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At least 343 records · Page 19

Aerosol properties computed from aircraft-based observations during the ACE- Asia campaign: A case study of lidar ratio closure and aerosol radiative effects - 2

For a vertical profile with three distinct layers (marine boundary, pollution and dust), observed during the ACE-Asia campaign, we carried out a comparison between the modeled lidar ratio vertical profile and that obtained from collocated airborne NASA AATS-14 sunphotometer and shipborne Micro-Pulse Lidar (MPL) measurements. Vertically resolved lidar ratio was calculated from two size distribution vertical profiles - one obtained by inversion of sunphotometer-derived extinction spectra, and one measured in-situ - combined with the same refractive index model based on aerosol chemical composition. The aerosol model implies single scattering albedos of 0.78 - 0.81 and 0.93 - 0.96 at 0.523 microns (the wavelength of the lidar measurements), in the pollution and dust layers, respectively. The lidar ratios calculated from the two size distribution profiles have close values in the dust layer; they are however, significantly lower than the lidar ratios derived from combined lidar and sunphotometer measurements, most probably due to the use of a simple nonspherical model with a single particle shape in our calculations. In the pollution layer, the two size distribution profiles yield generally different lidar ratios. The retrieved size distributions yield a lidar ratio which is in better agreement with that derived from lidar/sunphotometer measurements in this layer, with still large differences at certain altitudes (the largest relative difference was 46%). We explain these differences by non-uniqueness of the result of the size distribution retrieval and lack of information on vertical variability of particle refractive index. Radiative transfer calculations for this profile showed significant atmospheric radiative forcing, which occurred mainly in the pollution layer. We demonstrate that if the extinction profile is known then information on the vertical structure of absorption and asymmetry parameter is not significant for estimating forcing at TOA and the surface, while it is of importance for estimating vertical profiles of radiative forcing and heating rates.

Kuzmanoski, Maja↗

C-12/C-13 Ratio in Ethane on Titan and Implications for Methane's Replenishment

The C-12/C-13 abundance ratio in ethane in the atmosphere of Titan has been measured at 822 cm(sup -1) from high spectral resolution ground-based observations. The value 89(8), coincides with the telluric standard and also agrees with the ratio seen in the outer planets. It is almost identical to the result for ethane on Titan found by the composite infrared spectrometer (CIRS) on Cassini. The C-12/C-13 ratio for ethane is higher than the ratio measured in atmospheric methane by Cassini/Huygens GCMS, 82.3(l), representing an enrichment of C-12 in the ethane that might be explained by a kinetic isotope effect of approximately 1.1 in the formation of methyl radicals. If methane is being continuously resupplied to balance photochemical destruction, then we expect the isotopic composition in the ethane product to equilibrate at close to the same C-12/C-13 ratio as that in the supply. The telluric value of the ratio in ethane then implies that the methane reservoir is primordial.

Jennings, Donald E.↗

Extinction-to-Backscatter Ratios of Saharan Dust Layers Derived from In-Situ Measurements and CALIPSO Overflights During NAMMA

We determine the extinction-to-backscatter (Sa) ratios of dust using (1) airborne in-situ measurements of microphysical properties, (2) modeling studies, and (3) the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) observations recorded during the NASA African Monsoon Multidisciplinary Analyses (NAMMA) field experiment conducted from Sal, Cape Verde during Aug-Sept 2006. Using CALIPSO measurements of the attenuated backscatter of lofted Saharan dust layers, we apply the transmittance technique to estimate dust Sa ratios at 532 nm and a 2-color method to determine the corresponding 1064 nm Sa. This method yielded dust Sa ratios of 39.8 plus or minus 1.4 sr and 51.8 plus or minus 3.6 sr at 532 nm and 1064 nm, respectively. Secondly, Sa at both wavelengths is independently calculated using size distributions measured aboard the NASA DC-8 and estimates of Saharan dust complex refractive indices applied in a T-Matrix scheme. We found Sa ratios of 39.1 plus or minus 3.5 sr and 50.0 plus or minus 4 sr at 532 nm and 1064 nm, respectively, using the T-Matrix calculations applied to measured size spectra. Finally, in situ measurements of the total scattering (550 nm) and absorption coefficients (532 nm) are used to generate an extinction profile that is used to constrain the CALIPSO 532 nm extinction profile and thus generate a stratified 532 nm Sa. This method yielded an Sa ratio at 532 nm of 35.7 sr in the dust layer and 25 sr in the marine boundary layer consistent with a predominantly seasalt aerosol near the ocean surface. Combinatorial simulations using noisy size spectra and refractive indices were used to estimate the mean and uncertainty (one standard deviation) of these Sa ratios. These simulations produced a mean (plus or minus uncertainty) of 39.4 (plus or minus 5.9) sr and 56.5 (plus or minus 16.5) sr at 532 nm and 1064 nm, respectively, corresponding to percent uncertainties of 15% and 29%. These results will provide a measurements-based estimate of the dust Sa for use in backscatter lidar inversion algorithms such as CALIOP.

Omar, Ali H.↗

Pressure Ratio to Thermal Environments

A pressure ratio to thermal environments (PRatTlE.pl) program is a Perl language code that estimates heating at requested body point locations by scaling the heating at a reference location times a pressure ratio factor. The pressure ratio factor is the ratio of the local pressure at the reference point and the requested point from CFD (computational fluid dynamics) solutions. This innovation provides pressure ratio-based thermal environments in an automated and traceable method. Previously, the pressure ratio methodology was implemented via a Microsoft Excel spreadsheet and macro scripts. PRatTlE is able to calculate heating environments for 150 body points in less than two minutes. PRatTlE is coded in Perl programming language, is command-line-driven, and has been successfully executed on both the HP and Linux platforms. It supports multiple concurrent runs. PRatTlE contains error trapping and input file format verification, which allows clear visibility into the input data structure and intermediate calculations.

Lopez, Pedro↗

Cause and Cure - Deterioration in Accuracy of CFD Simulations With Use of High-Aspect-Ratio Triangular Tetrahedral Grids

Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD re-searchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions and also cause numerical instability. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where triangular/tetrahedral elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identities the reason behind the difficulties in use of such high-aspect ratio triangular/tetrahedral elements is presented here. As will be shown, it turns out that the degree of accuracy deterioration of gradient computation involving a triangular element is hinged on the value of its shape factor Gamma def = sq sin Alpha1 + sq sin Alpha2 + sq sin Alpha3, where Alpha1; Alpha2 and Alpha3 are the internal angles of the element. In fact, it is shown that the degree of accuracy deterioration increases monotonically as the value of Gamma decreases monotonically from its maximal value 9/4 (attained by an equilateral triangle only) to a value much less than 1 (associated with a highly obtuse triangle). By taking advantage of the fact that a high-aspect ratio triangle is not necessarily highly obtuse, and in fact it can have a shape factor whose value is close to the maximal value 9/4, a potential solution to avoid accuracy deterioration of gradient computation associated with a high-aspect ratio triangular grid is given. Also a brief discussion on the extension of the current mathematical framework to the tetrahedral-grid case along with some of the practical results of this extension is also provided. Furthermore, through the use of numerical simulations of practical viscous problems involving high-Reynolds number flows, the effectiveness of the gradient evaluation procedures within the CESE framework (that have their basis on the analysis presented here) to produce accurate and stable results on such high-aspect ratio meshes is also showcased.

CESE Method↗

Modeling the Effects of Liquid-to-Gas Density Ratio on Slosh Dynamics

Mechanical models are commonly used in Guidance, Navigation and Controls (GN&C) system-level models to represent propellant slosh forces on launch vehicles and spacecraft. The slosh model parameters are typically predicted using semi-empirical analytical methods that are based on experimental data for high liquid-to-gas density ratios (such as water and air at standard sea level conditions). Model parameter calculations typically neglect any contribution to slosh dynamics from the gas phase. However, some cryogenic propellant systems operate in conditions where the density ratio can be orders of magnitude smaller. Analytical and computational modeling was used in this effort to investigate the effects of liquid-to-gas density ratio on slosh dynamics. No experimental data nor previous studies are available at this time that quantify the effect of liquid-to-gas density ratio on slosh dynamics. However, in a recent CFD study, results showed that density ratio can have a significant effect on slosh model parameters. In this study, a dual pendulum slosh model was created that distinctly represents both liquid and gas phase dynamics. Solution of the model, which invokes the Euler-Lagrange equations of motion, demonstrates that slosh frequency is a combination of liquid slosh frequency and gas phase slosh frequency. Additionally, it shows that slosh mass is reduced due to the opposing motion of the gas phase with respect to that of the liquid phase. The slosh model parameter trends were verified using Computational Fluid Dynamics (CFD) analysis results for various liquid-to-gas density ratios, tanks, and fill levels.

Christopher D Moore↗

Equivalence Ratio Scans in a Rotating Detonation Engine

Published data for run times exceeding a few seconds in rotating detonation engines (RDEs) is rare, but long duration tests are necessary to understand both transient and persistent phenomena in RDE operation. Previous work has noted different detonation wave modes at different equivalence ratios. In the current study, multiple long-duration runs with constant air flow rate and variable equivalence ratio are conducted in a hydrogen-fueled, water-cooled RDE. Analysis of the capillary tube averaged pressure (CTAP) data reveals a strong correlation with equivalence ratio as well as a small time dependency due to transient thermal processes. Ion probe measurements are used to analyze detonation wave frequencies and modes, both of which are strongly dependent on the equivalence ratio. Mode transitions are observed to occur consistently as the equivalence ratio is traversed between 0.55 and 0.60. These transitions are also found to be a function of the direction of changing equivalence ratio (ascending or descending) and time.

Boyette, Wesley R.↗

Equivalence Ratio Scans in a Rotating Detonation Engine

Published data for run times exceeding a few seconds in rotating detonation engines (RDEs) is rare, but long duration tests are necessary to understand both transient and persistent phenomena in RDE operation. Previous work has noted different detonation wave modes at different equivalence ratios. In the current study, multiple long-duration runs with constant air flow rate and variable equivalence ratio are conducted in a hydrogen-fueled, water-cooled RDE. Analysis of the capillary tube averaged pressure (CTAP) data reveals a strong correlation with equivalence ratio as well as a small time dependency due to transient thermal processes. Ion probe measurements are used to analyze detonation wave frequencies and modes, both of which are strongly dependent on the equivalence ratio. Mode transitions are observed to occur consistently as the equivalence ratio is traversed between 0.55 and 0.60. These transitions are also found to be a function of the direction of changing equivalence ratio (ascending or descending) and time.

Boyette, Wesley R.↗

System efficiency of packed bed TES with radial flow vs. axial flow – Influence of aspect ratio

Here, this paper compares the net system efficiency, including thermal efficiency and pressure drop effects, of radial versus axial flow packed beds for thermal energy storage. The traditional packed bed system is a cylindrical geometry where fluid flows axially from one end to another. However, issues of thermal stratification and high-pressure drop have led to recent studies on radial flow systems. One potential benefit is the reduced pressure drop in a radial flow system. This paper compares the performance of radial flow and axial flow systems at a range of aspect ratios (AR = H/D bed ) from 0.21 to 1.92 using a numerical model where the storage volume is held constant in all cases. When the radial flow bed is at a low aspect ratio (short/wide), the thermal front is improved but the pressure drop is high. At a high aspect ratio, the velocity is reduced in radial flow, leading to decreased pressure drop but an increased spreads in the thermal front that lowers thermal efficiency. The opposite trends are noted in axial flow. Thermal efficiencies of 83–91 % were noted for radial flow, while they ranged from 85 to 94 % in axial flow. Net efficiencies including pressure drop ranged from 74 to 82 % for radial flow and 80–87 % for axial flow. In both systems, a peak net efficiency was noted between the highest and lowest aspect ratio. While some aspect ratios with radial flow outperform axial flow from a net efficiency perspective, the results show that the highest net efficiency from axial flow is higher than that from radial flow. Overall, this paper highlights the importance of innovative TES designs and their potential to improve energy efficiency.

25 ENERGY STORAGE↗

Improved plutonium and americium photon branching ratios from microcalorimeter gamma spectroscopy

Photon branching ratios are critical input data for activities such as nuclear materials protection and accounting because they allow material compositions to be extracted from measurements of gamma-ray intensities. Uncertainties in these branching ratios are often a limiting source of uncertainty in composition determination. Here, we use high statistics, high resolution - (60–70 eV full-width-at-half-maximum at 100 keV) gamma-ray spectra acquired using microcalorimeter sensors to substantially reduce the uncertainties for 11 plutonium ( 238 Pu, 239 Pu, 241 Pu) and 241 Am branching ratios important for material control and accountability and nuclear forensics in the energy range of 125 keV to 208 keV. Lastly, we show a reduction in uncertainty of over a factor of three for one branching ratio and a factor of 2–3 for four branching ratios.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Application of helium line intensity ratio spectroscopy to xenon plasma in E × B Penning discharge

Here, we propose the application of helium line intensity ratio spectroscopy in a low-pressure (0.3 mTorr) xenon E × B discharge with an electron temperature of ~2 eV and a density of 10 10 –10 11 cm –3 . We successfully identified the helium atom line emissions at 388.9, 447.1, 501.6, 504.8, and 706.5 nm with helium pressures of up to ~20 mTorr. The measured electron temperature, density, and I–V characteristics of the discharge remained almost constant in all helium pressures in the present experiment, indicating the suitability of the helium gas as a diagnostic gas. The results of helium line intensity ratio spectroscopy using the line emissions at 388.9, 447.1, and 504.8 nm showed fair agreement with the Langmuir probe measurement. Considering the trade-off relationship between the disturbance introduced by the helium gas and the signal-to-noise ratio, we conclude that a helium pressure of approximately 4 mTorr (approximately 13 times the partial pressure of xenon) represents the optimal pressure range for the application of the helium line emission intensity ratio method to this xenon plasma. It is found that the use of the line emissions at 501.6 and 706.5 nm result in a significant disturbance in the helium line intensity ratio method due to the radiation trapping effect.

helium line intensity ratio spectroscopy↗

A Novel Framework for Quantifying past Methane Recycling by Sphagnum-Methanotroph Symbiosis Using Carbon and Hydrogen Isotope Ratios of Leaf Wax Biomarkers

The concentration of atmospheric methane is strongly linked to variations in Earth's climate. Currently, we can directly reconstruct the total atmospheric concentration of methane, but not individual terms of the methane cycle. Northern wetlands, dominated by Sphagnum, are an important contributor of atmospheric methane, and we seek to understand the methane cycle in these systems. We present a novel method for quantifying the proportion of carbon Sphagnum assimilates from its methanotrophic symbionts using stable isotope ratios of leaf-wax biomarkers. Carbon isotope ratios of Sphagnum compounds are determined by two competing influences, water content and the isotope ratio of source carbon. We disentangled these effects using a combined hydrogen and carbon isotope approach. We constrained Sphagnum water content using the contrast between the hydrogen isotope ratios of Sphagnum and vascular plant biomarkers. We then used Sphagnum water content to calculate the carbon isotope ratio of Sphagnum's carbon pool. Using a mass balance equation, we calculated the proportion of recycled methane contributed to the Sphagnum carbon pool, 'PRM.' We quantified PRM in peat monoliths from three microhabitats in the Mer Bleue peatland complex. Modern studies have shown that water table depth and vegetation have strong influences on the peatland methane cycle on instrumental time scales. With this new approach, delta C-13 of Sphagnum compounds are now a useful tool for investigating the relationships among hydrology, vegetation, and methanotrophy in Sphagnum peatlands over the time scales of entire peatland sediment records, vital to our understanding of the global carbon cycle through the Late Glacial and Holocene.

air pollution↗

A preliminary investigation into the feasibility of laser ablation U–Pb isotope ratio measurement via all‐faraday cup detection with 10 11 ‐ and 10 13 ‐Ω amplifiers on the Neoma multicollector‐inductively coupled plasma‐mass spectrometer

Rationale Signal detection for uranium–lead (U–Pb) dating of zircon is typically performed via ion counters. Here, we develop a preliminary understanding of the strengths and limitations of faraday‐cup‐based detection. Methods A suite of zircon reference materials and the NIST‐610 glass were sampled using laser ablation followed by U–Pb isotope ratio measurement on a Neoma multicollector‐inductively coupled plasma‐mass spectrometer. Results We were able to produce geologically accurate 207 Pb/ 206 Pb, 206 Pb/ 238 U, and 207 Pb/ 235 U ratios for the NIST‐610 glass and the zircon standards, with ages ranging from ~2.5 Ga to ~337 Ma (TanBrown A, Oracle, 91550, Mud Tank, Temora, and Plešovice). Two of the younger zircon standards examined (94‐35, ~55.6 Ma, and Fish Canyon, 28.6 Ma) yielded accurate 206 Pb/ 238 U but not 207 Pb/ 235 U or 207 Pb/ 206 Pb ratios, whereas the youngest zircon standard (Penglai, ~4.4 Ma) failed for all three ratios of interest. The accuracy and precision of the all‐faraday method are directly tied to signal intensity, with reliable data capable of being produced even when both isotopes in a ratio have signals below ~0.001 V (equivalent to ~62 500 cps on an ion counter). Conclusion The all‐faraday cup multicollection method provides sufficient sensitivity to obtain geologically meaningful U–Pb data, with possible advantages being that laser pit depth‐dependent changes in the observed interelemental fractionation behavior may be easier to correct using a static collector configuration compared to when the ion beam is swept across a single detector while also removing the need for an interdetector‐type calibration. Further work is needed to refine the all‐faraday cup method (e.g., application of background subtraction and common Pb corrections, outlier removal, and interelement as well as down‐hole fractionation corrections), but our initial results demonstrate that the faraday detector method has sufficient sensitivity to warrant further study.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Measurement of material isotopics and atom number ratio with α-particle spectroscopy for a NIFFTE fission Time Projection Chamber actinide target

In this work, we present the results of a measurement of isotopic concentrations and atomic number ratio of a double-sided actinide target using α-spectroscopy and mass spectrometry. The double-sided actinide target, with predominantly 239 Pu on one side and 235 U on the other, was used in the fission Time Projection Chamber (fissionTPC) for a measurement of the neutron-induced fission cross-section ratio between the two isotopes. The measured atomic number ratio is needed to extract an absolute measurement fission cross-section ratio. The 239 Pu/ 235 U atom number ratio was measured with a combination of mass spectrometry and α-spectroscopy with a planar silicon detector achieving uncertainties of less than 1%. Different strategies for estimating isotopic concentration from the α-spectrum are presented to demonstrate the potential of these methods for non-destructive target assay. We found that a combination of fitting spectra with constraints from mass spectrometry, and summing counts in a region of the spectrum provided the most consistent results with the lowest uncertainty.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Calibration-free analysis of Li isotope ratios using laser ablation and laser absorption spectroscopy

We introduce a rapid, calibration-free, all-optical method for high-precision lithium isotope ratio measurements in solid materials using laser ablation combined with tunable laser absorption spectroscopy. A new asynchronous acquisition method is used to acquire time-resolved, high-resolution spectra of the 6Li and 7Li D1 and D2 transitions near 671 nm. Isotope ratios and atomic column densities are extracted from measured spectra via a physics-based fitting model including hyperfine structure. Under 1 Torr air, spectra recorded = 0.75 ms after plasma onset exhibit narrow linewidths corresponding to Doppler temperatures = 400 K, enabling resolution of the isotope peaks with high signal-to-noise ratios. Analysis of LiAlO2 samples with varying 6Li:7Li ratios demonstrates isotopic precisions of 0.6–1.7% for spectra acquired in 30 s. Isotope ratios determined from the spectral fits show accuracy within –0.3% to –1.7% of reference ICP-MS measurements without requiring calibration to external standards. By eliminating sample preparation and enabling spatially resolved isotopic mapping, this method offers a rapid analysis approach to lithium isotope determination in solid materials relevant to nuclear energy, safeguards, and geochemistry.

Phillips, Mark C.↗

Size distribution of polycyclic aromatic hydrocarbons in space: an old new light on the 11.2/3.3 μm intensity ratio

The intensity ratio of the 11.2/3.3 μm emission bands is considered to be a reliable tracer of the size distribution of polycyclic aromatic hydrocarbons (PAHs) in the interstellar medium (ISM). This paper describes the validation of the calculated intrinsic infrared (IR) spectra of PAHs that underlie the interpretation of the observed ratio. The comparison of harmonic calculations from the NASA Ames PAH IR spectroscopic database to gas-phase experimental absorption IR spectra reveals a consistent underestimation of the 11.2/3.3 μm intensity ratio by 34%. IR spectra based on higher level anharmonic calculations, on the other hand, are in very good agreement with the experiments. While there are indications that the 11.2/3.3 μm ratio increases systematically for PAHs in the relevant size range when using a larger basis set, it is unfortunately not yet possible to reliably calculate anharmonic spectra for large PAHs. Based on these considerations, we have adjusted the intrinsic ratio of these modes and incorporated this in an interstellar PAH emission model. This corrected model implies that typical PAH sizes in reflection nebulae such as NGC 7023 – previously inferred to be in the range of 50 to 70 carbon atoms per PAH are actually in the range of 40 to 55 carbon atoms. The higher limit of this range is close to the size of the C 60 fullerene (also detected in reflection nebulae), which would be in line with the hypothesis that, under appropriate conditions, large PAHs are converted into the more stable fullerenes in the ISM.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Advances in phosphor two-color ratio method thermography for full-field surface temperature measurements

We report thermographic phosphors can be employed for optical sensing of surface, gas phase, and bulk material temperatures through different strategies including the time-decay method, time-integrated method, and frequency-domain method. We focus on the time-integrated method, also known as the ratio method, as it can be more practical in many situations. This work advances the ratio method using two machine vision cameras with CMOS detectors for full-field temperature measurements of a solid surface. A phosphor calibration coupon is fabricated using aerosol deposition and employed for in situ determination of the temperature-versus-intensity ratio relationship. Algorithms from digital image correlation are employed to determine the stereoscopic imaging system intrinsic and extrinsic parameters, and accurately register material points on the sample to subpixel locations in each image with 0.07 px or better accuracy. Detector nonlinearity is carefully characterized and corrected. Temperature-dependent, spatial non-uniformity of the full-field intensity ratio—posited to be caused by a blue-shift effect of the bandpass filter for non-collimated light and/or a wavelength-dependent transmission efficiency of the lens—is assessed and treated for cases where a standard flat-field correction fails to correct the non-uniformity. In sum, pixel-wise calibration curves relating the computed intensity ratio to temperature in the range of T = 300–430 K are generated, with an embedded error of less than 3 K. This work offers a full calibration methodology and several improvements on two-color phosphor thermography, opening the door for full-field temperature measurements in dynamic tests with deforming test articles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Inertial-confinement fusion-plasma-based cross-calibration of the deuterium-tritium γ-to-neutron branching ratio

The deuterium-tritium (D-T) γ -to-neutron branching ratio [ H 3 ( d , γ ) He 5 / H 3 ( d , n ) He 4 ] has been determined previously under inertial-confinement fusion (ICF) conditions and in beam-target based experiments. In the former case, neutron-induced backgrounds are mitigated compared to the latter due to the short pulse nature of ICF implosions and the use of gas Cherenkov γ -ray detectors. Furthermore, an added benefit of ICF based measurements is the ability to achieve lower center-of-mass energies as compared to accelerators. Previous ICF based experiments however report a large uncertainty in the D-T γ -to-neutron branching ratio of ≈ 48 % , which arises from the necessity of an absolute detector calibration and/or a cross-calibration against the D- He 3 γ -to-proton branching ratio. A more precise value for the branching ratio based on data taken at the OMEGA laser facility is reported here, which relies on a cross-calibration against the better known C 12 neutron inelastic scattering cross section. A D-T branching ratio value of ( 4.6 ± 0.6 ) × 10 - 5 is determined by this method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗