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NASA NTRS1995

Emission line signatures of anisotropic turbulence in accretion disks

We investigate observable effects of anisotropic turbulence on the velocity profiles and eclipse behavior of emission lines from accretion disks. Turbulence expands the local line broadening profile, enhancing the surface brightness of saturated emission lines. Anisotropic turbulence produces anisotropic emission in such lines. The effects become observable when the turbulence exceeds the thermal velocity. Each term in the velocity-velocity correlation matrix produces a distinctive azimuthal pattern of enhanced emission-line surface brightness on the face of the accretion disk. These patterns express themselves as changes in the observable shapes of the disk's emission lines. The best place to look for turbulence effects is in saturated emission lines of heavy elements such as Ca, Mg, and Fe, which have a smaller thermal velocity at a given sound speed and at moderate inclination (60-70 degrees), since the Keplerian shear broadening dominates at higher inclinations.

Horne, Keith↗

NASA NTRS1994

Steps toward determination of the size and structure of the broad-line region in active galactic nuclei. 8: An intensive HST, IUE, and ground-based study of NGC 5548

We present the data and initial results from a combined HST/IUE/ground-based spectroscopic monitoring campaign on the Seyfert 1 galaxy NGC 5548 that was undertaken in order to address questions that require both higher temporal resolution and higher signal-to-noise ratios than were obtained in our previous multiwavelength monitoring of this galaxy in 1988-89. IUE spectra were obtained once every two days for a period of 74 days beginning on 14 March 1993. During the last 39 days of this campaign, spectroscopic observations were also made with the HST Faint Object Spectrograph (FOS) on a daily basis. Ground-based observations, consisting of 165 optical spectra and 77 photometric observations (both CCD imaging and aperture photometry), are reported for the period 1992 October to 1993 September, although much of the data are concentrated around the time of the satellite-based program. These data constitute a fifth year of intensive optical monitoring of this galaxy. In this contribution, we describe the acquisition and reduction of all of the satellite and ground-based data obtained in this program. We describe in detail various photometric problems with the FOS and explain how we identified and corrected for various anomalies. During the HST portion of the monitoring campaign, the 1350 A continuum flux is found to have varied by nearly a factor of two. In other wavebands, the continuum shows nearly identical behavior, except that the amplitude of variability is larger at shorter wavelengths, and the continuum light curves appear to show more short time-scale variability at shorter wavelengths. The broad emission lines also vary in flux, with amplitudes that are slightly smaller than the UV continuum variations and with a small time delay relative to the UV continuum. On the basis of simple time-series analysis of the UV and optical continuum and emission line light curves, we find (1) that the ultraviolet and optical continuum variations are virtually simultaneous, with any lag between the 1350 A continuum and the 5100 A continuum amounting to less than about one day; (2) that the variations in the highest ionization lines observed, He II lambda 1640 and N V lambda 1240, lag behind the continuum variations by somewhat less than 2 days, and (3) that the velocity field of the C IV-emitting region is not dominated by radial motion. The results on the C IV velocity field are preliminary and quite uncertain, but there are some weak indications that the emission-line (wings absolute value of Delta upsilon is greater than or equal to 3000 km/s) respond to continuum variations slightly more rapidly than does the core. The optical observations show that the variations in the broad H beta line flux follow the continuum variations with a time lag of around two weeks, about twice the lag for Ly alpha and C IV, as in our previous monitoring campaign on this same galaxy. However, the lags measured for Ly alpha, C IV, and H Beta are each slightly smaller than previously determined. We confirm two trends reported earlier, namely (1) that the UV/optical continuum becomes 'harder' as it gets brighter, and (2) that the highest ionization emission lines have the shortest lags, thus indicating radial ionization stratificatin of a broad-line region that spans over an order of magnitude range in radius.

Korista, K.↗

NASA NTRS1995

Thermal Line Shift and Broadening of Ho(3+) in Y3AI5O12 and Lu3AIO12

The interaction between the active ion and the host lattice manifests itself in two distinct ways: the static interaction with the crystal field that causes the splitting of the free ion energy levels and the active interaction through the surrounding phonon system that produces temperature dependent characteristics in the optical spectrum of the ion (e.g. line broadening and line shift). The strength of the splitting depends heavily on the electronic configuration of the atom. The model give by McCumber and Sturge describes the thermal effects on line width and position above 77 K with Raman scattering of Debye model phonons. These processes predict a Lorentzian line shape. However, below 77 K the principal contributions are from crystal inhomogeneities that result in a Gaussian line shape. We have investigated the experimental Stark levels as well as the thermal effects on the line width and the position of trivalent holmium ions in both yttrium aluminum garnet, Y3Al5O12 (YAG) and lutetium aluminum garnet, Lu3Al5O12 (LuAG) crystals. We have compared the Stark levels of the (5)I(6) state, and the thermal line shift and broadening of an isolated transition (Z2 to X13) between the (5)I(8) and (5)I(6) stark levels in these crystals. This transition occurs in the near infrared region at approximately 1117 nm.

Snoke, Elizabeth R.↗

NASA NTRS1995

Flow properties along field lines in a 3-D tilted-dipole geometry

A 3-D MHD simulation of a global, tilted-dipole solar wind flow pattern is analyzed to determine flow properties along individual magnetic field lines. In the model, flow conditions near the Sun are chosen to provide a reasonable match to the interplanetary configuration prevailing during the recent south polar passage by Ulysses, i.e., a streamer belt inclined approximately 30 deg to the solar equator and speeds ranging from 325-800 km/s. Field lines all across the stream pattern are traced from 1 to 10 AU by following the motion of marker particles embedded in the flow. It is found that those field lines threading the core of the interaction region are subject to significant latitudinal and relative longitudinal displacement over this range of heliocentric distance. Thus, observations taken at a fixed latitude in the inner solar system sample, over the course of a solar rotation, field lines which connect to a range of latitudes in the outer heliosphere. Maps of the field line displacements are presented to help visualize these connections. In addition, it is found that depending upon the location relative to the CIR structure, the radial evolution of fluid elements frozen to different field lines can deviate considerably from that of the canonical solar wind. That is, for selected subsets of field lines, large speed changes (not just at shocks) can be experienced; the density variation can be far from 1/r(exp 2), and the magnetic field intensity need not decay monotonically with distance.

Pizzo, V. J.↗

NASA NTRS1996

The Micromechanics of the Moving Contact Line

The proposed research is divided into three components concerned with molecular structure, molecular orientation, and continuum averages of discrete systems. In the experimental program, we propose exploring how changes in interfacial molecular structure generate contact line motion. Rather than rely on the electrostatic and electrokinetic fields arising from the molecules themselves, we augment their interactions by an imposed field at the solid/liquid interface. By controling the field, we can manipulate the molecular structure at the solid/liquid interface. In response to controlled changes in molecular structure, we observe the resultant contact line motion. In the analytical portion of the proposed research we seek to formulate a system of equations governing fluid motion which accounts for the orientation of fluid molecules. In preliminary work, we have focused on describing how molecular orientation affects the forces generated at the moving contact line. Ideally, as assumed above, the discrete behavior of molecules can be averaged into a continuum theory. In the numerical portion of the proposed research, we inquire whether the contact line region is, in fact, large enough to possess a well-defined average. Additionally, we ask what types of behavior distinguish discrete systems from continuum systems. Might the smallness of the contact line region, in itself, lead to behavior different from that in the bulk? Taken together, our proposed research seeks to identify and accurately account for some of the molecular dynamics of the moving contact line, and attempts to formulate a description from which one can compute the forces at the moving contact line.

Han, Minsub↗

NASA NTRS1997

Evaluating Possible Heating Mechanisms Using the Transition Region Line Profiles of Late-Type Stars

Our analysis of high-resolution Goddard High-Resolution Spectrograph (GHRS) spectra of late-type stars shows that the Si IV and C IV lines formed near 10(exp 5) K can be decomposed into the sum of two Gaussians, a broad component and a narrow component. We find that the flux contribution of the broad components is correlated with both the C IV and X-ray surface fluxes. For main-sequence stars, the widths of the narrow components suggest subsonic nonthermal velocities, and there appears to be a tight correlation between these nonthermal velocities and stellar surface gravity [xi(sub nc) varies as g(sup (-.68 +/-.07))]. For evolved stars with lower surface gravities, the nonthermal velocities suggested by the narrow components are at or just above the sound speed. Nonthermal velocities computed from the widths of the broad components are always highly supersonic. We propose that the broad components are diagnostics for microflare heating. Turbulent dissipation and Alfven waves are both viable candidates for the narrow component heating mechanism. A solar analog for the broad components might be the 'explosive events' detected by the High-Resolution Telescope and Spectrograph (HRTS) experiment. The broad component we observe for the Si IV lambda 1394 line of alpha Cen A, a star that is nearly identical to the Sun, has a FWHM of 109 +/- 10 km/s and is blueshifted by 9 +/- 3 km/s relative to the narrow component. Both of these properties are consistent with the properties of the solar explosive events. However, the alpha Cen A broad component accounts for 25% +/- 4% of the total Si IV line flux, while solar explosive events are currently thought to account for no more than 5% of the Sun's total transition region emission. This discrepancy must be resolved before the connection between broad components and explosive events can be positively established. In addition to our analysis of the Si IV and C IV lines of many stars, we also provide a more thorough analysis of all of the available GHRS data for alpha Cen A (G2 V) and alpha Cen B (K1 V). We find that the transition region lines of both stars have redshifts almost identical to those observed on the Sun: showing an increase with line formation temperature up to about log T = 5.2 and then a rapid decrease. Using the O IV] lines as density diagnostics, we compute electron densities of log n(sub e) = 9.65 +/- 0.20 and log n(sub e) = 9.50 +/- 0.30 for alpha Cen A and alpha Cen B, respectively.

Wood, Brian E.↗

NASA NTRS1996

Line Profile of H Lyman-Beta Emission from Dissociative Excitation of H2

A high-resolution ultraviolet spectrometer was employed for a measurement of the H Lyman-Beta(H L(sub Beta)) emission Doppler line profile at 1025.7 A from dissociative excitation of H2 by electron impact. Analysis of the deconvolved line profile reveals the existence of a narrow central peak, less than 30 mA full width at half maximum (FWHM), and a broad pedestal base about 260 mA FWHM. Analysis of the red wing of the line profile is complicated by a group of Wemer and Lyman rotational lines 160-220 mA from the line center. Analysis of the blue wing of the line profile gives the kinetic-energy distribution. There are two main kinetic-energy components to the H(3p) distribution: (1) a slow distribution with a peak value near 0 eV from singly excited states, and (2) a fast distribution with a peak contribution near 7 eV from doubly excited states. Using two different techniques, the absolute cross section of H L(sub Beta)p is found to be 3.2+/-.8 x 10(exp -19)sq cm at 100-eV electron impact energy. The experimental cross-section and line-profile results can be compared to previous studies of H(alpha) (6563.7 A) for principal quantum number n=3 and L(sub alpha)(1215.7 A) for n=2.

Ajello, Joseph M.↗

NASA NTRS1997

Using Strong Solar Coronal Emission Lines as Coronal Flux Proxies

A comparison of Skylab results with observations of the strong EUV lines of Fe XVI at 335 A and 361 A from the Goddard Solar EUV Rocket Telescope and Spectrograph (SERTS) flight of 1989 suggests that these lines, and perhaps others observed with SERTS, might offer good proxies for estimating the total coronal flux over important wavelength ranges. In this paper, we compare SERTS observations from a later, 1993 flight with simultaneous cospatial Yohkoh soft X-ray observations to test this suggestion over the energy range of the Soft X-ray Telescope (SXT) on Yohkoh. Both polynomial and power-law fits are obtained, and errors are estimated, for the SERTS lines of Fe XVI 335 A and 361 A, Fe XV 284 A and 417 A, and Mg IX 368 A. It is found that the power-law fits best cover the full range of solar conditions from quiet Sun through active region, though not surprisingly the 'cooler' Mg IX 368 A line proves to be a poor proxy. The quadratic polynomial fits yield fair agreement over a large range for all but the Mg IX line, but the linear fits fail conspicuously when extrapolated into the quiet Sun regime. The implications of this work for the He 11 304 A line formation problem are briefly considered. The paper concludes with a discussion of the value of these iron lines observed with SERTS for estimating stellar coronal fluxes, as observed for example with the EUVE satellite.

Falconer, David A.↗

NASA NTRS1999

The Role of Velocity Redistribution in Enhancing the Intensity of the He II 304 A Line in the Quiet Sun Spectrum

We present observational evidence of the effect of small scale ("microturbulent") velocities in enhancing the intensity of the He II lambda304 line with respect to other transition region emission lines, a process we call "velocity redistribution". We first show results from the 1991 and 1993 flights of SERTS (Solar EUV Rocket Telescope and Spectrograph). The spectral resolution of the SERTS instrument was sufficient to infer that, at the spatial resolution of 5", the line profile is nearly gaussian both in the quiet Sun and in active regions. We were then able to determine, for the quiet Sun, a lower limit for the amplitude of non-thermal motions in the region of formation of the 304 A line of the order of 10 km/s. We estimated that, in the presence of the steep temperature gradients of the solar Transition Region (TR), velocities of this magnitude can significantly enhance the intensity of that line, thus at least helping to bridge the gap between calculated and observed values. We also estimated the functional dependence of such an enhancement on the relevant parameters (non-thermal velocities, temperature gradient, and pressure). We then present results from a coordinated campaign, using SOHO/CDS and H-alpha spectroheliograms from Coimbra Observatory, aimed at determining the relationship between regions of enhanced helium emission and chromospheric velocity fields and transition region emission in the quiescent atmosphere. Using these data, we examined the behavior of the He II lambda304 line in the quiet Sun supergranular network and compared it with other TR lines, in particular with O III lambda600. We also examined the association of 304 A emission with the so-called "coarse dark mottle", chromospheric structures seen in H-alpha red wing images and associated with spicules. We found that all these observations are consistent with the velocity redistribution picture.

Andretta, Vincenzo↗

NASA NTRS2000

Emission Line Spectra from Low-Density Laboratory Plasmas

Using spectroscopic equipment optimized for laboratory astrophysics, we are performing systematic measurements of the line emission from astrophysically relevant ions in the wavelength band between 1 and 400 Angstroms important to X-ray missions such as Chandra, XMM, Astro-E, and EUVE. Obtained in a controlled laboratory setting at electron densities similar to those found in stellar coronae, the data are used to test spectral modeling codes for accuracy and completeness. Our effort includes the compilation of the iron L-shell emission lines from 6-18 Angstroms and the iron M-shell emission lines from 50-200 Angstroms. Many lines have been identified for the first time, and the fluxes from lines missing in the spectral modeling codes are assessed. Our measurements also assess the accuracy of line excitation calculations, including direct electron-impact excitation, dielectronic recombination, and resonance excitation. These measurements yield a calibration of specific diagnostic line ratios. Examples of our current measurements are given.

Beiersdorfer, P.↗

NASA NTRS2000

Limits on Line Bisector Variability for Stars with Extrasolar Planets

We present an analysis of high-resolution synoptic spectra of ten F- and G-type stars, seven of which exhibit periodic radial velocity variations due to the presence of one or more substellar companions. We searched for subtle periodic variations in photospheric line asymmetry, as characterized by line bisectors. In principle, periodic variations in line asymmetry observed at lower spectral resolution could mimic the radial velocity signature of a companion, but we find no significant evidence of such behavior in our data. Observations were obtained from 1998 March to 1999 February using the National Solar Observatory (NSO) 1.52-m McMath-Pierce Solar Telescope Facility on Kitt Peak in conjunction with the solar-stellar spectrograph, achieving a resolving power of 1.2x10(exp5). To characterize line asymmetry, we first measured line bisectors for the unblended Fe I photospheric line at 625.26 nm. To improve sensitivity to small fluctuations, we then combined points in each bisector to form a velocity displacement with respect to the line core. We searched for periodic variations in this displacement, finding no substantial difference between stars with substellar companions and those without reported companions. We find no correlation between bisector velocity displacement and the known orbital phase of substellar companions around our target stars. Simulations of a periodic signal with noise levels that mimic our measurement errors suggest that we can exclude bisector variations with amplitudes greater than about 20 m/s. These results support the conclusion that extrasolar planets best explain the observed periodic variations in radial velocity.

Povich, M. S.↗

NASA NTRS2001

First Detection of a Foreground Damped Ly-Alpha Absorber Along a GRB Line of Sight?

We present a VLT spectrum of the optical afterglow of GRB 991216, taken 1.5 days after the burst, and HST (Hubble Space Telescope) imaging of the host galaxy, obtained four months later. The spectrum contains three metal absorption-line systems with redshifts z = 1.024, z = 0.803, and z = 0.771, where the highest redshift most likely reflects the distance to the host galaxy. For the z = 1.024 and z = 0.803 systems we tentatively detect MgI which suggests a dense environment at these redshifts. This and the strength of the z = 0.803 Fe lines indicate that this system very likely is a damped Ly-alpha absorber (DLA), which would be the first foreground DLA to be detected along a GRB afterglow sight line. The HST images are consistent with these findings: they show two blobs of light, one underneath the projected OT position, the presumed host galaxy, and the other 0.6" away, which is probably responsible for the absorption lines at z = 0.803. The lowest redshift system can be explained by either one of the two galaxies that are located roughly 2" away from the transient. Including these newly found systems, the total number of DLAS and Lyman limit systems along GRB afterglow sight lines is consistent with the number expected from QSO (quasi-stellar object) absorption line studies. We expect early spectroscopy of GRB afterglows to significantly increase the number of detected foreground absorption systems, and we discuss some advantages over QSO lines of sight.

Vreeswijk, P. M.↗

NASA NTRS2001

Resonance Scattering of Fe XVII X-ray and EUV Lines

Bhatia, A. K.↗

NASA NTRS2001

Resonance Scattering of Fe XVII X-Ray and EUV Lines

Over the years a number of calculations have been carried out to derive intensities of various X-ray and EUV lines in Fe XVII to compare with observed spectra. The predicted intensities have not agreed with solar observations, particularly for the line at 15.02 Angstroms; resonance scattering has been suggested as the source for much of the disagreement. The atomic data calculated earlier used seven configurations, 2s(sup 2) 2p(sup 6),2s(sup 2) 2p(sup 5)3s, 2s(sup 2) 2p(sup 5)3p, 2s(sup 2)2p(sup 5)3d, 2s2 p(sup 6)3s, 2s2p(sup 6)3p, and 2s2p(sup 6)3d, having n=3 orbitals and the scattering calculations in the distorted wave approximation were carried out only for incident energies above the threshold of the highest fine-structure level. These calculations have now been extended to thirteen configurations by adding six more configurations having n=4 orbitals, namely 2s(sup 2) 2p(sup 5)4s, 2s(sup 2) 2p(sup 5)4p, 2s(sup 2) 2p(sup 5)4d, 2s2p(sup 6)4s, 2s2p(sup 6)4p, and 2s2p(sup 6)4d, giving rise to 73 fine structure levels. The scattering calculations are carried out below as well as above the threshold of the highest fine-structure level. The incident energies below the threshold are 55.8, 65, 70, and 76 Ry and those above are 85, 127.5, 170, 212.5, 255, 340, and 425 Ry. The collision strengths are calculated up to total angular momentum L(sup T) = 33. Level populations and intensity ratios are calculated at various electron temperatures and densities. It is not possible to predict how the ratios would change when configurations with n=5 and 6 orbitals are added but some estimates have been made for a few transitions by Liedhal, who indicates an asymptotic convergence when n=5 and 6 orbitals are added. These improved calculations of Fe XVII change the intensity ratios compared to those obtained earlier, bringing the optically thin F(15.02)/F(16.78) ratio and several other ratios closer to the observed values: However, some disagreement with the solar observations still persists, even though the agreement of the presently calculated optically thin F(15.02)/F(15.26) ratio with the experimental results of Brown et al. and Laming et al. has improved. Some of the remaining discrepancy is still thought to be the effect of opacity, which is consistent with expected physical conditions for solar sources. EUV intensity ratios are also calculated and compared with observations. Level populations and intensity ratios are calculated, as a function of column density of Fe XVII, in the slab and cylindrical geometries. As found previously, the predicted intensities for the resonance lines at 15.02 and 15.26 Angstroms exhibit initial increases in flux relative to the forbidden line at 17.10 Angstroms and the resonance line at 16.78 Angstroms as optical thickness increases. The same behavior is predicted for the lines at 12.262 and 12.122 Angstroms. Predicted intensities for some of the allowed EUV lines are also affected by opacity.

Bhatia, A. K.↗

NASA NTRS1995

'Party Line' Information Use Studies and Implications for ATV Datalink Communications

The perceived importance and utilization of 'party line' information by air carrier flight crews was investigated through pilot surveys and a flight simulation study. The Importance, Availability, and Accuracy of party line information elements were explored through surveys of pilots of several operational types. The survey identified numerous traffic and weather party line information elements which were considered important. These elements were scripted into a full-mission flight simulation which examined the utilization of party line information by studying subject responses to specific information element stimuli. The awareness of the different Party Line elements varied, and awareness was also affected by pilot workload. In addition, pilots were aware of some traffic information elements, but were reluctant to act on Party Line Information alone. Finally, the importance of party line information appears to be greatest for operations near or on the airport. This indicates that caution should be exercised when implementing datalink communications in tower and close-in terminal control sectors.

Pritchett, Amy↗

NASA NTRS1995

"Party Line" Information Use Studies and Implications for ATC Datalink Communications

The perceived importance and utilization of 'party line' information by air carrier flight crews was investigated through pilot surveys and a flight simulation study. The importance, availability, and accuracy of party line information elements were explored through surveys of pilots of several operational types. The survey identified numerous traffic and weather party line information elements which were considered important. These elements were scripted into a full-mission flight simulation which examined the utilization of party line information by studying subject responses to specific information element stimuli. The awareness of the different Party Line elements varied, and awareness was also affected by pilot workload. In addition, pilots were aware of some traffic information elements, but were reluctant to act on Party Line Information alone. Finally, the results of both the survey and the simulation indicated that the importance of party line information appeared to be greatest for operations near or on the airport. This indicates that caution should be exercised when implementing datalink communications in tower and close-in terminal control sectors.

Hansman, R. John↗

NASA NTRS2001

The Effect of Changes in the ASCA Calibration on the Fe-K Lines in Active Galaxies

The ASCA calibration has evolved considerably since launch and indeed, is still evolving. There have been concerns in the literature that changes in the ASCA calibration have resulted in the Fe-K lines in active galaxies (AGN) now being systematically narrower than was originally thought. If this were true, a large body of ASCA results would be impacted. In particular, it has been claimed that the broad red wing (when present) of the Fe-K line has been considerably weakened by changes in the ASCA calibration. We demonstrate explicitly that changes in the, ASCA calibration over a period of about eight years have a negligible effect on the width, strength, or shape of the Fe-K lines. The reduction in both width and equivalent width is only approximately 8% or less. We confirm this with simulations and individual sources, as well as sample average profiles. The average profile for type 1 AGN is still very broad, with the red wing extending down to approximately 4 keV. The reason for the claimed, apparently large, discrepancies is that in some sources the Fe-K line is complex, and a single-Gaussian model, being an inadequate description of the line profile, picks up different portions of the profile with different calibration. However, one cannot make inferences about calibration or astrophysics of the sources using models which do not describe the data. Better modeling of the Fe-K in such cases gives completely consistent results with both old and current calibration. Thus, inadequate modeling of the Fe-K line in these sources can seriously underestimate the line width and equivalent width, and therefore lead to incorrect deductions about the astrophysical implications.

Yaqoob, T.↗

NASA NTRS1998

Line Assignments and Position Measurements in Several Weak CO2 Bands Between 4590/cm and 7930/cm

A substantial set of CO2 spectra from 4500 to 12000/cm has been obtained at Ames with 1500 m path length using a Bomem DA8 FTS. The signal/noise was improved compared to prior spectra obtained in this laboratory by including a filter wheel limiting the band-pass of each spectrum to several hundred per cm. We have measured positions of lines in several weak bands not previously resolved in laboratory spectra. Using our positions and assignments of lines of the Qbranch of the 31103-00001 vibrational band at 4591/cm, we have redetermined the rotational constants for the 31103f levels. Q-branch lines of this band were previously observed, but misassigned, in Venus spectra by Mandin. The current HITRAN values of the rotational constants for this level are incorrect due to the Q-branch misassignments. Our prior measurements of the 21122-00001 vibrational band at 7901/cm were limited to Q-and R-branch lines; with the improved signal/noise of these new spectra we have now measured lines in the weaker P branch. The 21122 (Gv = 790148/cm) levels are known to be perturbed by the 32211 (G(sub v) = 789757/cm) levels; new DND calculations predict that high-J lines of the forbidden 32211-00001 vibrational band 'borrow' intensity from the corresponding transitions of the 21122-00001 band. We have identified such Q- and R-branch transitions of the 32211-00001 band from 26 < J" < 44, based on our position measurements of lines in the 32211-02201 band at 6562/cm.

Giver, L. P.↗