Velocity-changing Collisions Research Articles

Full non-LTE spectral line formation

In the present paper we consider the full nonlocal thermodynamic equilibrium (non-LTE) radiation transfer problem. This formalism allows us to account for deviation from equilibrium distribution of both the radiation field and the massive particles. In the present study, two-level atoms with broadened upper level represent the massive particles. In the absence of velocity-changing collisions, we demonstrate the analytic equivalence of the full non-LTE source function with the corresponding standard non-LTE partial frequency redistribution (PFR) model. We present an iterative method based on operator splitting techniques that can be used to numerically solve the problem at hand. We benchmark it against the standard non-LTE transfer problem for a two-level atom with PFR. We illustrate the deviation of the velocity distribution function of excited atoms from the equilibrium distribution. We also discuss the dependence of the emission profile and the velocity distribution function on elastic collisions and velocity-changing collisions.

Extended measurements and calculations of CH3C14N-N2 rotational lineshape parameters

Spectroscopic parameters of methyl cyanide are of interest for astrophysical applications because of presence of this molecule in planetary atmospheres, comets, and interstellar medium. For radiative-transfer modeling a key role is played by the pressure-induced linewidths which are strongly influenced by the collision partner and the temperature. To complete the extremely scarce experimental data available, rotational lines of room-temperature CH3C14N in collision with molecular nitrogen have been recorded in a very large (180–1400 GHz) frequency range for J = 9 → 10, 12 → 13, 15 → 16, 21 → 22, 27 → 28, 33 → 34, 42 → 43, 48 → 49, 63 → 64, 69 → 70, 75 → 76 and K = 0–15. The high sensitivity of the frequency-modulated spectrometer has enabled observation of clear deviations of the recorded lineshapes from the usual Voigt profile. Their additional analyses performed with advanced non-Voigt models have demonstrated that the observed lineshapes are mainly governed by the speed dependence of relaxation rates and that the optical diffusion related to velocity changing collisions (Dicke effect) has a nearly negligible role. Compared to infrared-region results available in the literature, our Voigt-profile values lie systematically lower by about 0.5 MHz/Torr, which argues in favor of observable vibrational dependence for the CH3CN-N2 system. Line-broadening parameters have been also evaluated by a semi-empirical method based on the Anderson-Tsao-Curnutte theory. The model parameters determined from fits on some selected experimental values confirm the tendences previously stated for the case of vibrotational transitions and allow better theoretical predictions for extended ranges of rotational quantum numbers. Being temperature-independent, these parameters can be directly used in calculations for other temperatures concerned by radiative transfer models.

Spectral profile of ro-vibrational transitions of HCl broadened by He, Ar and SF6: Testing the β-correction to the Hartmann-Tran profile and the speed dependent (complex) hard collision model

The β-correction to the Hartmann-Tran (HT) profile, recently introduced to model the spectral shape of a molecular transition strongly affected by the Dicke narrowing effect (Konefal et al., JQSRT 242 (2020) 106,784), the HT profile (Ngo et al., JQSRT 129 (2013) 89), and the speed dependent (complex) hard collision model (SDcHC, in which the velocity changing collision rate is characterized by a complex number) are tested using spectra of two rovibrational lines of HCl. The R(5) and R(9) lines of the fundamental band of HCl broadened by He, Ar and SF6 have been recorded with a difference-frequency laser spectrometer for total pressures ranging from 12 to 930 mbar. These lines, measured in large pressure ranges with different collision-partners provide a meaningful test of the above-mentioned line-shape models. The results confirm that non-Voigt effects are significant for HCl broadened by Ar and SF6 and mainly due to the large influence of the Dicke narrowing effect. For HCl-SF6 and HCl-Ar, especially for the R(9) line, using the β-correction together with the HT profile (and with the speed-dependent hard collision model, SDHC) significantly improves the fit residuals while it has no effect on (or tends to deteriorate) the quality of the fit for HCl-He and for the R(5) line of HCl-SF6, for which the influence of velocity changing collisions is smaller. Except for HCl-He, the SDcHC model leads to better quality of fit compared to the HT profile. The results also show that numerical correlations between refined line-shape parameters of the HT profile are important and can lead to ill-determined parameters while they are more properly determined with the SDcHC model.

Artifact side peaks in saturated absorption spectroscopy caused by inappropriate lock-in amplification

Saturated absorption spectroscopy is a powerful technique that provides valuable information about gas-phase atomic targets, including not only the precise positions of transitions but also the effects of velocity-changing collisions, which manifest as changes in the shape of the peaks. However, using a lock-in amplifier inappropriately can generate artifact side peaks, potentially leading to a misinterpretation of results. To investigate the emergence of these artifacts, we conducted numerical calculations based on the basic Lambert–Beer’s law. Our model reproduced the artifact side peaks and revealed that these artifacts become more significant as the transmittance of the probe laser decreases.

Spectral line shape in the limit of frequent velocity-changing collisions

Spectral line shape in the limit of frequent velocity-changing collisions

Pressure and temperature dependencies of air-perturbed O[formula omitted] B-band line shapes

The air-broadened lines from the oxygen B band were measured for the first time in controlled laboratory conditions with a high signal-to-noise ratio using frequency-stabilized cavity ring-down spectroscopy (FS-CRDS) referenced to the optical frequency comb. Spectra measured at various pressures and temperatures were analyzed with an advanced line-shape model, considering the speed-dependence of collisional broadening and shift, and the effect of velocity-changing collisions. The temperature dependence of collisional broadening and shift is determined, whereas no significant temperature dependence of speed-dependent parameters and Dicke narrowing was observed. In addition, we have demonstrated that reasonable estimation of temperature dependence for pressure broadening is possible even from measurements done in single temperature where the speed dependence of pressure broadening was determined. New spectroscopic data improve the accuracy of the air-broadened oxygen B-band spectra description by an order of magnitude.

High-precision cavity-enhanced spectroscopy for studying the H2-Ar collisions and interactions.

Information about molecular collisions is encoded in the shapes of collision-perturbed molecular resonances. This connection between molecular interactions and line shapes is most clearly seen in simple systems, such as the molecular hydrogen perturbed by a noble gas atom. We study the H2-Ar system by means of highly accurate absorption spectroscopy and ab initio calculations. On the one hand, we use the cavity-ring-down-spectroscopy technique to record the shapes of the S(1) 3-0 line of molecular hydrogen perturbed by argon. On the other hand, we simulate the shapes of this line using ab initio quantum-scattering calculations performed on our accurate H2-Ar potential energy surface (PES). In order to validate the PES and the methodology of quantum-scattering calculations separately from the model of velocity-changing collisions, we measured the spectra in experimental conditions in which the influence of the latter is relatively minor. In these conditions, our theoretical collision-perturbed line shapes reproduce the raw experimental spectra at the percent level. However, the collisional shift, δ0, differs from the experimental value by 20%. Compared to other line-shape parameters, collisional shift displays much higher sensitivity to various technical aspects of the computational methodology. We identify the contributors to this large error and find the inaccuracies of the PES to be the dominant factor. With regard to the quantum scattering methodology, we demonstrate that treating the centrifugal distortion in a simple, approximate manner is sufficient to obtain the percent-level accuracy of collisional spectra.

PRESSURE DEPENDENCES OF LINE PARAMETERS OF THE 𝝂𝟑 + 𝝂𝟒 R(7)F1 TRANSITION OF METHANE DILUTED IN NITROGEN USING THE HARDAND SOFT-COLLISION MODELS

In this work, the affection of the Dicke narrowing effect on the spectral shape of the 𝜈3 + 𝜈4 R(7)F1 transition of methane diluted in nitrogen was studied using the Hard- and the Soft- collision line-shape models. Room-temperature absorption spectra of CH4 broadened by N2 were measured at a wide range of pressure using a difference-frequency laser spectrometer. Measured spectra of the studied transition were then one-by-one fitted with the simple Voigt profile as well as the two line-shape models considered the Dicke narrowing effect at two different assumptions of velocity-changing collisions: hard- and soft- collisions. The obtained results confirmed that using these two models leads to better qualities of fit with respect to the Voigt profile. Pressure-dependences of the line-shape parameters were also observed for the considered transition. The results showed a good agreement with other studies.

Optical pumping and relaxation of atomic population in assorted conditions

Precise control and knowledge over atomic dynamics is central to the advancement of quantum technology. The different experimental conditions namely, atoms in a vacuum, antirelaxation coated and buffer gas filled atomic cells provide complementary platforms for such investigations. The extent of changes in optical pumping, velocity changing collision and hyperfine changing collision rates associated with these conditions are discussed. There is a phenomenal change in the optical density by a factor of >25 times in the presence of a control field in a buffer gas environment. We found confinement induced enhanced optical pumping as the mechanism behind the observed transparency in buffer gas cell. The diffusive velocity of atoms were measured to be ∼25 ± 12 m s−1 and ⩽8 ± 4 m s−1 for antirelaxation coated and buffer gas filled cells respectively. The measurements were carried out for 85Rb atoms in natural isotopic composition using pump–probe spectroscopy. The studies will have useful application in measurements of relaxation rates, quantum memory, quantum repeaters and atomic devices.

Inhomogeneous broadening, narrowing and shift of molecular lines under frequent velocity-changing collisions

We demonstrate that speed-dependent hard-collision profiles collapse into a simple Lorentz profile in the regime dominated by the velocity-changing collisions. We present simple analytical formulas for the effective width and shift of the Lorentzian, derived from the speed-dependent collisional broadening and shift. While the effective width increases with speed dependence of collisional shift, it is reduced by speed dependence of collisional width. On the other hand, the effective shift is modified by thermal average of speed dependence of the product of collisional width and shift. We validate these formula numerically applying the quadratic speed dependence of the collisional width and shift.

Laser-induced-fluorescence imaging of a spin-polarized ultracold neutral plasma in a magnetic field

We report Doppler-sensitive laser-induced-fluorescence (LIF) imaging of an ultracold neutral plasma in a magnetic field. Local values of ion density, hydrodynamic fluid velocity, temperature, and spin polarization are obtained using a fluorescence model based on velocity-resolved rate equations (REs) including the transfer of ions between states due to laser coupling and spontaneous emission. The RE approach captures optical pumping of ions into states that are not driven by the LIF excitation laser, and this is validated with experimental data. Combined molecular-dynamics and quantum-trajectories simulations verify that velocity-changing collisions have a negligible impact on the state population evolution for typical experimental conditions. Relative intensities of Zeeman components of the LIF spectra provide clear evidence that the ions are electron-spin-polarized when created by photoionization of magnetically trapped $^{88}\mathrm{Sr}$ atoms. This probe opens many possibilities for studying thermal transport and the equilibration of neutral plasmas in overlapping regimes of strong coupling and magnetization.

DETERMINATION OF THE MASS DIFFUSION COEFFICIENT OF H2O DILUTED IN N2 USING CLASSICAL MOLECULAR DYNAMIC SIMULATION

In this work, the auto-correlation function of the center of mass velocity has been used to deduce the mass diffusion coefficient (D) of water diluted in nitrogen using the Classical Molecular Dynamics Simulations (CMDS). The calculations have been performed at room temperature (296 K) for different mixtures of H2O in N2 and 2.107 molecules from a five-sites potential. The results show that the auto-correlation functions expected exponential decay behavior [i.e. v v t exp( ) τ      ] and from the decay times τv , the mass diffusion coefficient and the velocity changing collisions frequency have been determined. The comparison between the CMDS results and experimental results are presented and discussed.

Line-shape parameters for the first rotational lines of HD in He

We report theoretical and experimental line-shape parameters for He-perturbed pure rotational HD lines that are relevant for the studies of gas giants atmospheres. Besides the usual pressure broadening and shift parameters, we also report their speed dependencies and Dicke parameters. The theoretical values, obtained from quantum dynamical calculations, are for the R(j=0-3) lines and S(j=0-2) and temperatures from 10 to 500 K. The measurements, performed using stimulated Raman spectroscopy, were done for the S(j=0-2) rotational Raman lines at 77, 195 and 298 K. We also compare the results of our calculations with pressure broadening and line shift coefficients available in the literature at 77, 195 and 300 K for the studied R lines. We demonstrate that a simple Voigt profile is insufficient to accurately model the shapes of He-perturbed HD lines at conditions relevant to gas giants atmospheres, and one should incorporate also the speed-dependent effects and velocity-changing collisions.

Combined molecular-dynamics and quantum-trajectories simulation of laser-driven, collisional systems

We introduce a combined molecular dynamics (MD) and quantum trajectories (QT) code to simulate the effects of near-resonant optical fields on state-vector evolution and particle motion in a collisional system. In contrast to collisionless systems, in which the quantum dynamics of multi-level, laser-driven particles with spontaneous emission can be described with the optical Bloch equations (OBEs), particle velocities in sufficiently collisional systems change on timescales comparable to those of the laser-induced, quantum-state dynamics. These transient velocity changes can cause the time-averaged velocity dependence of the quantum state to differ from the OBE solution. We use this multiscale code to describe laser-cooling in a strontium ultracold neutral plasma. Important phenomena described by the simulation include suppression of electromagnetically induced transparencies through rapid velocity changing collisions and thermalization between cooled and un-cooled directions for anisotropic laser cooling.

Fully quantum calculations of the line-shape parameters for the Hartmann-Tran profile: A CO-Ar case study

We present a procedure for generating the parameters of the Hartmann-Tran profile (HTP) from purely first principles calculations. Starting from an absorber-perturber interaction potential, we calculate S-matrices describing the effect of collisions on the absorbing molecule. We then use the generalized Hess method to calculate speed-dependent pressure shift and broadening parameters, and the complex Dicke parameter, νopt, which accounts for such effects as the Dicke effect and correlations between dephasing and velocity-changing collisions. Based on these ab initio results, we derive the Hartmann-Tran profile parameters and evaluate the validity of the quadratic approximation of speed dependence and the hard-collision model of velocity-changing collisions adopted in the Hartmann-Tran profile. We also discuss the interpretation and speed dependence of νopt. Finally, we evaluate the approximation scheme for temperature dependence of HTP line-shape parameters adopted in the 2016 edition of the HITRAN database.

Analytical-function correction to the Hartmann–Tran profile for more reliable representation of the Dicke-narrowed molecular spectra

The β-corrected Hartmann–Tran profile (HTP) constitutes an approximation of the partially correlated quadratic speed-dependent billiard-ball profile (SDBBP) easily applicable in calculations. We extend the approach originally developed for self-perturbed molecules [Wcisło et al. J. Quant. Spectrosc. Radiat. Transf. 177, 75–91 (2016)] to systems with a wide range of perturber-to-absorber mass ratios, including those relevant for atmospheric studies. This approach combines the computational simplicity of the HTP with the more physically justified rigid-sphere model for velocity-changing collisions. It is important for the analysis of high-resolution spectra influenced by the Dicke-narrowing effect. The β-corrected HTP enables high quality analytical representation of experimental spectra without incurring the high computational cost of more advanced line-shape models. This correction is directly applicable to any other line-shape model based on the hard-collision model for velocity-changing collisions.

Evaluation of different parameterizations of temperature dependences of the line-shape parameters based on ab initio calculations: Case study for the HITRAN database

Temperature dependences of molecular line-shape parameters are important for the spectroscopic studies of the atmospheres of the Earth and other planets. A number of analytical functions have been proposed as candidates that may approximate the actual temperature dependences of the line-shape parameters. In this article, we use our ab initio collisional line-shape calculations for several molecular systems to compare the four temperature ranges (4TR) representation, adopted in the HITRAN database [J. Quant. Spectrosc. Radiat. Transfer 2017;203:3] in 2016, with the double-power-law (DPL) representation. Besides the collisional broadening and shift parameters, we consider also the most important line-shape parameters beyond Voigt, i.e., the speed dependence of broadening and shift parameters, and real and imaginary parts of the complex Dicke parameter. We demonstrate that DPL gives better overall approximation of the temperature dependencies than 4TR. It should be emphasized that DPL requires fewer parameters and its structure is much simpler and more self-consistent than the structure of 4TR. We recommend the usage of DPL representation in HITRAN, and present DPL parametrization for Voigt and beyond-Voigt line profiles that will be adopted in the HITRAN database. We also discuss the problem of the Hartmann-Tran profile parametrization in which the correlation parameter, η, and frequency of the velocity-changing collisions parameter, νvc, diverges to infinity when collisional shift crosses zero; we recommend a simple solution for this problem.

Numerical Study of Change in Shape of Saturated Absorption Spectrum of Argon Arcjet Plasma by Strong Velocity-Changing Collisions

Saturated absorption (SA) spectra of argon arcjet plasma with the effect of strong velocity-changing collisions were numerically investigated. The spectrum was numerically reproduced by simulating the change of the velocity distribution interacting with the pump laser using the rate equation system representing two electronic states in the argon atoms. The SA spectra were classified into five types, which are composed of the linear combination of the Gaussian function, Lorentzian function, and inverted pedestals. We drew the maps of the types of the SA spectrum by varying the collision-induced velocity redistribution rate in the two electronic states and the decay rate among them. The possibility of the determination of the collisional parameters from the experiments was also discussed.

Differentiation of the Contribution of Velocity-Changing Gas-Particle Collisions to Attenuation of the Stimulated Photon Echo Response

The effect of velocity-changing gas-particle collisions on the intensity of the stimulated photon echo response is investigated. The intensity is influenced most by such collisions if the exciting-pulse wave vectors are nonparallel. An approximation of the intensity of the stimulated photon echo response as a function of the time interval between the second and third exciting laser pulses is proposed and enables differentiation of the contribution of velocity-changing particle collisions to attenuation of the response. The results are of interest for optical coherent echo spectroscopy.

Ultraviolet laser spectroscopy of aluminum atoms in hollow-cathode lamp

We report on the precision measurement of aluminum atoms transition at 394 nm and transition at 396 nm in a hollow-cathode lamp. Both absorption and saturated absorption spectra are measured. From the absorption spectra, the Doppler linewidth is estimated to be 2.65 GHz. The saturated absorption spectra are analyzed based on a velocity-changing collisions model. With a frequency comb calibrated wavemeter, the frequencies of transition and transition are measured to be 759.905 204(1) THz and 756.547 133(3) THz, respectively. The hyperfine coupling constants of aluminum atoms are determined, and are compared with previously reported measurement results and theoretical calculation results. Reasonable agreement is found for the magnetic dipole constant (A constant), while the electric quadrupole constant (B constant) has a large deviation.