Calculated Line Shapes Research Articles

Second-order spectral line shift comparisons

The second-order spectral line width formulae from the projection operator and kinetic theory methods were recently compared. It was shown that a systematic expansion of the projection operator width expression including initial correlations formally agrees with the second-order kinetic theory result. It is now shown that the second-order dynamic shifts are also formally the same. The static shifts, however, differ due to an ad hoc treatment of electron-electron correlations in the projection operator method. The approximation is necessary in order to screen the radiator-electron interactions. The differences, however, are expected to be small. The results suggest using the rigorous and more compact second-order width and shift expressions from the kinetic theory method as the starting point for spectral line shape calculations. At line center, however, the projection operator second-order expression for the width and shift simplifies and reduces to the kinetic theory result.

Temperature and density dependence of Kr L-shell spectrum in hot dense plasmas

Kr L-shell spectroscopy modeling results are discussed in this paper, focusing on the n = 4 to n = 2 line transitions of Be- and Li-like Kr ions. Collisional radiative atomic kinetic and Stark-broadened spectral line shape calculations show electron temperature Te and density ne sensitivity in the spectrum. The combination of the Te dependence due to the relative intensity of Be-like to Li-like line emissions in the range from 1.5 to 3 keV and the ne sensitivity from the Stark broadening effect on the line shapes in the range from 5×1023 to 2×1024/ cc results in a spectrum that can be employed to diagnose Te and ne. Two different collisional radiative atomic kinetic models i.e., Prismspect [J. J. MacFarlane, et al., Int. Fusion Sci. Appl. Conf. Proc. 457 (2003)] and ABAKO [Florido, et al., PRE, 80, 056402 (2009)] produce similar results in level populations and spectra. In x-ray spectroscopy of implosion cores, this Kr L-shell spectrum may prove useful in an intermediate Te range in which Ar is too ionized for its K-shell to be of diagnostic value and Kr is not ionized enough for its K-shell emission to be useful.

Study on a curvature compensation method for improving the end face matching of large-segment steel box girders during full-span erection

As precast segments are increasingly preferred for bridge construction owing to their efficiency and environmentally benign attributes, this study aims to enhance the end face matching technology for large-segment steel box girders. The curvature compensation method, which is a form of extension of the elevation compensation for pre-camber setting, is proposed based on the unstressed geometry of the steel box girder. It is found that the curvature compensation is equivalent to the end face angle compensation of segments if the construction technology of “combining several straight lines into a curve” is adopted. Three practical formulas for calculating curvature compensation angles are derived, namely, the moment method, intersection angle secant method, and incremental moment method, and theoretical values of the errors caused by using matching line shape calculation are provided. Furthermore, considering the specific continuous bridge with large-segment steel box girders in the Shenzhen-Zhongshan Channel as a case study, the calculation results of manufacturing parameters, matching line shapes, and end matching are presented. The findings indicate that the curvature compensation angle's maximum error reaches 55.7 % when calculated conservatively using erection geometry, while the manufacturing geometry's maximum error reaches 4.84 cm if the curvature compensation angle is disregarded. The results of on-site monitoring show that the curvature compensation method proposed in this study is able to provide the continuous fabrication geometry and achieve the perfect matching of end faces of neighbouring large-segment steel box girders.

Review of Rydberg Spectral Line Formation in Plasmas

The present review is dedicated to the problem of an array of transitions between highly-excited atomic levels. Hydrogen atoms and hydrogen-like ions in plasmas are considered here. The presented methods focus on calculation of spectral line shapes. Fast and simple methods of universal ionic profile calculation for the Hnα (Δn=1) and Hnβ (Δn=2) spectral lines are demonstrated. The universal dipole matrix elements formulas for the Hnα and Hnβ transitions are presented. A fast method for spectral line shape calculations in the presence of an external magnetic field using the formulas for universal dipole matrix elements is proposed. This approach accounts for the Doppler and Stark–Zeeman broadening mechanisms. Ion dynamics effects are treated via the frequency fluctuation model. The accuracy of the presented model is discussed. A comparison of this approach with experimental data and the results of molecular dynamics simulation is demonstrated. The kinetics equation for the populations of highly-excited ionic states is solved in the parabolic representation. The population source associated with dielectronic recombination is considered.

Heisenberg Spin Exchange Between Nitroxide Probes Diffusing in a Percolation Network

AbstractHeisenberg spin exchange between nitroxide (Tempone) spin probes has been measured as a function of concentration in the aqueous phase of the hydrated ion exchange membrane Nafion 117. The observed fast-motional electron paramagnetic resonance spectra were analyzed in terms of the stochastic Liouville equation lineshape calculation of Freed and coworkers and the “new paradigm” for interpreting spin exchange effects proposed by Salikhov. Differences between the effective spin exchange measured from the spectrum by these methods are presented and compared, and indicate that dipolar interactions make a significant contribution to spin exchange in this system. In acidic Nafion membranes, the spin probes are deactivated over time, allowing simultaneous measurement of the decay kinetics and spin exchange as a function of paramagnetic probe concentration. Both these processes deviate from the behavior that would be expected from classical chemical kinetics in isotropic media. The results are discussed in terms of currently available models for diffusion and reaction in a percolation network.

Effect of collisions on motional Stark broadening of spectral lines

The shape of spectral lines in strongly magnetized plasmas is investigated theoretically in the framework of astrophysical research. Under certain conditions, the broadening of lines observed on white dwarf spectra is dominated by the so-called motional Stark effect, which occurs due to the Lorentz electric field v→×B→. If the plasma density is high enough, collisions between the emitter and perturbers change the atomic velocity v→ and the resulting motional Stark broadening is modified. We illustrate this modification through dedicated line shape calculations based on a stochastic model for the atomic velocity. A universal line shape formula, which is applicable to any isolated atomic line, is proposed for implementation in line shape codes.

An Analytical Algorithm for Determining Optimal Thin-Walled Hollow Pier Configuration with Sunlight Temperature Differences

Formulas for computing the line shape of a thin-walled hollow pier body based on structural characteristics and measured sunlight temperature difference are derived using an analytical algorithm. In a case study of the No. 5 pier of a newly constructed continuous beam bridge on a mountainous expressway of Guizhou Province in China, the pier top’s displacement calculated by the analytical algorithm, currently accepted code, and a FEM program were each compared to its measured values. Furthermore, the effects of sunlight temperature difference, pier height, and wall thickness on the line shape of the pier body were explored, and the results show that the calculation values from these formulas were closer to the measured values than the currently accepted code, with a maximum error of 0.507 mm, demonstrating that the formulas have a more dependable result, higher precision, and more specific applicability. Thus, the algorithm provides a better method for the line shape calculation and construction control of thin-walled hollow piers because it can accurately account for sunlight temperature differences and pier height.

Combining experiments on luminescent centres in hexagonal boron nitride with the polaron model and ab initio methods towards the identification of their microscopic origin.

The two-dimensional material hexagonal boron nitride (hBN) hosts luminescent centres with emission energies of ∼2 eV which exhibit pronounced phonon sidebands. We investigate the microscopic origin of these luminescent centres by combining ab initio calculations with non-perturbative open quantum system theory to study the emission and absorption properties of 26 defect transitions. Comparing the calculated line shapes with experiments we narrow down the microscopic origin to three carbon-based defects: C2CB, C2CN, and VNCB. The theoretical method developed enables us to calculate so-called photoluminescence excitation (PLE) maps, which show excellent agreement with our experiments. The latter resolves higher-order phonon transitions, thereby confirming both the vibronic structure of the optical transition and the phonon-assisted excitation mechanism with a phonon energy ∼170 meV. We believe that the presented experiments and polaron-based method accurately describe luminescent centres in hBN and will help to identify their microscopic origin.

Polarised line shape calculations for conditions encountered in stellar magnetic atmospheres

We present new investigations into spectral line shapes under conditions typical for magnetic stellar atmospheres. Our method for simulating line profiles takes into account the coupled Zeeman and Stark effects. The calculations presented here will ultimately help to correctly model the Stokes parameters of peculiar stellar objects such as the Magnetic White Dwarfs (MWDs), retrieving their magnetic field geometries from spectropolarimetric observations. For the magnetic analysis of this class of stars, in general only Stokes I profiles as a function of rotational phase have been used in the past, in a very few cases, also Stokes V. The present improved simulations of the full Stokes parameters are expected to provide a powerful tool for the analysis of strong magnetic fields like those found in the MWDs.

Satellite Excitations and Final State Interactions in Atomic Photoionization

Satellite excitations and final state configuration interactions appear due to the many-electron correlations and result in a photoelectron spectrum complex final state structure instead of single lines corresponding to one-hole states. In the present work, both processes are considered in a framework of the many-body perturbation theory, and two techniques, namely the spectral function and CI (configuration interaction) methods are considered. It is shown that for the calculation of satellite lineshapes and low-energy Auger decay, the spectral function method is more appropriate, but in the case of strong final state interactions, the methods of solution of Dyson equation or secular matrix are superior. The results obtained for satellites and low energy Auger decay in the Ne 1s, Ne 2p photoelectron spectra, the Co 3s, and the Th 5p photoelectron spectra are in agreement with the experimental data.

Hydrogen Line Shape Uncertainties in White Dwarf Model Atmospheres

For isolated white dwarf (WD) stars, fits to their observed spectra provide the most precise estimates of their effective temperatures and surface gravities. Even so, recent studies have shown that systematic offsets exist between such spectroscopic parameter determinations and those based on broadband photometry. These large discrepancies (10% inTeff, 0.1 M⊙in mass) provide scientific motivation for reconsidering the atomic physics employed in the model atmospheres of these stars. Recent simulation work of ours suggests that the most important remaining uncertainties in simulation-based calculations of line shapes are the treatment of 1) the electric field distribution and 2) the occupation probability (OP) prescription. We review the work that has been done in these areas and outline possible avenues for progress.

Stark–Zeeman line-shape model for multi-electron radiators in hot dense plasmas subjected to large magnetic fields

We present a Stark–Zeeman spectral line-shape model and the associated numerical code, PPPB, designed to provide fast and accurate line shapes for arbitrary atomic systems for a large range of plasma conditions. PPPB is based on the coupling of the PPP code—a Stark-broadened spectral line-shape code developed for multi-electron ion spectroscopy in hot dense plasmas—and the MASCB code developed recently to generate B-field-dependent atomic physics. The latter provides energy levels, statistical weights, and reduced matrix elements of multi-electron radiators by diagonalizing the atomic Hamiltonian that includes the well know B-dependent term. These are then used as inputs to PPP working in the standard line-broadening approach, i.e., using the quasi-static ion and impact electron approximations. The effects of ion dynamics are introduced by means of the frequency fluctuation model, and the physical model of electron broadening is based on the semi-classical impact approximation including the effects of a strong collision term, interference, and cyclotron motion. Finally, to account for polarization effects, the output profiles are calculated for a given angle of observation with respect to the direction of the magnetic field. The potential of this model is presented through Stark–Zeeman spectral line-shape calculations performed for various experimental conditions.

Stark broadening of low-[formula omitted] hydrogen lines in strongly magnetized hydrogen plasmas: Influence of [formula omitted]-degeneracy removal due to the quadratic Zeeman effect

The Stark broadening of hydrogen lines with a low upper principal quantum number n is reexamined in the case of plasmas subject to a large (≳1 kT) external magnetic field. This investigation has been motivated by the observation of strong Zeeman splitting in a significant number of white dwarf spectra. The diamagnetic Zeeman effect term present in the Hamiltonian removes the degeneracy of the energy levels in orbital quantum number l, which results in an alteration of the Stark perturbation due to the microfield. In this work, we investigate this effect by applying a computer simulation method designed for Stark broadening modeling. A focus is put on the Lyman α and H-α lines. Based on line shape calculations, we show that the width of the Zeeman components is strongly dependent on the magnetic field.

Quantum-Classical Approach for Calculations of Absorption and Fluorescence: Principles and Applications.

Absorption and fluorescence spectroscopy techniques provide a wealth of information on molecular systems. The simulations of such experiments remain challenging, however, despite the efforts put into developing the underlying theory. An attractive method of simulating the behavior of molecular systems is provided by the quantum–classical theory—it enables one to keep track of the state of the bath explicitly, which is needed for accurate calculations of fluorescence spectra. Unfortunately, until now there have been relatively few works that apply quantum–classical methods for modeling spectroscopic data. In this work, we seek to provide a framework for the calculations of absorption and fluorescence lineshapes of molecular systems using the methods based on the quantum–classical Liouville equation, namely, the forward–backward trajectory solution (FBTS) and the non-Hamiltonian variant of the Poisson bracket mapping equation (PBME-nH). We perform calculations on a molecular dimer and the photosynthetic Fenna–Matthews–Olson complex. We find that in the case of absorption, the FBTS outperforms PBME-nH, consistently yielding highly accurate results. We next demonstrate that for fluorescence calculations, the method of choice is a hybrid approach, which we call PBME-nH-Jeff, that utilizes the effective coupling theory [GelzinisA.;J. Chem. Phys.2020, 152, 05110332035455] to estimate the excited state equilibrium density operator. Thus, we find that FBTS and PBME-nH-Jeff are excellent candidates for simulating, respectively, absorption and fluorescence spectra of real molecular systems.

High-temperature absorption line shape parameters for CO2 in the 6800–7000 cm-1 region from dual frequency comb measurements up to 1000 K

We present the first systematic study of self-broadened CO2 line shape parameters in the 00031 ← 00001 and 01131 ← 01101 bands at high temperature. We report temperature-dependent broadening coefficients and pressure shift coefficients for more than 40 transitions in the 00031 ← 00001 band, and 75 transitions in the 01131 ← 01101 hot band. The majority of these parameters have never been measured at high temperature. The new parameters are determined from 12 spectra measured with a broadband, high-resolution dual frequency comb absorption spectrometer in a high-temperature gas cell from room temperature to 980 K. We fit the measured spectra using a multispectrum fitting approach to derive line shape parameters with both a Voigt and speed-dependent Voigt profile. We compare the measured parameters to calculated line shape parameters as well as to the new parameter set developed for the HITRAN2020 database. The new measurements demonstrate strong agreement with HITRAN2020 (within 1% in some cases), and provide new measurements of the temperature dependence of the broadening and pressure shift coefficient that will improve the accuracy of the database at high temperature. We extend our results to high |m| transitions using a set of empirical models for the broadening and pressure shift coefficients, which we fit to our data and validate for high-temperature transitions up to |m| = 98. We use these models to construct a set of database files that can be used to supplement the HITRAN database for self-broadened CO2 in the 6800 – 7000 cm-1 region. These new parameters significantly improve the accuracy of absorption models for high-temperature CO2 in this frequency range, and also provide useful data to test and improve methods used to calculate CO2 line shape parameters.

Absorption in exoplanet atmospheres: Combining experimental and theoretical databases to facilitate calculations of the molecular opacities of water

We developed a method to reduce large theoretical molecular rovibrational line lists to significantly shorter lists that capture both the morphology of the spectrum and the total opacity. Water is used as a test case: the routines are demonstrated using the state-of-the-art POKAZATEL (H2O, 5.7 billion transitions) and VTT (HDO, 700 million transitions) databases. We validate the methods, and, using only 2.3 million transitions, we reproduce spectra from the full databases over the entire wavelength domain, at all resolutions, and in a fraction of the computational time that would be required were the full line lists used. As the variational line lists are applicable to much higher temperatures than commonly used experimentally-based databases, realistic simulations of high-temperature exoplanet atmospheres are possible. The approach is specifically developed to be applied in radiative transfer studies where larger line lists would result in prohibitively large calculation times. In addition to the light line lists, we collected collisional-broadening parameters of water in H2, He, CO2, and self-broadened, from several literature sources, and produced rotational quantum number dependent broadening tables, which can be used in combination with the line list to produce pressure broadened spectra for different atmospheres. The light line lists, in combination with the broadening parameters, allows the calculation of full Voigt line shapes in line-by-line, layer-by-layer calculations of radiative transfer models on personal computers. We demonstrate the new line lists in: 1) James Webb Space Telescope and Large UV/Optical/IR Surveyor simulations to detect HDO in an oxygen dominated atmosphere on Trappist-1 b and 2) simulated high-resolution emission spectra from HD 189733 b, constraining the water detectability using the cross-correlation method.

The Coulomb Symmetry and a Universal Representation of Rydberg Spectral Line Shapes in Magnetized Plasmas

A new method of line shape calculations of hydrogen-like atoms in magnetized plasmas is presented. This algorithm makes it possible to solve two fundamental problems in the broadening theory: the analytical description of the radiation transition array between excited atomic states and an account of a thermal ion motion effect on the line shapes formation. The solution to the first problem is based on the semiclassical approach to dipole matrix elements calculations and the usage of the specific symmetry properties of the Coulomb field. The second one is considered in terms of the kinetic treatment of the frequency fluctuation model (FFM). As the result, one has a universal description of line shapes under the action of the dynamic of ion’s microfield. The final line shape is obtained by the convolution of the ionic line shape with the Voigt electron Doppler profile. The method is applicable formally for large values of principal quantum numbers. However, the efficiency of the results is demonstrated even for well known first members of the hydrogen Balmer series Dα and Dβ lines. The comparison of obtained results with accurate quantum calculations is presented. The new method may be of interest for investigations of spectral line shapes of hydrogen-like ions presented in different kinds of hot ionized environments with the presence of a magnetic field, including So L and divertor tokamak plasmas.

Hydrogen Line Shapes in Plasmas with Large Magnetic Fields

We report on hydrogen line shape calculations in the presence of an external magnetic field, at conditions such that the quadratic Zeeman effect is important. The latter is described through a term proportional to B2 in the Hamiltonian, accounting for atomic diamagnetism. It provides a shift and an asymmetry on Lorentz triplets, and it leads to the occurrence of forbidden components. Motivated by investigations performed at the fifth edition of the Spectral Line Shape in Plasmas (SLSP5) code comparison workshop, we perform new calculations of hydrogen Lyman line profiles. Field values representative of magnetized white dwarf atmosphere conditions are taken. The calculations are done using a computer simulation technique, designed for Stark broadening modeling. A discussion of the results is done in the framework of plasma diagnostics.

Donor-acceptor nature of orange photoluminescence in AlN

Recombination dynamics, photoluminescence and photoluminescence excitation spectra have been investigated for 1.9 eV photoluminescence band in AlN in the temperature range of 5–650 K. The recombination dynamics for the 1.9 eV photoluminescence band has been described by a model of donor-acceptor recombination with taking into account a broadening due to electron coupling with local lattice vibrations of a deep level defect. The experimental results have been compared with density functional theory calculations of luminescence peak energies and line shapes of band to defect and donor-acceptor transitions, and possible origin of the orange photoluminescence band in AlN has been discussed.

Effect of incident laser sheet orientation on the OH-PLIF imaging of detonations

This study aims to investigate the effect of laser sheet orientation on the OH-planar laser-induced fluorescence (OH-PLIF) imaging of a detonation wave and to identify the potential benefit of using a transverse laser orientation, compared to the conventional frontal orientation. In this study, we developed a new laser-induced fluorescence (LIF) model, based on a preexisting one, to include a more fundamental calculation of the absorption lineshape and the effects of the laser orientation on the fluorescence signal. One- and two-dimensional simulations are used to validate this new LIF model for both laser orientations using OH-PLIF images from the literature. The effect of the two laser orientations on detonation imaging is investigated numerically on a two-dimensional OH field. Based on these results, the frontal orientation seems more suitable to collect information near the detonation front, while the transverse laser orientation can give more quantitative information far from the front and only for short optical paths. With the present laser configuration and experimental conditions, both laser orientations present the same limitation with a strong laser energy absorption for long optical paths. While these first results show a qualitative agreement with experimental data, new experimental data are required to quantitatively validate this promising transverse laser orientation and confirm its relevance for OH-PLIF imaging of detonations.