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Rotational excitation of HCN by para- and ortho-H{sub 2}

Rotational excitation of the hydrogen cyanide (HCN) molecule by collisions with para-H{sub 2}( j = 0, 2) and ortho-H{sub 2}( j = 1) is investigated at low temperatures using a quantum time independent approach. Both molecules are treated as rigid rotors. The scattering calculations are based on a highly correlated ab initio 4-dimensional (4D) potential energy surface recently published. Rotationally inelastic cross sections among the 13 first rotational levels of HCN were obtained using a pure quantum close coupling approach for total energies up to 1200 cm{sup −1}. The corresponding thermal rate coefficients were computed for temperatures ranging from 5 to 100 K. The HCN rate coefficients are strongly dependent on the rotational level of the H{sub 2} molecule. In particular, the rate coefficients for collisions with para-H{sub 2}( j = 0) are significantly lower than those for collisions with ortho-H{sub 2}( j = 1) and para-H{sub 2}( j = 2). Propensity rules in favor of even Δj transitions were found for HCN in collisions with para-H{sub 2}( j = 0) whereas propensity rules in favor of odd Δj transitions were found for HCN in collisions with H{sub 2}( j ⩾ 1). The new rate coefficients were compared with previously published HCN-para-H{sub 2}( j = 0) rate coefficients. Significant differences were found due the inclusion of the H{sub 2} rotational structure in the scattering calculations. These new rate coefficients will be crucial to improve the estimation of the HCN abundance in the interstellar medium.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Detection and Signal Processing for Near-Field Nanoscale Fourier Transform Infrared Spectroscopy

Researchers from a broad spectrum of scientific and engineering disciplines are increasingly using scattering-type near-field infrared spectroscopic techniques to characterize materials non-destructively with nanoscale spatial resolution. However, a sub-optimal understanding of a technique's implementation can complicate data interpretation and act as a barrier to entering the field. Here the key detection and processing steps involved in producing scattering-type near-field nanoscale Fourier transform infrared spectra (nano-FTIR) are outlined. The self-contained mathematical and experimental work derives and explains: i) how normalized complex-valued nano-FTIR spectra are generated, ii) why the real and imaginary components of spectra qualitatively relate to dispersion and absorption respectively, iii) a new and generally valid equation for spectra which can be used as a springboard for additional modeling of the scattering processes, and iv) an algebraic expression that can be used to extract an approximation to the sample's local extinction coefficient from nano-FTIR. The algebraic model for weak oscillators is validated with nano-FTIR and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectra on samples of polystyrene and Kapton and further provides a pedagogical pathway to cementing some of the technique's key qualitative attributes.

36 MATERIALS SCIENCE↗

An Innovative Concept for Spacebased Lidar Measurement of Ocean Carbon Biomass

Beam attenuation coefficient, c, provides an important optical index of plankton standing stocks, such as phytoplankton biomass and total particulate carbon concentration. Unfortunately, c has proven difficult to quantify through remote sensing. Here, we introduce an innovative approach for estimating c using lidar depolarization measurements and diffuse attenuation coefficients from ocean color products or lidar measurements of Brillouin scattering. The new approach is based on a theoretical formula established from Monte Carlo simulations that links the depolarization ratio of sea water to the ratio of diffuse attenuation Kd and beam attenuation C (i.e., a multiple scattering factor). On July 17, 2014, the CALIPSO satellite was tilted 30Âdeg off-nadir for one nighttime orbit in order to minimize ocean surface backscatter and demonstrate the lidar ocean subsurface measurement concept from space. Depolarization ratios of ocean subsurface backscatter are measured accurately. Beam attenuation coefficients computed from the depolarization ratio measurements compare well with empirical estimates from ocean color measurements. We further verify the beam attenuation coefficient retrievals using aircraft-based high spectral resolution lidar (HSRL) data that are collocated with in-water optical measurements.

Hu, Yongxiang↗

Quantum mechanical differential and integral cross sections for the C({sup 1}D) + H{sub 2}(ν = 0, j = 0) → CH(ν′, j′) + H reaction

Accurate quantum dynamics calculations for the C({sup 1}D) + H{sub 2} reaction are performed using a real wave packet approach with full Coriolis coupling. The newly constructed ZMB-a ab initio potential energy surface [Zhang et al., J. Chem. Phys. 140, 234301 (2014)] is used. The integral cross sections (ICSs), differential cross sections (DCSs), and product state distributions are obtained over a wide range of collision energies. In contrast to previous accurate quantum dynamics calculations on the reproducing kernel Hilbert space potential energy surface, the present total ICS is much larger at low collision energies, yielding larger rate coefficients in better agreement with experiment and with slight inverse temperature dependence. Meanwhile, interesting nonstatistical behaviors in the DCSs are revealed. In particular, the DCSs display strong oscillations with the collision energy; forward biased product angular distribution appears when only small J partial wave contributions are included; alternate forward and backward biases emerge with very small increments of collision energy; and the rotational state-resolved DCSs show strong oscillations with the scattering angle. Nevertheless, the total DCSs can be roughly regarded as backward–forward symmetric over the whole energy range and are in reasonably good agreement with the available experimental measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Distributed Fiber Sensors With High Spatial Resolution in Extreme Radiation Environments in Nuclear Reactor Cores

This paper is a comprehensive experimental report on the neutron radiation effects of distributed optical fiber sensors with enhanced Rayleigh scattering profiles in an in-pile environment. Femtosecond laser direct writing was used to inscribe Type-II modifications in standard telecom fibers and radiation-hardened fibers with fluorine-doped cores. Rayleigh backscattering signals were enhanced for continuous 1.5 m. In-pile lead-out sensors tests were carried out at the MIT Research Reactor for two months, which was operated at a nominal power of 5.7 MW with fast neutron (>0.1 MeV) flux of 1.29 × 1014 n/cm2/s and an in-core temperature of up to 560°C. Using the Optical Frequency Domain Reflectometry technique, the backscattering profiles of fiber sensors were interrogated with a 3-cm spatial resolution to monitor the temperature profile of the reactor. Results show that laser inscribed Type-II modifications in the form of nanogratings are highly stable against extreme temperature and ionizing radiation. Both standard telecom fibers and radiation-hardened fibers with laser-enhanced Rayleigh profiles can continuously perform distributed temperature measurements over the entire duration of the in-pile testing. Temperature coefficients of sensors and spectral shift quality were studied as functions of total radiation fluence. To the best of our knowledge, we present for the first time, the temperature profile of an operating nuclear reactor core with 3-cm spatial resolution, enabled by distributed fiber sensors with laser-enhanced Rayleigh scattering profiles. The high spatial resolution measurements can provide valuable data for the design and validation of digital twin and virtual reality of nuclear energy systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Pan-Arctic seasonal cycles and long-term trends of aerosol properties from 10 observatories

Even though the Arctic is remote, aerosol properties observed there are strongly influenced by anthropogenic emissions from outside the Arctic. This is particularly true for the so-called Arctic haze season (January through April). In summer (June through September), when atmospheric transport patterns change, and precipitation is more frequent, local Arctic sources, i.e., natural sources of aerosols and precursors, play an important role. Over the last few decades, significant reductions in anthropogenic emissions have taken place. At the same time a large body of literature shows evidence that the Arctic is undergoing fundamental environmental changes due to climate forcing, leading to enhanced emissions by natural processes that may impact aerosol properties. In this study, we analyze 9 aerosol chemical species and 4 particle optical properties from 10 Arctic observatories (Alert, Kevo, Pallas, Summit, Thule, Tiksi, Barrow/Utgiavik, Villum, and Gruvebadet and Zeppelin Observatory – both at Ny-Ålesund Research Station) to understand changes in anthropogenic and natural aerosol contributions. Variables include equivalent black carbon, particulate sulfate, nitrate, ammonium, methanesulfonic acid, sodium, iron, calcium and potassium, as well as scattering and absorption coefficients, single scattering albedo and scattering Ångström exponent. First, annual cycles are investigated, which despite anthropogenic emission reductions still show the Arctic haze phenomenon. Second, long-term trends are studied using the Mann–Kendall Theil–Sen slope method. We find in total 41 significant trends over full station records, i.e., spanning more than a decade, compared to 26 significant decadal trends. The majority of significantly declining trends is from anthropogenic tracers and occurred during the haze period, driven by emission changes between 1990 and 2000. For the summer period, no uniform picture of trends has emerged. Twenty-six percent of trends, i.e., 19 out of 73, are significant, and of those 5 are positive and 14 are negative. Negative trends include not only anthropogenic tracers such as equivalent black carbon at Kevo, but also natural indicators such as methanesulfonic acid and non-sea-salt calcium at Alert. Positive trends are observed for sulfate at Gruvebadet. No clear evidence of a significant change in the natural aerosol contribution can be observed yet. However, testing the sensitivity of the Mann–Kendall Theil–Sen method, we find that monotonic changes of around 5 % yr –1 in an aerosol property are needed to detect a significant trend within one decade. This highlights that long-term efforts well beyond a decade are needed to capture smaller changes. It is particularly important to understand the ongoing natural changes in the Arctic, where interannual variability can be high, such as with forest fire emissions and their influence on the aerosol population. To investigate the climate-change-induced influence on the aerosol population and the resulting climate feedback, long-term observations of tracers more specific to natural sources are needed, as well as of particle microphysical properties such as size distributions, which can be used to identify changes in particle populations which are not well captured by mass-oriented methods such as bulk chemical composition.

54 ENVIRONMENTAL SCIENCES↗

Geometric phase effects in ultracold hydrogen exchange reaction

The role of the geometric phase effect on chemical reaction dynamics is explored by examining the hydrogen exchange process in the fundamental H+HD reaction. Results are presented for vibrationally excited HD molecules in the v = 4 vibrational level and for collision energies ranging from 1 μK to 100 K. It is found that, for collision energies below 3 K, inclusion of the geometric phase leads to dramatic enhancement or suppression of the reaction rates depending on the final quantum state of the HD molecule. The effect was found to be the most prominent for rotationally resolved integral and differential cross sections but it persists to a lesser extent in the vibrationally resolved and total reaction rate coefficients. However, no significant GP effect is present in the reactive channel leading to the D+H 2 product or in the D+H 2 $(v=4,j=0)\,\to $ HD+H reaction. A simple interference mechanism involving inelastic (nonreactive) and exchange scattering amplitudes is invoked to account for the observed GP effects. The computed results also reveal a shape resonance in the H+HD reaction near 1 K and the GP effect is found to influence the magnitude of the resonant part of the cross section. In conclusion, experimental detection of the resonance may allow a sensitive probe of the GP effect in the H+HD reaction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Air Mass Factor Formulation for Spectroscopic Measurements from Satellites: Application to Formaldehyde Retrievals from the Global Ozone Monitoring Experiment

We present a new formulation for the air mass factor (AMF) to convert slant column measurements of optically thin atmospheric species from space into total vertical columns. Because of atmospheric scattering, the AMF depends on the vertical distribution of the species. We formulate the AMF as the integral of the relative vertical distribution (shape factor) of the species over the depth of the atmosphere, weighted by altitude-dependent coefficients (scattering weights) computed independently from a radiative transfer model. The scattering weights are readily tabulated, and one can then obtain the AMF for any observation scene by using shape factors from a three dimensional (3-D) atmospheric chemistry model for the period of observation. This approach subsequently allows objective evaluation of the 3-D model with the observed vertical columns, since the shape factor and the vertical column in the model represent two independent pieces of information. We demonstrate the AMF method by using slant column measurements of formaldehyde at 346 nm from the Global Ozone Monitoring Experiment satellite instrument over North America during July 1996. Shape factors are cumputed with the Global Earth Observing System CHEMistry (GEOS-CHEM) global 3-D model and are checked for consistency with the few available aircraft measurements. Scattering weights increase by an order of magnitude from the surface to the upper troposphere. The AMFs are typically 20-40% less over continents than over the oceans and are approximately half the values calculated in the absence of scattering. Model-induced errors in the AMF are estimated to be approximately 10%. The GEOS-CHEM model captures 50% and 60% of the variances in the observed slant and vertical columns, respectively. Comparison of the simulated and observed vertical columns allows assessment of model bias.

Palmer, Paul I.↗

Simulating PACE Global Ocean Radiances

The NASA PACE mission is a hyper-spectral radiometer planned for launch in the next decade. It is intended to provide new information on ocean biogeochemical constituents by parsing the details of high resolution spectral absorption and scattering. It is the first of its kind for global applications and as such, poses challenges for design and operation. To support pre-launch mission development and assess on-orbit capabilities, the NASA Global Modeling and Assimilation Office has developed a dynamic simulation of global water-leaving radiances, using an ocean model containing multiple ocean phytoplankton groups, particulate detritus, particulate inorganic carbon (PIC), and chromophoric dissolved organic carbon (CDOC) along with optical absorption and scattering processes at 1 nm spectral resolution. The purpose here is to assess the skill of the dynamic model and derived global radiances. Global bias, uncertainty, and correlation are derived using available modern satellite radiances at moderate spectral resolution. Total chlorophyll, PIC, and the absorption coefficient of CDOC (aCDOC), are simultaneously assimilated to improve the fidelity of the optical constituent fields. A 5-year simulation showed statistically significant (P < 0.05) comparisons of chlorophyll (r = 0.869), PIC (r = 0.868), and a CDOC (r =0.890) with satellite data. Additionally, diatoms (r = 0.890), cyanobacteria (r = 0.732), and coccolithophores (r = 0.716) were significantly correlated with in situ data. Global assimilated distributions of optical constituents were coupled with a radiative transfer model (Ocean-Atmosphere Spectral Irradiance Model, OASIM) to estimate normalized water-leaving radiances at 1 nm for the spectral range 250-800 nm. These unassimilated radiances were within 0.074 mW/sq cm/micron/sr of MODIS-Aqua radiances at 412, 443, 488, 531, 547, and 667 nm. This difference represented a bias of 10.4% (model low). A mean correlation of 0.706 (P < 0.05) was found with global distributions of MODIS radiances. These results suggest skill in the global assimilated model and resulting radiances. The reported error characterization suggests that the global dynamical simulation can support some aspects of mission design and analysis. For example, the high spectral resolution of the simulation supports investigations of band selection. The global nature of the radiance representations supports investigations of satellite observing scenarios. Global radiances at bands not available in current and past missions support investigations of mission capability. PACE, ocean color, water-leaving radiances, biogeochemical model, radiative transfer model

PIC↗

Analytic Sensitivity Coefficients for General Multigroup Infinite Medium k-Eigenvalue Problems

This work presents a general set of equations that can be used to rapidly generate new benchmarks to verify nuclear data sensitivity calculations. The general multigroup infinite medium k-eigenvalue neutron transport equation is used to derive analytic expressions for the infinite medium k-eigenvalue, the scalar neutron flux and adjoint flux, and the sensitivity of k∞ to perturbations in the multigroup nuclear data of a single species, isotropic and elastic scattering, material. The multigroup nuclear data for U-235 and U-238 is presented along with their corresponding k-eigenvalues, forward flux, adjoint flux, and sensitivity profiles, which include the sensitivity of k∞ to the total, fission, capture, and scattering macroscopic cross sections as well as to the group-to-group scattering cross section matrix, group-wise fission neutron production, and the unconstrained and constrained fission neutron energy distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Experimental flow coefficients of a full-coverage film-cooled-vane chamber

Ambient- and elevated-temperature flow tests were performed on a four-times-actual-size model of an impingement- and film-cooled segment of a core engine turbine vane. Tests were conducted with the impingement and film cooling plates combined to form a chamber and also with each of the individual separated plates. For the combined tests, the proximity of the film cooling plate affected the flow of coolant through the impingement plate, but not conversely. Impingement flow is presented in terms of a discharge coefficient, and the film cooling flow discharging into still air with no main stream gas flow is presented in terms of a total pressure-loss coefficient. The effects of main stream gas flow on discharge from the film cooling holes are evaluated as a function of coolant to main-stream gas momentum flux ratio. A smoothing technique is developed that identifies and helps reduce flow measurement data scatter.

Meitner, P. L.↗

LASE validation experiment: preliminary processing of relative humidity from LASE derived water vapor in the middle to upper troposphere

Lidar Atmospheric Sensing Experiment (LASE) is the first fully engineered, autonomous airborne DIAL (Differentials Absorption Lidar) system to measure water vapor, aerosols, and clouds throughout the troposphere. This system uses a double-pulsed Ti:sapphire laser, which is pumped by a frequency-doubled flashlamp-pumped Nd: YAG laser, to transmit light in the 815 mn absorption band of water vapor. LASE operates by locking to a strong water vapor line and electronically tuning to any spectral position on the absorption line to choose the suitable absorption cross-section for optimum measurements over a range of concentrations in the atmosphere. During the LASE Validation Experiment, which was conducted over Wallops Island during September, 1995, LASE operated on either the strong water line for measurements in middle to upper troposphere, or on the weak water line for measurements made in the middle to lower troposphere including the boundary layer. Comparisons with water vapor measurements made by airborne dew point and frost point hygrometers, NASA/GSFC (Goddard Space Flight Center) Raman Lidar, and radiosondes showed the LASE water vapor mixing ratio measurements to have an accuracy of better than 6% or 0.01 g/kg, whichever is larger, throughout the troposphere. In addition to measuring water vapor mixing ratio profiles, LASE simultaneously measures aerosol backscattering profiles at the off-line wavelength near 815 nm from which atmospheric scattering ratio (ASR) profiles are calculated. ASR is defined as the ratio of total (aerosol + molecular) atmospheric scattering to molecular scattering. Assuming a region with very low aerosol loading can be identified, such as that typically found just below the tropopause, then the ASR can be determined. The ASR profiles are calculated by normalizing the scattering in the region containing enhanced aerosols to the expected scattering by the "clean" atmosphere at that altitude. Images of the total ASR clearly depict cloud regions, including multiple cloud layers, thin upper level cirrus, etc., throughout the troposphere. New data products that are being derived from the LASE aerosol and water measurements include: 1) aerosol extinction coefficient, 2) aerosol optical thickness, 3) precipitable water vapor, and 4) relative humidity (RH). These products can be compared with airborne in-situ, and ground and satellite remote sensing measurements,. This paper presents a preliminary examination of RH profiles in the middle to upper troposphere that are generated from LASE measured water vapor mixing ratio profiles coupled with rawinsonde profiles of temperature and pressure.

Brackett, Vincent G.↗

Monte Carlo calculations of the extraction of scintillation light from cryogenic $N$-type GaAs

We report the high scintillation luminosity of n-type GaAs at 10 °K is surprising because (1) with a refractive index of 3.5, escape is inhibited by total internal reflection and (2) narrow-beam experiments at 90 °K report infrared absorption coefficients of several per cm. This paper presents Monte Carlo calculations showing that the high luminosity at 10 °K can be explained if (1) the narrow-beam absorption is almost all optical scattering and (2) the absolute absorption coefficient is below 0.1 per cm. Sixteen surface reflector configurations are simulated for a range of internal scattering and absolute absorption coefficients, and these can guide the design of cryogenic scintillating GaAs targets for the direct detection of dark matter. The discussion section presents a possible infrared scattering mechanism based on the metallic nature of n-type GaAs. A supplement file describes (1) the Monte Carlo program steps in detail and (2) how narrow-beam and integrating sphere experiments can measure the cryogenic optical scattering and absolute absorption coefficients.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Theoretical calculations of rotationally inelastic collisions of He with NaK(A {sup 1}Σ{sup +}): Transfer of population, orientation, and alignment

We have performed extensive calculations to investigate thermal energy, rotationally inelastic collisions of NaK (A{sup 1}Σ{sup +}) with He. We determined a potential energy surface using a multi-reference configuration interaction wave function as implemented by the GAMESS electronic structure code, and we have performed coupled channel scattering calculations using the Arthurs and Dalgarno formalism. We also calculate the Grawert coefficients B{sub λ}(j, j′) for each j → j′ transition. These coefficients are used to determine the probability that orientation and alignment are preserved in collisions taking place in a cell environment. The calculations include all rotational levels with j or j′ between 0 and 50, and total (translational and rotational) energies in the range 0.0002–0.0025 a.u. (∼44–550 cm{sup −1}). The calculated cross sections for transitions with even values of Δj tend to be larger than those for transitions with odd Δj, in agreement with the recent experiments of Wolfe et al. (J. Chem. Phys. 134, 174301 (2011)). The calculations of the energy dependence of the cross sections and the calculations of the fraction of orientation and alignment preserved in collisions also exhibit distinctly different behaviors for odd and even values of Δj. The calculations also indicate that the average fraction of orientation or alignment preserved in a transition becomes larger as j increases. We interpret this behavior using the semiclassical model of Derouard, which also leads to a simple way of visualizing the distribution of the angles between the initial and final angular momentum vectors j and j′. Finally, we compare the exact quantum results for j → j′ transitions with results based on the simpler, energy sudden approximation. That approximation is shown to be quite accurate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Predicting CaO-(MgO)-Al2O3-SiO2 glass reactivity in alkaline environments from force field molecular dynamics simulations

In this investigation, force field-based molecular dynamics (MD) simulations have been employed to generate detailed structural representations for a range of amorphous quaternary CaO-MgO-Al{sub 2}O{sub 3}-SiO{sub 2} (CMAS) and ternary CaO-Al{sub 2}O{sub 3}-SiO{sub 2} (CAS) glasses. Comparison of the simulation results with select experimental X-ray and neutron total scattering and literature data reveals that the MD-generated structures have captured the key structural features of these CMAS and CAS glasses. Based on the MD-generated structural representations, we have developed two structural descriptors, specifically (i) average metal oxide dissociation energy (AMODE) and (ii) average self-diffusion coefficient (ASDC) of all the atoms at melting. Both structural descriptors are seen to more accurately predict the relative glass reactivity than the commonly used degree of depolymerization parameter, especially for the eight synthetic CAS glasses that span a wide compositional range. Hence these descriptors hold great promise for predicting CMAS and CAS glass reactivity in alkaline environments from compositional information.

36 MATERIALS SCIENCE↗

Sci—Thur PM: Imaging — 05: Calibration of a SPECT/CT camera for quantitative SPECT with {sup 99m}Tc

While quantitation is the norm in PET, it is not widely available yet in SPECT. This work's aim was to calibrate a commercially available SPECT/CT system to perform quantitative SPECT. Counting sensitivity, dead-time (DT) constant and partial volume effect (PVE) of the system were assessed. A dual-head Siemens SymbiaT6 SPECT/CT camera equipped with low energy high-resolution collimators was studied. {sup 99m}Tc was the radioisotope of interest because of its wide usage in nuclear medicine. First, point source acquisitions were performed (activity: 30–990MBq). Further acquisitions were then performed with a uniform Jaszczak phantom filled with water at high activity (25–5000MBq). PVE was studied using 6 hot spheres (diameters: 9.9–31.2 mm) filled with {sup 99m}Tc (2.8MBq/cc) in the Jaszczak phantom, which was: (1) empty, (2) water-filled and (3) water-filled with low activity (0.1MBq/cc). The data was reconstructed with the Siemens's Flash3D iterative algorithm with 4 subsets and 8 iterations, attenuation-correction (AC) and scatter-correction (SC). DT modelling was based on the total spectrum counting rate. Sensitivity was assessed using AC-SC reconstructed SPECT data. Sensitivity and DT for the sources were 99.51±1.46cps/MBq and 0.60±0.04µs. For the phantom, sensitivity and DT were 109.9±2.3cps/MBq and 0.62±0.13µs. The recovery-coefficient varied from 5% for the 9.9mm, to 80% for the 31.2mm spheres. With our calibration methods, both sensitivity and DT constant of the SPECT camera had little dependence on the object geometry and attenuation. For small objects of known size, recovery-coefficient can be applied to correct PVE. Clinical quantitative SPECT appears to be possible and has many potential applications.

07 ISOTOPE AND RADIATION SOURCES↗

Bremsstrahlung in the scattering of low-energy electrons by neutral atomic systems

By elementary methods, the cross section for electron-atom and electron-molecule bremsstrahlung is computed in the limit when the incident electron energy is much less than Ry. The procedure employs the classical soft-photon emission probability formula for general (h/2pi)(omega), yielding a simple expression for the bremsstrahlung cross section in terms of the total elastic scattering cross section. The validity of the method is discussed, and results are compared with more elaborate and accurate calculations. Comparison is made with ('free-free') opacity calculations for the associated process at the temperature (6300 K) of the solar atmosphere. For chi sub omega = (h/2pi)(omega)/kT = 1, the computed absorption coefficient is within 2, 7, and 12 percent of accurate calculations for scatterings by H, He, and H2, respectively. The general dependence of the opacity on chi sub omega is described well by the simple formula, although the error is larger for higher chi sub omega; it is suggested that the inaccuracy at high frequencies is due to the failure of the soft-photon approximation.

Gould, R. J.↗