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At least 1,567 records · Page 87

THE MASS DISTRIBUTION AND M/L RATIOS IN NGC 5953/5954

In this first paper, we combine a structural analysis of the near-IR surface brightness profiles and [N II] rotation curves for the galaxies in the pair NGC 5953/5954 to model the mass distribution in each member by using two independent axisymmetric analytical mass models: (1) a standard model given by the sum of a spherical bulge with the Sérsic law, a stellar exponential disk, and a cold dark matter halo represented by the improved fitting formula of Navarro et al.; and (2) a simple model given by the sum of a spherical bulge, a finite oblate spheroid representing the disk, and a spherical dark halo, all three mass components with simple density laws. In our surface brightness fits, a central luminous source is considered in both galaxies. We obtained K-band M/L ratios, Y {sub D}, Y {sub B}, for the disks and bulges, and total masses for each mass component in both galaxies. With the standard model we find in NGC 5953, (Y {sub D},Y {sub B}) = (0.29{sub -0.29}{sup +1}, 0.37 ± 0.03) M {sub ☉}/L {sub ☉}, and in NGC 5954, (Y {sub D},Y {sub B}) = (0.88 ± 0.18, 0.21 ± 0.09) M {sub ☉}/L {sub ☉}. Corresponding values found with the simple model are (Y {sub D},Y {sub B}) = (1.41 ± 0.15, 0.29 ± 0.04) M {sub ☉}/L {sub ☉} and (Y {sub D},Y {sub B}) = (0.51 ± 0.05, 0.52{sub -0.12}{sup +0.23}) M {sub ☉}/L {sub ☉}. Our M/L estimates are compared with predictions from other methods in the literature, finding reasonable agreement. The dark halos estimated using the simple model have a small mass, of the order of 10{sup 7} M {sub ☉}, within the maximum distance in the rotation velocity data.

79 ASTRONOMY AND ASTROPHYSICS↗

ANALYTICAL THEORY FOR THE INITIAL MASS FUNCTION. III. TIME DEPENDENCE AND STAR FORMATION RATE

The present paper extends our previous theory of the stellar initial mass function (IMF) by including time dependence and by including the impact of the magnetic field. The predicted mass spectra are similar to the time-independent ones with slightly shallower slopes at large masses and peak locations shifted toward smaller masses by a factor of a few. Assuming that star-forming clumps follow Larson-type relations, we obtain core mass functions in good agreement with the observationally derived IMF, in particular, when taking into account the thermodynamics of the gas. The time-dependent theory directly yields an analytical expression for the star formation rate (SFR) at cloud scales. The SFR values agree well with the observational determinations of various Galactic molecular clouds. Furthermore, we show that the SFR does not simply depend linearly on density, as is sometimes claimed in the literature, but also depends strongly on the clump mass/size, which yields the observed scatter. We stress, however, that any SFR theory depends, explicitly or implicitly, on very uncertain assumptions like clump boundaries or the mass of the most massive stars that can form in a given clump, making the final determinations uncertain by a factor of a few. Finally, we derive a fully time dependent model for the IMF by considering a clump, or a distribution of clumps accreting at a constant rate and thus whose physical properties evolve with time. In spite of its simplicity, this model reproduces reasonably well various features observed in numerical simulations of converging flows. Based on this general theory, we present a paradigm for star formation and the IMF.

79 ASTRONOMY AND ASTROPHYSICS↗

AN UNDERSTANDING OF THE SHOULDER OF GIANTS: JOVIAN PLANETS AROUND LATE K DWARF STARS AND THE TREND WITH STELLAR MASS

Analyses of exoplanet statistics suggest a trend of giant planet occurrence with host star mass, a clue to how planets like Jupiter form. One missing piece of the puzzle is the occurrence around late K dwarf stars (masses of 0.5-0.75 M{sub Sun} and effective temperatures of 3900-4800 K). We analyzed four years of Doppler radial velocity (RVs) data for 110 late K dwarfs, one of which hosts two previously reported giant planets. We estimate that 4.0% {+-} 2.3% of these stars have Saturn-mass or larger planets with orbital periods <245 days, depending on the planet mass distribution and RV variability of stars without giant planets. We also estimate that 0.7% {+-} 0.5% of similar stars observed by Kepler have giant planets. This Kepler rate is significantly (99% confidence) lower than that derived from our Doppler survey, but the difference vanishes if only the single Doppler system (HIP 57274) with completely resolved orbits is considered. The difference could also be explained by the exclusion of close binaries (without giant planets) from the Doppler but not Kepler surveys, the effect of long-period companions and stellar noise on the Doppler data, or an intrinsic difference between the two populations. Our estimates for late K dwarfs bridge those for solar-type stars and M dwarfs, and support a positive trend with stellar mass. Small sample size precludes statements about finer structure, e.g., a ''shoulder'' in the distribution of giant planets with stellar mass. Future surveys such as the Next Generation Transit Survey and the Transiting Exoplanet Satellite Survey will ameliorate this deficiency.

79 ASTRONOMY AND ASTROPHYSICS↗

THE LANDSCAPE OF THE NEUTRINO MECHANISM OF CORE-COLLAPSE SUPERNOVAE: NEUTRON STAR AND BLACK HOLE MASS FUNCTIONS, EXPLOSION ENERGIES, AND NICKEL YIELDS

If the neutrino luminosity from the proto-neutron star formed during a massive star core collapse exceeds a critical threshold, a supernova (SN) results. Using spherical quasi-static evolutionary sequences for hundreds of progenitors over a range of metallicities, we study how the explosion threshold maps onto observables, including the fraction of successful explosions, the neutron star (NS) and black hole (BH) mass functions, the explosion energies (E {sub SN}) and nickel yields (M {sub Ni}), and their mutual correlations. Successful explosions are intertwined with failures in a complex pattern that is not simply related to initial progenitor mass or compactness. We predict that progenitors with initial masses of 15 ± 1, 19 ± 1, and ∼21-26 M {sub ☉} are most likely to form BHs, that the BH formation probability is non-zero at solar-metallicity and increases significantly at low metallicity, and that low luminosity, low Ni-yield SNe come from progenitors close to success/failure interfaces. We qualitatively reproduce the observed E {sub SN}-M {sub Ni} correlation, we predict a correlation between the mean and width of the NS mass and E {sub SN} distributions, and that the means of the NS and BH mass distributions are correlated. We show that the observed mean NS mass of ≅ 1.33 M {sub ☉} implies that the successful explosion fraction is higher than 0.35. Overall, we show that the neutrino mechanism can in principle explain the observed properties of SNe and their compact objects. We argue that the rugged landscape of progenitors and outcomes mandates that SN theory should focus on reproducing the wide ranging distributions of observed SN properties.

79 ASTRONOMY AND ASTROPHYSICS↗

Investigating nuclear structure near N=32 and N=34: Precision mass measurements of neutron-rich Ca, Ti, and V isotopes

Nuclear mass measurements of isotopes are key to improving our understanding of nuclear structure across the chart of nuclides, in particular, for the determination of the appearance or disappearance of nuclear shell closures. Here, we present high-precision mass measurements of neutron-rich Ca, Ti, and V isotopes performed at TRIUMF's Ion Trap for Atomic and Nuclear science (TITAN) and the Low Energy Beam and Ion Trap (LEBIT) facilities. These measurements were made using the TITAN multiple-reflection time-of-flight mass spectrometer (MR-ToF-MS) and the LEBIT 9.4T Penning trap mass spectrometer. In total, 13 masses were measured, 8 of which represent increases in precision over previous measurements. These measurements refine trends in the mass surface around N=32 and N=34, and support the disappearance of the N=32 shell closure with increasing proton number. Additionally, our data do not support the presence of a shell closure at N=34.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Mass spectrum and thermodynamics of quasiconformal gauge theories from gauge/gravity duality

We use gauge/gravity duality to study simultaneously the mass spectrum and the thermodynamics of a generic quasiconformal gauge theory, specified by its beta function. The beta function of a quasiconformal theory almost vanishes, and the coupling is almost constant between two widely separated energy scales. Depending on whether the gravity dual has a black hole or not, the mass spectrum is either a spectrum of quasinormal oscillations or a normal T=0 mass spectrum. The mass spectrum is quantitatively correlated with the thermal properties of the system. As the theory approaches conformality, the masses have to vanish. We show that in this limit, the masses calculated via gauge/gravity duality satisfy expected scaling properties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Evidence for Different Disk Mass Distributions between Early- and Late-type Be Stars in the BeSOS Survey

The circumstellar disk density distributions for a sample of 63 Be southern stars from the BeSOS survey were found by modeling their H α emission line profiles. These disk densities were used to compute disk masses and disk angular momenta for the sample. Average values for the disk mass are 3.4 × 10{sup −9} and 9.5 × 10{sup −10} M {sub ⋆} for early (B0–B3) and late (B4–B9) spectral types, respectively. We also find that the range of disk angular momentum relative to the star is (150–200) J {sub ⋆}/ M {sub ⋆} and (100–150) J {sub ⋆}/ M {sub ⋆}, again for early- and late-type Be stars, respectively. The distributions of the disk mass and disk angular momentum are different between early- and late-type Be stars at a 1% level of significance. Finally, we construct the disk mass distribution for the BeSOS sample as a function of spectral type and compare it to the predictions of stellar evolutionary models with rapid rotation. The observed disk masses are typically larger than the theoretical predictions, although the observed spread in disk masses is typically large.

79 ASTRONOMY AND ASTROPHYSICS↗

Dynamical Formation of Low-mass Merging Black Hole Binaries like GW151226

Using numerical models for star clusters spanning a wide range in ages and metallicities (Z) we study the masses of binary black holes (BBHs) produced dynamically and merging in the local universe ( z ≲ 0.2). After taking into account cosmological constraints on star formation rate and metallicity evolution, which realistically relate merger delay times obtained from models with merger redshifts, we show here for the first time that while old, metal-poor globular clusters can naturally produce merging BBHs with heavier components, as observed in GW150914, lower-mass BBHs like GW151226 are easily formed dynamically in younger, higher-metallicity clusters. More specifically, we show that the mass of GW151226 is well within 1 σ of the mass distribution obtained from our models for clusters with Z/Z{sub ⊙} ≳ 0.5. Indeed, dynamical formation of a system like GW151226 likely requires a cluster that is younger and has a higher metallicity than typical Galactic globular clusters. The LVT151012 system, if real, could have been created in any cluster with Z/Z{sub ⊙} ≲ 0.25. On the other hand, GW150914 is more massive (beyond 1 σ ) than typical BBHs from even the lowest-metallicity (Z/Z{sub ⊙} = 0.005) clusters we consider, but is within 2 σ of the intrinsic mass distribution from our cluster models with Z/Z{sub ⊙} ≲ 0.05; of course, detection biases also push the observed distributions toward higher masses.

79 ASTRONOMY AND ASTROPHYSICS↗

Small Body GN and C Research Report: G-SAMPLE - An In-Flight Dynamical Method for Identifying Sample Mass [External Release Version]

G-SAMPLE is an in-flight dynamical method for use by sample collection missions to identify the presence and quantity of collected sample material. The G-SAMPLE method implements a maximum-likelihood estimator to identify the collected sample mass, based on onboard force sensor measurements, thruster firings, and a dynamics model of the spacecraft. With G-SAMPLE, sample mass identification becomes a computation rather than an extra hardware requirement; the added cost of cameras or other sensors for sample mass detection is avoided. Realistic simulation examples are provided for a spacecraft configuration with a sample collection device mounted on the end of an extended boom. In one representative example, a 1000 gram sample mass is estimated to within 110 grams (95% confidence) under realistic assumptions of thruster profile error, spacecraft parameter uncertainty, and sensor noise. For convenience to future mission design, an overall sample-mass estimation error budget is developed to approximate the effect of model uncertainty, sensor noise, data rate, and thrust profile error on the expected estimate of collected sample mass.

in-flight sample-mass identification↗

Characterization of Two Different Clay Materials by Thermogravimetry (TG), Differential Scanning Calorimetry (DSC), Dilatometry (DIL) and Mass Spectrometry (MS) - 12215

An illitic clay containing higher amounts of organic materials was investigated by dilatometry, thermogravimetry and differential scanning calorimetric. The evolved gases were studied during simultaneous TG-DSC (STA) and dilatometer measurements with simultaneous mass spectrometry in inert gas and oxidizing atmosphere. The dilatometer results were compared with the STA-MS results which confirmed and explained the reactions found during heating of the clay, like dehydration, dehydroxylation, shrinkage, sintering, quartz phase transition, combustion or pyrolysis of organics and the solid state reactions forming meta-kaolinite and mullite. The high amount of organic material effects in inert gas atmosphere most probably a reduction of the oxides which leads to a higher mass loss than in oxidizing atmosphere. Due to this reduction an additional CO{sub 2} emission at around 1000 deg. C was detected which did not occur in oxidizing atmosphere. Furthermore TG-MS results of a clay containing alkali nitrates show that during heating, in addition to water and CO{sub 2}, NO and NO{sub 2} are also evolved, leading to additional mass loss steps. These types of clays showed water loss starting around 100 deg. C or even earlier. This relative small mass loss affects only less shrinkage during the expansion of the sample. The dehydroxylation and the high crystalline quartz content result in considerable shrinkage and expansion of the clay. During the usual solid state reaction where the clay structure collapses, the remaining material finally shrinks down to a so-called clinker. With the help of MS the TG steps can be better interpreted as the evolved gases are identified. With the help of the MS it is possible to distinguish between CO{sub 2} and water (carbonate decomposition, oxidation of organics or dehydration/dehydroxylation). The MS also clearly shows that mass number 44 is found during the TG step of the illitic clay at about 900 deg. C in inert gas, which was interpreted as oxidation of pyrolytic carbon by reducing oxides. Additionally, without MS results, the mass loss steps of the nitrate contaminated clay could hardly be interpreted. (authors)

36 MATERIALS SCIENCE↗

Transmission Geometry Laser Ablation into a Non-Contact Liquid Vortex Capture Probe for Mass Spectrometry Imaging

RATIONALE: Capture of material from a laser ablation plume into a continuous flow stream of solvent provides the means for uninterrupted sampling, transport and ionization of collected material for coupling with mass spectral analysis. Reported here is the use of vertically aligned transmission geometry laser ablation in combination with a new non-contact liquid vortex capture probe coupled with electrospray ionization for spot sampling and chemical imaging with mass spectrometry. Methods: A vertically aligned continuous flow liquid vortex capture probe was positioned directly underneath a sample surface in a transmission geometry laser ablation (355 nm, 10 Hz, 7 ns pulse width) setup to capture into solution the ablated material. The outlet of the vortex probe was coupled to the Turbo V ion source of an AB SCIEX TripleTOF 5600+ mass spectrometer. System operation and performance metrics were tested using inked patterns and thin tissue sections. Glass slides and slides designed especially for laser capture microdissection, viz., DIRECTOR slides and PEN 1.0 (polyethylene naphthalate) membrane slides, were used as sample substrates. Results: The estimated capture efficiency of laser ablated material was 24%, which was enabled by the use of a probe with large liquid surface area (~ 2.8 mm2) and with gravity to help direct ablated material vertically down towards the probe. The swirling vortex action of the liquid surface potentially enhanced capture and dissolution of not only particulates, but also gaseous products of the laser ablation. The use of DIRECTOR slides and PEN 1.0 (polyethylene naphthalate) membrane slides as sample substrates enabled effective ablation of a wide range of sample types (basic blue 7, polypropylene glycol, insulin and cyctochrome c) without photodamage using a UV laser. Imaging resolution of about 6 m was demonstrated for stamped ink on DIRECTOR slides based on the ability to distinguish features present both in the optical and in the chemical image. This imaging resolution was 20 times better than the previous best reported results with laser ablation/liquid sample capture mass spectrometry imaging. Using thin sections of brain tissue the chemical image of a selected lipid was obtained with an estimated imaging resolution of about 50 um. Conclusions: A vertically aligned, transmission geometry laser ablation liquid vortex capture probe, electrospray ionization mass spectrometry system provides an effective means for spatially resolved spot sampling and imaging with mass spectrometry.

DIRECTOR slides↗

The structure of quark mass corrections in the gg → HH amplitude at high-energy

The leading and next-to-leading order QCD predictions for Higgs boson pair production at hadron colliders suffer from a significant mass renormalisation scheme uncertainty related to the choice of the top-quark mass. The functional dependence of the result on the value of the intermediate quark mass can be understood in the high-energy limit using the Method of Regions and the tools of Soft-Collinear Effective Theory. In this work, we study the origin of the sizeable logarithmic mass corrections in the gg → HH amplitudes at leading and next-to-leading power in the limit s, |t|, |u| ≫ ${m}_t^2$ ≫ ${m}_H^2$. We argue that the mass corrections follow a predictable factorised pattern that can be exploited to simplify their computation. We present results for the leading power leading logarithmic corrections, our analysis leads to a significant reduction in the theoretical uncertainty of the double Higgs production amplitudes at scattering energies ≳ 1 TeV due to the top-quark mass scheme.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Development, feasibility, and uncertainty of radioactive 22 Na tracer dilution and gamma spectroscopy for mass determination of molten salt for pyroprocessing spent nuclear fuels

Accurate knowledge of the total mass of molten salts both for pyroprocessing spent nuclear fuels and for molten salt reactors is necessary for safeguards purposes. However, it is challenging to know or measure the total mass of molten salt due to the complicated shapes as well as the compositional—and thus density—changes that occur over time during operation. Here, we investigated radioactive tracer dilution (RTD) as a potential safeguards technique for application to the total mass measurement of LiCl–KCl–UCl 3 salt used for uranium electrorefining, with a focus on the feasibility, uncertainty, and fission product effect of RTD for salt mass measurement. To this end, experimental-scale RTD tests (600–700 g of total mass) were initially carried out by adding 22 Na tracer salt into LiCl–KCl salt containing 0, 5, and 28wt% radioactive salts from an electrorefiner (ER) for refining uranium. Upon the completion of the experimental-scale RTD tests, we performed a scale-up RTD test by directly adding 22 Na tracer salts to the ER, which uses about 12 kg of LiCl–KCl–UCl 3 salt during normal operation. This paper reports the main features of RTD for total mass measurement of molten salt and summarizes the results of the experimental-scale and scale-up RTD tests.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Analysis of an irradiated uranium sample for source attribution without chemical separation using microplasma ionization and ultrahigh resolution mass spectrometry

The use of element isotope ratios has great potential in not only determining the reactor type used to produce plutonium (Pu) but also in determining the burnup and the time since irradiation. While a powerful nuclear forensic technique, determining element isotope ratios is complicated by severe isobaric interferences when performed on typical inductively coupled plasma mass spectrometers. Such analyses require extensive chemical separations prior to analysis to alleviate the inter-elemental isobars. Ultrahigh mass resolution spectrometry provides a potential alternative, greatly reducing the complexity of sample preparation and turnaround times for these critical measurements. To demonstrate the power of the approach, a sample of irradiated, depleted uranium was analyzed with the liquid sampling—atmospheric pressure glow discharge ion source coupled to an Orbitrap mass spectrometer. The Orbitrap is augmented with an external data acquisition system, Spectroswiss’s FTMS-Booster X2T, allowing collection of extended ion transients, providing higher mass resolution. In using this approach, the 150 Sm/ 149 Sm and 152 Sm/ 149 Sm isotope ratios were found to be within 20% of predicted values without any chemical separations and without mass bias corrections. In addition, the 240 Pu/ 239 Pu isotope ratio was determined, free from the 238 UH + interferences common to the ICP-MS platforms, while at the same time allowing for the determination of U isotopic signatures. While these demonstrative results are from a single sample, the advantages of the microplasma/ultrahigh mass resolution approach to intra-element isotope ratio determinations are clear.

Fuel burnup↗

An Assessment of the General Applicability of the Relationship Between Nucleation of CO Bubbles and Mass Transfer of Phosphorus in Liquid Iron Alloys

The current paper seeks to demonstrate the general applicability of the authors’ recently developed treatment of surface renewal during decarburization of Fe-C-S alloys and its effect on the mass transport of phosphorus in the metal phase. The proposed model employs a quantitative model of CO bubble nucleation in the metal to predict the rate of surface renewal, which can then in turn be used to predict the mass-transfer coefficient for phosphorus. A model of mixed transport control in the slag and metal phases was employed to investigate the dephosphorization kinetics between a liquid iron alloy and oxidizing slag. Based on previous studies of the mass-transfer coefficient of FeO in the slag, it was possible to separate the mass transfer coefficient of phosphorus in metal phase, k m , from the overall mass-transfer coefficient k o . Using this approach, k m was investigated under a wide range of conditions and shown to be represented reasonably by the mechanism proposed. The mass-transfer model was tested against results from the literature over a wide range of conditions. The analysis showed that the FeO content in the slag, silicon in the metal and the experimental temperature have strong impact on, k m , almost entirely because of their effect on decarburization behavior.

36 MATERIALS SCIENCE↗

High-Resolution Mass Spectrometry Quantification: Impact of Differences in Data Processing of Centroid and Continuum Data

High-resolution mass spectrometry (HRMS) in full scan mode acquires all ions present in the sample of interest offering a lot of qualitative information. This, in combination with the improved performance of the new generation HRMS systems, triggers more (bio) analysts to switch from triple quad MS systems to HRMS for quantitative analysis. Quantitative processing of HRMS data is performed based on narrow mass extraction windows rather than on nominal mass product ion chromatograms (SRM or MRM). Optimal processing of HRMS data requires different considerations and software tools and can have an impact on data processing and final results. The selection of centroid versus continuum/profile data for processing, selection of the optimal narrow mass extraction window, using theoretical versus measured accurate mass for the extraction of the ion chromatograms as well as differences in calculations and data handling residing in the different vendor software packages are tackled in the presented manuscript. These differences are illustrated on HRMS data acquired for the same plasma samples on three different platforms, i.e., a Sciex QToF, a Waters QToF, and a Thermo Orbitrap system, and processed in four different software packages, i.e., Sciex Analyst® TF, Waters Masslynx, Waters Unifi, and Thermo Xcalibur. The impact of these differences on quantitative HRMS performance was evaluated on calibration curves of eight small molecule compounds in plasma using four different ways of processing. Simple guidelines are provided for the selection of an optimal mass extraction window for continuum and centroided data. .

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Taming nuclear mass models with Gaussian processes

We propose a new set of nuclear mass predictions based on multiple theoretical mass models. By employing Gaussian process regression with the Matérn kernel, we achieved root-mean-square (rms) deviations below 100 keV for the training dataset. The best-performing mass models achieved rms deviations below 150 keV for the new precise mass data from AME2020, whereas the ensemble average showed robust performance across the nuclear chart. Our approach uniquely combines: (1) systematic refinement of eight mass models through their residuals, (2) physics-informed features, including magic numbers, nucleon parity numbers, neutron excess, and nuclear collectivity, and (3) theory-to-theory validation demonstrating robust extrapolation capability. We find that the Matérn kernel provides superior uncertainty quantification compared to the RBF kernel, with a length-scale analysis revealing enhanced inter-nuclei correlations. We provide complete mass predictions for all unknown nuclides in AME2020, offering valuable constraints for nuclear structure studies and astrophysical modeling when used with proper uncertainty propagation.

Gaussian processes↗

Mass transport in nanoarray monolithic catalysts: An experimental-theory study

Reducing the mass transfer resistance globally of a catalyst is a key to enhancing the catalytic reaction kinetics and fully utilizing the catalyst activity. Despite the success in tailoring the external mass transfer in the widely studied washcoat monoliths, the internal mass transfer resistance is difficult to be reduced due to the requirement of increasing macroporosity while maintaining high specific surface area and mechanical stability. Therefore, nanostructured array-based monolithic catalysts (nanoarray catalysts) have been developed in the past decade as a promising class of structured catalysts that may complement or substitute washcoat catalysts. This work fundamentally elucidates the enhanced mass transport properties of the nanoarray monolithic catalysts by a combination of experimental measurements and theoretical modeling. Using a low-dimensional model, the relative contributions of resistances were quantified in terms of chemical kinetics, internal and external mass transfers based on a probe model of C2H4 oxidation over the TiO2 supported Pt-based monolithic catalysts. The nanoarray catalysts displayed a lower internal mass transfer resistance than the washcoat counterparts as a result of the high macroporosity and small thickness of nanoarray layers. Finally, the nanoarray configuration provides a new pathway towards designing high-performance monolithic reactors and catalysts with low internal diffusion limitations for various gas phase reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗