Calculated Line Shapes Research Articles

Spectral lineshapes of collision-induced absorption (CIA) and collision-induced light scattering (CILS) for molecular nitrogen using isotropic intermolecular potential. New insights and perspectives

The rototranslational collision-induced absorption (CIA) at different temperatures and collision-induced light scattering (CILS) at room temperature of nitrogen gas are analyzed in terms of new isotropic intermolecular potential, multipole-induced dipole functions and interaction-induced pair polarizability models, using quantum spectral lineshape computations. The irreducible spherical form for the induced operator of light scattering mechanisms was determined. The high frequency wings are discussed in terms of the collision-induced rotational Rayleigh effect and estimates for the dipole–octopole polarizability E4, is obtained and checked with the ab initio theoretical value. The quality of the present potential has been checked by comparing between calculated and experimental thermo-physical and transport properties over a wide temperature range, which are found to be in good agreement.

Influence of Microfield Directionality on Line Shapes

In the framework of the Spectral Line Shapes in Plasmas Code Comparison Workshop (SLSP), large discrepancies appeared between the different approaches to account for ion motion effects in spectral line shape calculations. For a better understanding of these effects, in the second edition of the SLSP in August, 2013, two cases were dedicated to the study of the ionic field directionality on line shapes. In this paper, the effects of the direction and magnitude fluctuations are separately analyzed. The effects of two variants of electric field models, (i) a pure rotating field with constant magnitude and (ii) a time-dependent magnitude field in a given direction, together with the effects of the time-dependent ionic field on shapes of the He II Lyman-α and -β lines for different densities and temperatures, are discussed.

Efficient calculation of inelastic vibration signals in electron transport: Beyond the wide-band approximation

We extend the simple and efficient lowest order expansion (LOE) for inelastic electron tunneling spectroscopy (IETS) to include variations in the electronic structure on the scale of the vibration energies. This enables first-principles calculations of IETS lineshapes for molecular junctions close to resonances and band edges. We demonstrate how this is relevant for the interpretation of experimental IETS using both a simple model and atomistic first-principles simulations.

The (13)C solid DNP mechanisms with perchlorotriphenylmethyl radicals--the role of (35,37)Cl.

The microwave frequency swept DNP enhancement, referred to as the DNP spectrum, is strongly dependent on the EPR spectrum of the polarizing radical and it reveals the underlying DNP mechanisms. Here we focus on two chlorinated trityl radicals that feature axially symmetric powder patterns at 95 GHz, the width of which are narrower than those of TEMPOL or TOTAPOL but broader than that of the trityl derivative OX63. The static DNP lineshapes of these commonly used radicals in DNP, have been recently analyzed in terms of a superposition of basic Solid Effect (SE) and Cross Effect (CE)-DNP lineshapes, with their relative contributions as a fit parameter. To substantiate the generality of this approach and further investigate an earlier suggestion that a (35,37)Cl-(13)C polarization transfer pathway, termed "hetero-nuclear assisted DNP", may be in effect in the chlorinated radicals (C. Gabellieri et al., Angew. Chem., Int. Ed., 2010, 49, 3360-3362), we measured the static (13)C-glycerol DNP spectra of solutions of ca. ∼10 mM of the two chlorinated trityl radicals as a function of temperature (10-50 K) and microwave power. Analysis of the DNP lineshapes was first done in terms of the SE/CE superposition model calculated assuming a direct e-(13)C polarization transfer. The CE was found to prevail at the high temperature range (40-50 K), whereas at the low temperature end (10-20 K) the SE dominates, as was observed earlier for (13)C DNP with OX63 and (1)H DNP with TEMPOL and TOTAPOL, thus indicating that this is rather general behavior. Furthermore, it was found that at low temperatures it is possible to suppress the SE, and increase the CE by merely lowering the microwave power. While this analysis gave a good agreement between experimental and calculated lineshapes when the CE dominates, some significant discrepancies were observed at low temperatures, where the SE dominates. We show that by explicitly taking into account the presence of (35/37)Cl nuclei through a e-(35,37)Cl-(13)C polarization pathway in the SE-DNP lineshape calculations, as proposed earlier, we can improve the fit significantly, thus supporting the existence of the "hetero-nuclear assisted DNP" pathway.

Efficient algorithms for Stark–Zeeman spectral line shape calculations

A stochastic microfield formulation to treat particle motion effects in Stark-broadening of ion spectral lines by plasmas is extended to include an external uniform static magnetic field. The results are in good agreement with available line profile calculations from computer simulations. In addition, recently developed efficient algorithms are applied to Stark–Zeeman profile calculations with both static and dynamic ions.

Polarization spectroscopy for the 85Rb D1 line in a strong pump field

We present polarization spectroscopy for the D1 transition line of 85Rb atoms in the strong pump region. When the intensity of the pump beam was increased, the signal for the transition ∣ 5S1/2, Fg = 2〉 → ∣5P1/2, Fe = 3〉 displayed a double structure in the dispersive signal whereas the other signals displayed no significant variation other than power broadening. Calculation of the spectral lineshape by using the rate equations demonstrated that the double structure was due to the relatively large signal for the ground state ∣5S1/2, Fg = 2,mg = 2〉 due to optical pumping and the large transition strength.

Iterative approach to line-shape calculations based on the transport-relaxation equation

The iterative approach to the line-shape calculations from the transport-relaxation equation was modified to allow its application for low pressures down to the Doppler limit. In our approach functions and operators are decomposed in the Burnett basis. This technique was applied to experimental data presenting the consistency between the line-shape model and measured spectrum corresponding to a signal-to-noise ratio higher than $9\ifmmode\times\else\texttimes\fi{}{10}^{4}$. Implications for precise molecular spectroscopy as well as for Doppler-width thermometry and spectroscopic Boltzmann constant determination are discussed.

Review of the 1st Spectral Line Shapes in Plasmas code comparison workshop

A review is given of the first workshop dedicated to the detailed comparison of various approaches to the calculation of spectral line shapes in plasmas. A standardized set of case problems was specified in advance, together with the prescribed atomic data and assumptions to be used. In this brief review, motivations for the case problems chosen are outlined, followed by a discussion of selected results. Plans for the next workshop are discussed in the conclusion.

Quasicontiguous frequency-fluctuation model for calculation of hydrogen and hydrogenlike Stark-broadened line shapes in plasmas

We present an analytical method for the calculation of shapes of Stark-broadened spectral lines in plasmas, applicable to hydrogen and hydrogenlike transitions (including Rydberg ones) with Δn>1. The method is based on the recently suggested quasicontiguous approximation of the static Stark line shapes, while the dynamical effects are accounted for using the frequency-fluctuation-model approach. Comparisons with accurate computer simulations show excellent agreement.

Collision operators for Stark line shapes: When does the unified theory fail?

It is shown that the unified theory for Stark broadening leads to incorrect results when correlated emitter–perturber collisions are present. With a kinetic theory treatment, we propose an extension of the model able to account for such correlations. The treatment presents analogies with renormalization techniques and the resulting collision operator has a structure similar to that obtained within the unified theory. We illustrate the applicability of the model through calculations of hydrogen line shapes in ideal cases.

Implementation of the Frequency Separation Technique in general lineshape codes

The Frequency Separation Technique (FST) has been proposed and theoretically documented. It is a technique capable of unifying and improving lineshape calculations, for both accuracy and speed. In this work, we briefly recall its key features and advantages and present a practical way of implementing it in lineshape codes. We note that the FST is a general technique, capable of working with practically any modern lineshape framework that can either employ or go beyond the standard framework.

Influence of the interaction potential shape on the Dicke narrowed spectral line profiles affected by speed-dependent collisional broadening and shifting

Variations of the Dicke narrowed spectral line profiles caused by change of the interaction potential shape are investigated. We propose line shape model, which incorporates the speed-dependent collisional broadening and shifting as well as the velocity-changing collisions, described by the class of r−ν-type repulsive potentials. Following Blackmore (1987) [55], calculations were carried out using the Liouville formalism. In contrast to previous analysis, we concluded that the pure Dicke narrowed profiles calculated for various potential types can differ by almost 20%. Assuming the same speed dependence of collisional broadening and changing the type of interaction potential responsible for velocity-changing collisions the subpercent variations of calculated line shapes were observed. It was shown that in the case when these both contributions, the collisional broadening and the velocity-changing collisions, are related to the r−ν-type interaction potential the variations of calculated line shapes are more than one order of magnitude bigger than in previous case and are dominated by speed-dependent collisional broadening. In the case of supersensitive spectroscopy, where accuracy of the line shapes measurements approaches 10−6, the accuracy of the retrieved line shape parameters can be strongly affected by the assumed type of interaction potential related to velocity-changing collisions.

Fine-structure electric-dipole matrix elements of He-like ions for x-ray line-shape calculations

Dipole matrix elements have been calculated with different methods in the intermediate-coupling scheme to study their impact on the Stark effect of highly charged ions. Special emphasis has been devoted to the 1$s$3$l$ fine structure of He-like ions that is widely employed for Stark broadening analysis in dense plasmas. Apart from a wavelength shift in the total He${}_{\ensuremath{\beta}}$ group in the x-ray energy range, important differences in the Stark width, induced line dips, and relative intensities of maxima are demonstrated for different methods of calculation. We found that these differences were related to the precision of the fine-structure dipole matrix elements and related wavelengths and explored the particularities of atomic structure precision for line broadening purposes that was distinct from the current database approaches. Based on advanced multi-configuration-Dirac-Fock simulations, we propose a complete set of high-precision matrix elements and wavelengths. Detailed numerical results are presented for He-like aluminum. We also discuss the influence of relativistic approximations in atomic structure on the line broadening.

Photoluminescence of inversion electrons with carbon acceptors in a single modulation-doped AlxGa1−xAs/GaAs heterostructure

The photoluminescence of inversion electrons with carbon acceptors in a modulation-doped Al${}_{x}$Ga${}_{1\ensuremath{-}x}$As-GaAs single heterostructure was studied for different temperatures and excitation intensities. Despite the essentially homogeneous distribution of residual acceptors in the GaAs buffer, well-resolved luminescence profiles are observed for the ground and first excited two-dimensional electron subbands. This is due to the fact that the inversion layer interface potential restricts the overlap of the electron and acceptor wave functions to limited spatial regions close to the Al${}_{x}$Ga${}_{1\ensuremath{-}x}$As-GaAs interface, where the transition energies are weakly dispersive. A simple model will be presented for the calculation of the luminescence line shape that allows a quantitative analysis of the experiment.

First principles calculation of inhomogeneous broadening in solid-state cw-EPR spectroscopy

We present a scheme for the first-principles calculation of EPR lineshapes for continuous-wave-EPR spectroscopy (cw-EPR) of spin centers in complex chemical environments. We specifically focus on poorly characterized systems, e.g. powders and frozen glasses with variable microsolvation structures. Our approach is based on ab initio molecular dynamics simulations and ab initio calculations of the ensemble of g- and A-tensors along the trajectory. The method incorporates temperature effects as well as the full anharmonicity of the intra- and intermolecular degrees of freedom of the system. We apply this scheme to compute the lineshape of a prototypical spin probe, the nitrosodisulfonate dianionic radical (Fremy's salt), dissolved in a 50 : 50 mixture of water and methanol. We are able to determine the specific effect of variations of local solvent composition and microsolvation structure on the cw-EPR lineshape. Our molecular dynamics reveal a highly anisotropic solvation structure with distinct spatial preferences for water and methanol around Fremy's salt that can be traced back to a combination of steric and polar influences. The overall solvation structure and conformational preferences of Fremy's salt as found in our MD simulations agree very well with the results obtained from EPR and orientation-selective ENDOR spectroscopy performed on the frozen glass. The simulated EPR lineshapes show good agreement with the experimental spectra. When combined with our MD results, they characterize the lineshape dependence on local morphological fluctuations.

First-Principles Calculations of Luminescence Spectrum Line Shapes for Defects in Semiconductors: The Example of GaN and ZnO

We present a theoretical study of the broadening of defect luminescence bands due to vibronic coupling. Numerical proof is provided for the commonly used assumption that a multidimensional vibrational problem can be mapped onto an effective one-dimensional configuration coordinate diagram. Our approach is implemented based on density functional theory with a hybrid functional, resulting in luminescence line shapes for important defects in GaN and ZnO that show unprecedented agreement with experiment. We find clear trends concerning effective parameters that characterize luminescence bands of donor- and acceptor-type defects, thus facilitating their identification.

Computational prediction of temperature dependence of 13C NMR lineshapes of planar molecules in structure I clathrate hydrates

We use the molecular dynamics-based method to predict the solid-state 13C NMR lineshape of a planar molecule in a nonspherical cage. Unlike linear molecules, three components of the chemical shielding tensor of a planar molecule are different which gives rise to a different lineshape and temperature dependence in the 13C NMR spectrum. We study the planar ethylene molecule in the oblate large cages of the structure I (sI) clathrate hydrate and extract the lineshapes from the angular distribution and dynamics at four temperatures (70, 150, 200, and 250 K) in the stability range of the hydrate. At low temperature, the C2H4 molecules have limited range of motion in the cages, but as the temperature is raised, they first gain greater rotational freedom about the molecular C=C axis, and then in other directions. These data allow for the calculation of the 13C NMR lineshapes of the C2H4 guests at each temperature.

Quantum-statistical line shape calculation for Lyman-α lines in dense H plasmas

We present results for the Lyman-α line of hydrogen in dense plasmas. Full line profiles are calculated within a quantum-statistical method, based on thermodynamic Green's functions. The contributions of plasma ions and electrons are considered separately. Linear and quadratic Stark effect as well as quadrupole effects are taken into account for ions. The model microfield method is used to include ion dynamics. The focus of this work lies on the contribution to broadening and shift by free electrons beyond the Born approximation. The effect of strong collisions can be identified as ladder-like diagrams of the electron-emitter propagator. In an effective two-particle approximation, the electronic self-energy is given in terms of scattering amplitudes, analogous to Baranger's expressions [Baranger, M 1958 Phys. Rev. 112 855]. We obtained scattering amplitudes from convergent close-coupling calculations including medium effects via Debye screening. Additionally, the electronic coupling between initial and final states is taken care of by a vertex correction. In our examples, the free electron density ranges between 1023 and 1025 m−3 at a plasma temperature of 1 and 2 eV, respectively.

Spectra of Rayleigh-Brillouin scattering in supersonic gas flows measured with a wide aperture spectrometer

We applied spontaneous Rayleigh-Brillouin scattering for measuring kinetic coefficients and velocity of flows. A kinetic model was used for spectral line shape calculation in case of wide aperture Fabri-Perot spectrometer. The calculation well corresponds to experimental spectra for stationary nitrogen and atmospheric air flow up to 3 Mach number.

Structure of magnetic order in Pauli limited unconventional superconductors

We analyze the magnetic structure of the antiferromagnetic order induced in Pauli limited $d$-wave superconductors by Zeeman coupling to magnetic field. We determine the phase diagram in the $H$-$T$ plane and find that the magnetic phase, which is stabilized at low temperatures and just below the upper critical field, can have two realizations depending primarily on the shape of the underlying Fermi surface. The double-$\mathbit{Q}$ magnetic ordering may persist over the entire coexistence range. Alternatively, there may exist a weak first order transition from a double-$\mathbit{Q}$ structure at lower fields to a single-$\mathbit{Q}$ modulation at higher fields. Together with the calculations of the NMR line shape these results suggest the second scenario as a serious candidate for describing the superconducting state of CeCoIn${}_{5}$.