event excess attributed to 2p2h-MEC processes is observed; most of the rate occurs in a contiguous phase space region $0.3 \le |\vec{q}| \le 1.0$ GeV$/c$ $0.0 \le E_{avail} \le 0.35$ GeV. This rate represents $12.0\pm 6.5\%$ of the observed CC inclusive cross section; its cross section ratio relative to CCQE scattering is estimated to be $44.3 \pm 23.9\%$.

Olson, Travis Grant↗
DOE OSTI2013

Fermi -LAT upper limits on gamma-ray emission from colliding wind binaries

Here, colliding wind binaries (CWBs) are thought to give rise to a plethora of physical processes including acceleration and interaction of relativistic particles. Observation of synchrotron radiation in the radio band confirms there is a relativistic electron population in CWBs. Accordingly, CWBs have been suspected sources of high-energy γ-ray emission since the COS-B era. Theoretical models exist that characterize the underlying physical processes leading to particle acceleration and quantitatively predict the non-thermal energy emission observable at Earth. Furthermore, we strive to find evidence of γ-ray emission from a sample of seven CWB systems: WR 11, WR 70, WR 125, WR 137, WR 140, WR 146, and WR 147. Theoretical modelling identified these systems as the most favourable candidates for emitting γ-rays. We make a comparison with existing γ-ray flux predictions and investigate possible constraints. We used 24 months of data from the Large Area Telescope (LAT) on-board the Fermi Gamma Ray Space Telescope to perform a dedicated likelihood analysis of CWBs in the LAT energy range. As a result, we find no evidence of γ-ray emission from any of the studied CWB systems and determine corresponding flux upper limits. For some CWBs the interplay of orbital and stellar parameters renders the Fermi -LAT data not sensitive enough to constrain the parameter space of the emission models. In the cases of WR140 and WR147, the Fermi -LAT upper limits appear to rule out some model predictions entirely and constrain theoretical models over a significant parameter space. A comparison of our findings to the CWB η Car is made.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Two-Dimensional Non-Fermi-Liquid Metals: A Solvable Large- N Limit

Significant effort has been devoted to the study of “non-Fermi-liquid” (NFL) metals: gapless conducting systems that lack a quasiparticle description. One class of NFL metals involves a finite density of fermions interacting with soft order parameter fluctuations near a quantum critical point. The problem has been extensively studied in a large- N limit ( N corresponding to the number of fermion flavors) where universal behavior can be obtained by solving a set of coupled saddle-point equations. However, a remarkable study by Lee revealed the breakdown of such approximations in two spatial dimensions. We show that an alternate approach, in which the fermions belong to the fundamental representation of a global SU( N ) flavor symmetry, while the order parameter fields transform under the adjoint representation (a “matrix large- N ” theory), yields a tractable large N limit. At low energies, the system consists of an overdamped boson with dynamical exponent z = 3 coupled to a non-Fermi-liquid with self-energy Σ(ω)~ω 2/3 , consistent with previous studies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Novel phases in strongly coupled four-fermion theories

Here, we study a lattice model comprising four massless reduced staggered fermions in four dimensions coupled through an SU(4)-invariant four-fermion interaction. We present both theoretical arguments and numerical evidence that no bilinear fermion condensates are present for any value of the four-fermi coupling, in contrast to earlier studies of Higgs{Yukawa models with different exact lattice symmetries. At strong coupling we observe the formation of a four-fermion condensate and a mass gap in spite of the absence of bilinear condensates. Unlike those previously studied systems we do not find a ferromagnetic phase separating this strong-coupling phase from the massless weak-coupling phase. Instead we observe long-range correlations in a narrow region of the coupling, still with vanishing bilinear condensates. While our numerical results come from relatively small lattice volumes that call for caution in drawing conclusions, if this novel phase structure is verified by future investigations employing larger volumes it may offer the possibility for new continuum limits for strongly interacting fermions in four dimensions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Downward quantum learning from element 118: Automated generation of Fermi–Löwdin orbitals for all atoms

A new algorithm based on a rigorous theorem and quantum data computationally mined from element 118 guarantees automated construction of initial Fermi–Löwdin-Orbital (FLO) starting points for all elements in the Periodic Table. It defines a means for constructing a small library of scalable FLOs for universal use in molecular and solid-state calculations. The method can be systematically improved for greater efficiency and for applications to excited states such as x-ray excitations and optically silent excitations. FLOs were introduced to recast the Perdew–Zunger self-interaction correction (PZSIC) into an explicit unitarily invariant form. The FLOs are generated from a set of N quasi-classical electron positions, referred to as Fermi-Orbital descriptors (FODs), and a set of N-orthonormal single-electron orbitals. FOD positions, when optimized, minimize the PZSIC total energy. However, creating sets of starting FODs that lead to a positive definite Fermi orbital overlap matrix has proven to be challenging for systems composed of open-shell atoms and ions. The proof herein guarantees the existence of a FLOSIC solution and further guarantees that if a solution for N electrons is found, it can be used to generate a minimum of N – 1 and a maximum of 2 N – 2 initial starting points for systems composed of a smaller number of electrons. As a result, applications to heavy and super-heavy atoms are presented. All starting solutions reported here were obtained from a solution for element 118, Oganesson.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Muon capture on Li 6 , C 12 , and O 16 from ab initio nuclear theory

Muon capture on nuclei is one of the most promising probes of the nuclear electroweak current driving the yet-hypothetical neutrinoless double-beta (0νββ) decay. Both processes involve vector and axial-vector currents at finite momentum transfer, q ~ 100 MeV, as well as the induced pseu doscalar and weak-magnetism currents. Comparing measured muon-capture rates with reliable ab initio nuclear-theory predictions could help us validate these currents. To this end, we compute partial muon-capture rates for 6 Li, 12 C and 16 O, feeding the ground and excited states in 6 He, 12 B and 16 N, using ab initio no-core shell model with two- and three-nucleon chiral interactions. Here, we remove the spurious center-of-mass motion by introducing translationally invariant operators and approximate the effect of hadronic two-body currents by Fermi-gas model. We solve the bound-muon wave function from the Dirac wave equations in the Coulomb field created by a finite nucleus. We find that the computed rates to the low-lying states in the final nuclei are in good agreement with the measured counterparts. We highlight sensitivity of some of the transitions to the sub-leading three-nucleon interaction terms. We also compare summed rates to several tens of final states with the measured total capture rates and note that we slightly underestimate the total rate with this simple approach due to limited range of excitation energies

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

The Thomas–Fermi quark model: Non-relativistic aspects

The first numerical investigation of non-relativistic aspects of the Thomas–Fermi (TF) statistical multi-quark model is given. We begin with a review of the traditional TF model without an explicit spin interaction and find that the spin splittings are too small in this approach. An explicit spin interaction is then introduced which entails the definition of a generalized spin “flavor”. We investigate baryonic states in this approach which can be described with two inequivalent wave functions; such states can however apply to multiple degenerate flavors. We find that the model requires a spatial separation of quark flavors, even if completely degenerate. Although the TF model is designed to investigate the possibility of many-quark states, we find surprisingly that it may be used to fit the low energy spectrum of almost all ground state octet and decuplet baryons. The charge radii of such states are determined and compared with lattice calculations and other models. The low energy fit obtained allows us to extrapolate to the six-quark doubly strange H-dibaryon state, flavor symmetric strange states of higher quark content and possible six quark nucleon–nucleon resonances. The emphasis here is on the systematics revealed in this approach. We view our model as a versatile and convenient tool for quickly assessing the characteristics of new, possibly bound, particle states of higher quark number content. -- Highlights: • First application of the statistical Thomas–Fermi quark model to baryonic systems. • Novel aspects: spin as generalized flavor; spatial separation of quark flavor phases. • The model is statistical, but the low energy baryonic spectrum is successfully fit. • Numerical applications include the H-dibaryon, strange states and nucleon resonances. • The statistical point of view does not encourage the idea of bound many-quark baryons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2012

FERMI LARGE AREA TELESCOPE STUDY OF COSMIC RAYS AND THE INTERSTELLAR MEDIUM IN NEARBY MOLECULAR CLOUDS

We report an analysis of the interstellar {gamma}-ray emission from the Chamaeleon, R Coronae Australis (R CrA), and Cepheus and Polaris flare regions with the Fermi Large Area Telescope. They are among the nearest molecular cloud complexes, within {approx}300 pc from the solar system. The {gamma}-ray emission produced by interactions of cosmic rays (CRs) and interstellar gas in those molecular clouds is useful to study the CR densities and distributions of molecular gas close to the solar system. The obtained {gamma}-ray emissivities above 250 MeV are (5.9 {+-} 0.1{sub stat}{sup +0.9}{sub -1.0sys}) Multiplication-Sign 10{sup -27} photons s{sup -1} sr{sup -1} H-atom{sup -1}, (10.2 {+-} 0.4{sub stat}{sup +1.2}{sub -1.7sys}) Multiplication-Sign 10{sup -27} photons s{sup -1} sr{sup -1} H-atom{sup -1}, and (9.1 {+-} 0.3{sub stat}{sup +1.5}{sub -0.6sys}) Multiplication-Sign 10{sup -27} photons s{sup -1} sr{sup -1} H-atom{sup -1} for the Chamaeleon, R CrA, and Cepheus and Polaris flare regions, respectively. Whereas the energy dependences of the emissivities agree well with that predicted from direct CR observations at the Earth, the measured emissivities from 250 MeV to 10 GeV indicate a variation of the CR density by {approx}20% in the neighborhood of the solar system, even if we consider systematic uncertainties. The molecular mass calibrating ratio, X{sub CO} = N(H{sub 2})/W{sub CO}, is found to be (0.96 {+-} 0.06{sub stat}{sup +0.15}{sub -0.12sys}) Multiplication-Sign 10{sup 20} H{sub 2}-molecule cm{sup -2} (K km s{sup -1}){sup -1}, (0.99 {+-} 0.08{sub stat}{sup +0.18}{sub -0.10sys}) Multiplication-Sign 10{sup 20} H{sub 2}-molecule cm{sup -2} (K km s{sup -1}){sup -1}, and (0.63 {+-} 0.02{sub stat}{sup +0.09}{sub -0.07sys}) Multiplication-Sign 10{sup 20} H{sub 2}-molecule cm{sup -2} (K km s{sup -1}){sup -1} for the Chamaeleon, R CrA, and Cepheus and Polaris flare regions, respectively, suggesting a variation of X{sub CO} in the vicinity of the solar system. From the obtained values of X{sub CO}, the masses of molecular gas traced by W{sub CO} in the Chamaeleon, R CrA, and Cepheus and Polaris flare regions are estimated to be {approx}5 Multiplication-Sign 10{sup 3} M{sub Sun }, {approx}10{sup 3} M{sub Sun }, and {approx}3.3 Multiplication-Sign 10{sup 4} M{sub Sun }, respectively. A comparable amount of gas not traced well by standard H I and CO surveys is found in the regions investigated.

79 ASTRONOMY AND ASTROPHYSICS↗