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Banner Highlight for Structure-Dependent Doppler Broadening Using a Generalized Thermal Scattering Law [DOI 10.3390/jne2020013].
Traditional Doppler broadening methods assume that target nuclei velocities follow a Maxwell-Boltzmann distribution which inherently assumes that the atoms are a free gas or that their velocities are independent of each other. This approximation is reasonable at high target temperatures and high neutron energies. However, nuclei are not independent: the lattice temperature and chemical binding will define the atomic motion. The thermal scattering law (i.e., TSL or S(α,β)) is a material property which describes the chemical binding and temperature response in terms of available momentum and energy states. In the thermal energy range, this TSL will define the thermal scattering cross sections. In the resonance region, the TSL offers a first-principles description of the probability distribution function for the velocity of the target nuclei. Using the TSL in Doppler broadening captures the structure of the material consistently from the thermal range into the resonance cross sections. In this work, both traditional free-gas and precise TSL Doppler broadening methods for resonance cross section evaluation have been implemented within the Full Law Analysis Scattering System Hub (FLASSH). This framework provides a generalized formulation for evaluating low-lying resonance data and streamlines nuclear data processing methods. TSL data generated using ab initio lattice dynamics (AILD) can be used to broaden cross section libraries in ENDF format for high-fidelity input into reactor physics calculations. These capabilities are demonstrated for the lowest absorption resonances of {sup 238}U in UO{sub 2}, UC and UN. (authors)
Coincidence Doppler Broadening (CDB) Positron Annihilation Spectroscopy (PAS) is a material analysis technique that can be used to non-destructively measure characteristics of structural defects in samples. Analyzing and comparing large datasets obtained using this technique, however, can be complicated and time intensive. The Coincidence Doppler Broadening Analysis Program (CDB-AP) is a graphical user interface that facilitates rapid analysis of many data files while using transparent processes. It is already used in three laboratories at Idaho National Laboratory and can be used in laboratories worldwide.
A general method of solutions for treating effects of Doppler-broadened Rayleigh backscattering in H2O Differential Absorption Lidar (DIAL) measurements are described and discussed. Errors in vertical DIAL measuremtns caused by this laser line broadening effect can be very large and, therfore, this effect has to be accounted for accurately. To analyze and correct effects of Doppler-broadened Rayleigh backscattering in DIAL experiments, a generalized DIAL approximation was derived starting from a lidar equation, which includes Doppler broadening. To evaluate the accuracy of H2O DIAL measurements, computer simulations were performed. It was concluded that correction of Doppler broadened Rayleigh backscattering is possible with good accuracy in most cases of tropospheric H2O DIAL measurements, but great care has to be taken when layers with steep gradients of Mie backscattering like clouds or inversion layers are present.
In this paper I attempt to document what I have learned and still remember about temperature effects, particularly Doppler broadening, on nuclear data, as it applies to ENDF formatted data. My focus is on the SIGMA1 method of Doppler broadening that I developed over 50 years ago. However, I do realize that there are currently many different methods used in computer codes, and I have tried to keep my discussion general as it applies to ALL of these methods. In particular, ALL of the MYTHS I describe below apply to all Doppler broadening methods: they all solve the parabolic diffusion equation in spherical geometry in (speed, reaction rate) versus temperature. These methods differ only in how the cross section is represented. So, at 85 years old here is what I still remember.
Anefficient routine for computing Legendre moments of the Doppler-broadened elastic scattering kernel, including resonance scattering effects, has been implemented in the ISOXML module of Griffin. Isotropic scattering in the center-of-mass system and the ideal gas model for target motion are assumed. A ladder-operator formulation is introduced to compute all Legendre moments from order 0 to N simultaneously, enabling near-linear scaling of computational cost with respect to the maximum Legendre order. A physics-based strategy for constructing outgoing energy grids has also been developed, in which a tailored base grid is combined with adaptive refinement to maintain accuracy while limiting the number of outgoing energy points. For energies between resonances, a constant cross-section model is employed to further reduce computational cost. In addition, a quantitative criterion is derived to determine isotope-wise cut-off incident energies based on a prescribed up-scattering probability coverage. For 238U, up to incident energies of approximately 75, 230, and 661 eV at 294, 900, and 2500 K (corresponding to a 2% up-scattering probability threshold), computation of P0 kernels requires 1–8 s and computation of P0–P5 kernels requires 0.4–4 min using a single thread, while maintaining 1–3% relative error in up-scattering probability. These results demonstrate that the proposed formulation enables accurate and computationally practical Doppler-broadened kernel generation for online multigroup cross-section production in Griffin.
Laser induced line narrowing in coupled Doppler broadened transitions, noting mode crossing and spontaneous emission
We present measurements and theoretical modeling demonstrating the capability of coincidence Doppler broadened (CDB) annihilation gamma spectroscopy to provide element-specific information from the topmost atomic layer of surfaces. Our measurements show that the energy spectra of Doppler-shifted annihilation gamma photons emitted following the annihilation of positrons from the topmost atomic layers of clean and adsorbate covered surfaces of gold (Au), silver (Ag) and copper (Cu) differ significantly. The shape of the Doppler-broadened gamma spectrum, as analyzed using ratio curves, indicates that the elemental composition of the surface can still be identified despite contributions from positronium annihilation and a significant reduction in core electron annihilation. We estimate the chemical composition of the various probed surfaces by modeling the ratios of the measured Doppler spectra with respect to the Doppler spectra from a clean Cu surface using a linear combination of calculated ratio curves. The fitting of the experimental ratio curves was used to obtain an estimate of the elemental composition of Cu surfaces with sulfur segregation, oxygen adsorption, a thin film of Selenium (Se), and a single layer of graphene (SLG). A similar analysis was performed on the Ag surface with environmental adsorbates, the same surface after argon ion sputtering, as well as a sputter cleaned Au surface. The surface compositions obtained from the analysis of the CDB data were compared to the compositions obtained using positron annihilation induced Auger electron spectroscopy (PAES). Our results show that CDB can detect, identify, and quantify, sub-monolayer adsorbates and a single atomic layer deposited on metal substrates.
Saturation behavior of Doppler broadened transition involving levels with closely spaced structure
Spectral lines Doppler broadening reduction in spectroscopy using foil and gas excited accelerator beams as light sources
Unidirectional gas laser amplifier using monochromatic optical pumping of coupled Doppler broadened transition
Several approximations to the Doppler broadening functions psi(x, theta) and chi(x, theta) are compared with respect to accuracy and speed of evaluation. A technique, due to A. M. Turning (1943), is shown to be at least as accurate as direct numerical quadrature and somewhat faster than Gaussian quadrature. FORTRAN 4 listings are included.
Nonlinear attenuation or gain characteristics of Doppler-broadened atomic resonance involving levels with small splittings, noting mode coupling of gas laser
A graphical user interface (GUI) that helps analyze data from coincidence Doppler broadening positron annihilation spectroscopy. It is a quick tool to rapidly reduce large data and conveniently analyze multiple datasets.
The surprising feature of the Doppler problem in threshold determination is the 'amplification effect' of the target's thermal energy spread. The small thermal energy spread of the target molecules results in a large dispersion in relative kinetic energy. The Doppler broadening effect in connection with thermal energy beam experiments is discussed, and a procedure is recommended for the deconvolution of molecular scattering cross-section functions whose dominant dependence upon relative velocity is approximately that of the standard low-energy form.
A plasma model, previously developed to interpret neutral-particle analyzer measurements on E x B heating devices, is adapted to analyze Doppler broadened charge-exchange-neutral lines measured by an optical monochromator. Comparison of theoretical with experimental results indicates that azimuthal drift as well as cyclotron motion are quite influential in determining line shapes and widths, and thus important in temperature determination, even when the monochromator line of sight is intersecting the plasma axis of symmetry. At this central sighting position, however, results are quite insensitive to radial ion density distribution when time lag between the charge-exchange-excitation events and emission is neglected. Line shapes and widths obtained by sighting across chords of plasma at various distances from the plasma axis of symmetry indicate a strong dependence on time lag.
Axial fatigue specimens of three superalloys, Inconel 718, Incoloy 903 and Haynes 188, were machined from solution-heat-treated material and artificially aged. They were subjected to cyclic loading for a selected number of cycles after which the S parameter was determined using Doppler broadening positron annihilation. Initially, the S parameter decreased, followed by a large increase and a subsequent decline leading to fracture. This has been interpreted as the removal of residual vacancies, the introduction of new defects by cyclic loading, and, finally, a clustering of the defects as microcracks which grow to cause failure.
Computer simulations have enabled the performance of a H2O Differential Absorption Lidar (DIAL) system to be studied by spectrally analyzing the forward propagating and backscattered laser energy. The simulations were done for a high altitude (21 km) DIAL system operating in a nadir-viewing mode. The influence of Rayleigh Doppler broadening on DIAL measurement accuracies were evaluated and show that the Rayleigh broadening influence, which can be corrected to first order in regions free of large aerosol gradients, reduces the sensitivity of DIAL H2O measurement errors in the upper tropospheric region. The ability to correct the Rayleigh broadening and the selection of H2O DIAL parameters when all the systematic effects are combined, were discussed.