Speed-dependent Voigt Profile Research Articles

Femtosecond time resolved coherent anti-Stokes Raman spectroscopy of H2–N2 mixtures in the Dicke regime: Experiments and modeling of velocity effects

In this paper, we present measurements and modeling of femtosecond time resolved coherent anti-Stokes Raman spectroscopy (CARS) signal in H(2)-N(2) mixtures at low densities. Three approaches have been used to model the CARS response. The first is the usual sum of Voigt profiles. In the second approach, the speed dependent Voigt profile is used. In the last approach, a model of the temporal CARS signal is developed, which takes into account the velocity changes induced by collisions and the speed dependence of the collisional parameters. The velocity changes are modeled using the Keilson and Storer memory function; the radiator speed dependences of the collisional parameters are determined from their temperature dependences. The results obtained are consistent with previous studies in the frequency domain, showing that the changes of the velocity have important effects for the H(2)/N(2) system in the Dicke narrowing density regime.

Asymmetry and speed-dependent effects on the 748.8 nm self-broadened neon line

Using an interferometric method, detailed analysis of the self-broadened 748.8 nm Ne line shapes emitted from the glow discharge of neon was performed, where departures from the ordinary Voigt profile were observed. These departures are shown to be consistent with fits of the speed-dependent asymmetric Voigt profile to experimental profiles. It was shown that neglecting the correlation between Doppler and collisional broadening may cause errors in determined line shape parameter values. Coefficients of the pressure broadening, shift and collision-time asymmetry are determined and compared with those calculated in the adiabatic approximation for the van der Waals and Lennard-Jones potentials.

Galatry versus speed-dependent Voigt profiles for millimeter lines of O 3 in collision with N 2 and O 2

Experimental and theoretical investigations of ozone lines broadened by nitrogen as well as oxygen have been carried out in the 300–320 GHz frequency range. Lineshape analysis has demonstrated clear departures from the usual Voigt profile, actual lineshapes being narrower and higher than expected. More refined models, such as the Galatry and speed-dependent Voigt profiles, have been used. Both of them have been found to reproduce the experimental lineshapes well. However, while for the latter, the narrowing parameter shows a linear behavior with pressure, for the Galatry profile a strong nonlinear behavior is observed. Such observations demonstrate that the Dicke narrowing effect, related to molecular diffusion, cannot be the leading process involved. Experimental results have also been compared to the theoretical ones. The relaxation rate dependence on molecular speed has been computed employing the Robert–Bonamy semiclassical theory. These calculations confirm the leading role of molecular speed dependence effects. Finally, it is inferred that optical diffusion rates are much lower than the kinetic diffusion rate, a conclusion well supported from the comparison of optical and Lennard–Jones radii.

Lineshapes of the 172 and 602 GHz rotational transitions of HC 15N

Experimental lineshapes of the 172 and 602 GHz millimeter lines of HC 15N in collision with H 2, N 2, O 2, CH 3CN and some rare gases are studied for the purpose of atmospheric applications and detailed collision analysis. Using of a sensitive frequency modulation technique allows highlighting clear deviations from the usual Voigt profile, these departures being generally considered as related to molecular diffusion effects or to the dependence of collisional relaxation rates on molecular speeds. Except the light buffer gases H 2 and He, the linefits using the Galatry profile lead to nonlinear pressure dependencies of relaxation rates, that rules out the frequent hypothesis of an exclusive role of molecular diffusion (Dicke effect). This observation is shown to be in accordance with the fact that optical radii related to relaxation are usually greater than kinetic Lennard-Jones radii tied to diffusion. In contrast, the actual lineshapes are well reproduced by the Speed-Dependent Voigt profile taking into account the speed dependence of relaxation rates which display linear pressure dependencies. For the particular cases of the N 2- and Ar-HCN pairs, the experimental results are rather well explained by semi-classical computations based on the Robert–Bonamy formalism improved by the model of exact trajectories. These computations show that relaxation rates are proportional to some power of the colliders’ relative speed. A detailed comparison of relaxation parameters deduced from low-pressure experiments with Galatry and Speed-Dependent Voigt profiles allows to infer that the optical diffusion rates are much smaller that kinetic ones, so that the experimental lineshapes depend nearly exclusively on the speed dependence of relaxation rates and are weakly affected by molecular diffusion effects. Extension of these conclusions to other molecules of atmospheric interest is discussed. Finally, an appendix presents unpublished results dealing with the collisional relaxation of some rotational lines of HC 15N (at 258 GHz for different temperatures and at 344 GHz) and HC 14N (at 355 GHz).

Lineshape analysis of the J = 3 ← 2 and J = 5 ← 4 rotational transitions of room temperature CO broadened by N 2, O 2, CO 2 and noble gases

Collisional relaxation has been considered for millimeter lines of carbon monoxide at room temperature. Accurate measurements of carbon dioxide- and rare gases-broadened widths have been performed on the J = 3 ← 2 rotational line of 12CO by using a video-type spectrometer. Measurements of nitrogen-, oxygen-, and xenon-broadened widths of the J = 5 ← 4 rotational line of 13CO were also carried by using a frequency-modulated spectrometer. A lineshape study performed on all the investigated binary systems provide confirmation that Voigt profile is not a suitable model to analyse experimental lines in the millimeter-waves region. On one hand, using this profile in the low pressure range, i.e. in the Doppler regime, the retrieved collisional linewidths do not follow a linear variation with the perturbing gas pressure. On the other hand, regardless of the pressure, lineshapes exhibit a narrowed profile. An accurate analysis of the pressure dependence of relaxation rates show that the Galatry profile is not appropriate and that experimental lineshapes are actually Speed Dependent Voigt profiles. Accurate broadening parameters were retrieved from this profile and compared to previous reported values and predictions calculated from the Robert–Bonamy formalism. Finally a variation of the ratio of relaxation speed dependence to broadening parameters versus relative masses of the collision partners is presented.

Line mixing effects in the ν2 + ν3 band of methane

This study provides the first direct experimental measurements of the off-diagonal relaxation matrix element coefficients for line mixing in air-broadened methane spectra for any vibrational band and the first off diagonal relaxation matrix elements associated with line mixing for pure methane in the ν 2 + ν 3 band of 12CH 4. The speed-dependent Voigt profile with line mixing is used with a multispectrum nonlinear least squares curve fitting technique to retrieve the various line parameters from 11 self-broadened and 10 air-broadened spectra simultaneously. The room temperature spectra analyzed in this work are recorded at 0.011 cm −1 resolution with the McMath-Pierce Fourier transform spectrometer located at the National Solar Observatory, Kitt Peak, Arizona. The off-diagonal relaxation matrix element coefficients of ν 2 + ν 3 transitions between 4410 and 4629 cm −1 are reported for eighteen pairs with upper state J values between 2 and 11. The observed line mixing coefficients for self broadening vary from 0.0019 to 0.0390 cm −1 atm −1 at 296 K. The measured line mixing coefficients for air broadening vary from 0.0005 to 0.0205 cm −1 atm −1 at 296 K.

Speed-dependent Voigt profile for water vapor in infrared remote sensing applications

The Voigt profile does not provide a sufficiently accurate representation of the line shape for air-broadened H 2O vapor over a significant range of conditions commonly encountered in atmospheric remote sensing. A speed-dependent Voigt profile yields much improved residuals in the analysis of water from infrared measurements collected by the atmospheric chemistry experiment (ACE), a satellite mission for remote sensing of the Earth's atmosphere. An analytical expression is presented for the rapid calculation of the speed-dependent Voigt profile.

K-Dependence and temperature dependence of N 2-, H 2-, and He-broadening coefficients for the J = 12–11 transition of acetonitrile CH 3C 14N located near 220.7 GHz

Extensive experiments on the K = 3 component of the J = 12–11 rotational transition of acetonitrile CH 3C 14N, located near 220.7 GHz, were performed at different temperatures in the range 235–350 K. They allow determining the N 2-, H 2-, and He-broadening coefficients, as well as their temperature dependences. More specific measurements on all the K-components of the involved transition perturbed by N 2 at 303 K allow to point out a clear decreasing of the broadening coefficient with increasing K. Narrowing effects are clearly observed, and experimental lines were analysed both with Voigt and speed dependent Voigt profiles; but no exhaustive lineshape study was carried out. All the experimental parameters are compared with results derived from a semiclassical calculation of collisional interactions, including electrostatic, induction, and dispersion energy contributions.

N2- and O2-broadening coefficients and profiles for millimeter lines of 14N2O

For the purpose of atmospheric applications, we have measured N2- and O2-induced broadenings and shapes of rotational lines of N2O in the 235–350K temperature range, precisely the J=8←7, J=22←21, and J=23←22 lines, located near 201, 552, and 577GHz, respectively. The analysis of experimental lineshapes shows up significant deviations from the Voigt profile, which are characteristic of line narrowing processes. In a first step, the Voigt profile was considered for the determination of pressure broadening parameters and of their temperature dependencies. Results are in good agreement with the dependence from rotational quantum number previously observed for other rotational and rovibrational lines. They are well explained by calculations based on a semiclassical formalism that includes the atom–atom Lennard-Jones potential in addition to electrostatic interactions up to hexadecapolar contributions. In a second step, observed lineshapes were analyzed by using the Galatry profile and a speed-dependent Voigt profile. The nonlinear pressure behavior observed for the diffusion rate β involved in the Galatry profile leads to rule out the possible role of velocity/speed changing collisions, and to infer that discrepancies from the Voigt profile result from the dependence of relaxation rates on molecular speeds. This interpretation is supported by the comparison of optical and kinetic radii and confirmed by theoretical calculations of relaxation rates. Finally, it can be claimed that, for the N2O–N2 and N2O–O2 systems, deviations from the Voigt profile are explained by a speed-dependent Voigt profile.

Infrared HCN Lineshapes as a Test of Galatry and Speed-Dependent Voigt Profiles

Absorption lineshapes of the ν2 infrared band of HCN in collision with He, Ne, Ar, Kr, Xe, N2, HCN, and CH3Br have been considered. Observed lineshapes differ significantly from the usual Voigt profile and are characteristic of line narrowing processes. The Galatry profile fairly reproduces lineshapes observed in the low-pressure regime, but leads to unexpected nonlinear behavior of optical diffusion rates in the high-pressure regime and strongly fails with the heaviest perturbers. On the other hand, fair results are obtained for all experimental conditions by using a speed-dependent Voigt profile that includes a pressure-dependent narrowing parameter. These observations are discussed by consideration of the polarization correlation functions related to considered line profiles and of the optical and kinetic radii involved in collision processes. It is shown that observed line narrowings primarily result from the dependence of relaxation rates on molecular speeds and that diffusion processes show up with the two lighter perturbers only, He and, to a small extent, Ne. Finally, it can be claimed that, for atmospheric applications, deviations from the Voigt profile must be taken into account by a speed-dependent Galatry profile that reduces to a speed-dependent Voigt profile in most cases.

Relaxation and Lineshape of the 500.4-GHz Line of Ozone Perturbed by N2 and O2

N2- and O2-broadened linewidths of the J = 342,32 ← 341,33 transition of ozone located at 500.4 GHz have been measured at three temperatures in the 247–295 K range by using a video-type spectrometer. Besides the Voigt profile commonly used as theoretical model for millimeter-wave investigations, different other theoretical lineshapes, the speed-dependent Voigt profile, the Galatry profile, and the speed-dependent Galatry profile, have been considered to analyze the experimental spectra, to retrieve the pressure-broadening parameters, and to give an account of the pointed out line-narrowing effect. The results for O3 perturbed by N2 and O2 are finally compared to calculations based on the complex semiclassical theory of Robert and Bonamy, and with previous reported values involving the same kind of transitions. Finally, it is shown that observed line narrowings result nearly exclusively from the dependence of relaxation on molecular speeds.

Laser-induced fluorescence study of collision-time asymmetry and speed-dependent effects on the114Cd326.1-nm line perturbed by Xe

Using a laser-induced fluorescence method detailed analysis of profiles of the ${}^{114}\mathrm{Cd}$ 326.1-nm line perturbed by xenon was performed, which revealed departures from the ordinary Voigt profile. These departures are shown to be consistent with fits of experimental profiles to a speed-dependent asymmetric Voigt profile. Coefficients of the pressure broadening, shift, and collision-time asymmetry are determined and compared with those calculated in the adiabatic approximation for the Czuchaj-Stoll potentials.

Self and Polar Foreign Gas Line Broadening and Frequency Shifting of CH3F: Effect of the Speed Dependence Observed by Millimeter-Wave Coherent Transients

The shape of the (J,K: 2, 1 ← 1, 1) millimeter line of CH3F in collision with polar buffer molecules has been investigated in the temperature range 140–300 K. The experiments exploit a Stark switching coherent transient technique, namely the optical free precession phenomenon, the Fourier transform of which is the usual steady state absorption lineshape. Using various buffer gases (CH3Br, CH3F, and NH3), the observed time domain signals provide the first experimental evidence in the millimeter range that line broadenings as well as frequency shiftings depend on the relative speed of collision partners; that is, lineshapes can become narrowed and asymmetric according to the molecular mass ratio and the type of collisional interaction involved. The experimental signals are analyzed with a time domain speed-dependent Voigt profile: for the polar buffer molecules considered, it is shown that a simultaneous interpretation of the broadening and narrowing parameters as well as of their temperature dependence can be satisfactorily obtained only with a realistic collision theory; in contrast with atomic buffer gases, velocity changing collisions play a negligible role.

Speed-dependent pressure broadening and shift in the soft collision approximation

The influence of speed-changing collisions and the correlation between Doppler and collisional broadening on the spectral line profiles is considered in a unified way using the Anderson-Talman classical phase-shift theory for collisional broadening and the Galatry diffusion model for the motion of radiating particles. A general formula for the correlation function is derived in the impact limit, which yields the well known speed-dependent Voigt profile in the case when the speed-changing collisions are neglected, but the Doppler-collision correlations are taken into account. In the opposite case, when the Doppler-collision correlations are omitted, but the speed-changing collisions are included this formula becomes identical to that derived by Galatry. This formula is shown to lead to the results close to those calculated from the line profile formula recently derived by Duggan et al [Phys. Rev. A51, 218 (1995)].

Response of Scanning Fabry-Pérot Interferometer to Speed-Dependent Asymmetric Voigt Profile

The Fabry—Perot interferometer (FPI) is one of a few spectroscopic instrumemts for which analytic approximation to its instrumental function is known with a high accuracy. If the real shape of a spectral line is known, the shape observed by means of the ΓΡI can be expressed as a convolution of the real shape and the instrumental function. The expression for such a convolution is called the response of the FΡI. The responses of the scanning FΡI to the Voigt profile (VP) [1], asymmetric Voigt profile (AVP) [2] and speed-dependent Voigt profile (SDVP) [3] have been reported in previous papers. In this paper we present a formula for the response of FΡI to the speed-dependent asymmetric Voigt profile. We also analyse the dependence of the collision-time asymmetry on the emitter velocity and discuss the influence of the correlation effects and collision-time asymmetry on the deviations of the real profile from the Voigt profile observed using the Fabry-Perot interferometer. In the near-wing region the line shape of the pressure broadened spectral line can be approximately described by a superposition of the Lorentzian and dispersion profiles [4,51:

Response of scanning Fabry-Pèrot interferometer to the speed dependent voigt profile

A detailed discussion of the influence of correlation effects on the combined Doppler and pressure broadening of spectral lines observed by means of a Fabry-Pèrot interferometer is presented. An expression for the response of scanning Fabry-Pèrot interferometer to the speed dependent Voigt profile is derived.

Response of scanning Fabry-Pèrot interferometer to the speed dependent Voigt profile

A detailed discussion of the influence of correlation effects on the combined Doppler and pressure broadening of spectral lines observed by means of a Fabry-Pèrot interferometer is presented. An expression for the response of scanning Fabry-Pèrot interferometer to the speed dependent Voigt profile is derived.

Lineshapes and broadening coefficients in the v 5 band of C 2H 2 in collision with Kr and He

General Voigt profiles (GVPs), including the speed dependence of collisional cross-sections, have been fitted to the following measured spectral lineshapes: the shapes of the R(7), R(11) and R(14) lines recorded with a tunable diode-laser spectrometer in the v 5 band of C 2H 2 in collision with He and Kr. The various GVPs and the resulting broadening coefficients are almost identical for light pertubers such as He and depend significantly on a simplified form in r - q of the interaction potential for heavy pertubers such as Kr. We consider three GVPs with q = 3 (Voigt function), q = 6 and q = 12, as well as the Galatry profile incorporating Dicke narrowing associated with velocity-changing collisions. The speed-dependent Voigt profile with q = 6 provides generally closer agreement with the spectral data of C 2H 2-Kr than the other GVPs and leads to Kr-broadening coefficients that are nearly 5% larger than those derived from the conventional Voigt profile.

Measurement of collisional broadening and shift parameters in X 1Σ+g→A 1Σ+u Li2 using Doppler scanning techniques

Line shift and broadening rates have been measured for three v′ j′ levels of the X→A manifold in Li2 with Xe as perturber gas. The lines are shifted and asymmetrically broadened and have been fitted using a speed dependent Voigt function that correlates the effect of velocity and broadening and shift rates. This asymmetric speed dependent Voigt profile (ASDVP) permits resolution of both effects at low foreign gas pressures, thus a shift corresponding to 11 MHz at line center was measured at 10 Torr xenon. Results are presented for the levels (v′,j′) 18,6; 20,20; 32,15 of A 1Σ+u and a reduction of shift and broadening rates is observed as j′ increases. This is attributed to the effective anisotropic contribution as rotor speed increases.

High-resolution spectroscopy of the oxygen A band

A high-resolution spectrometer incorporating a narrow linewidth (<10 −4 cm −1) tunable dye laser has been used to measure absorption profiles of 54 spectral lines of the b 1Σ g + ( ν = 0) ← X 3Σ g − ( ν = 0) band of molecular oxygen (the “ A band”) at pressures up to one atmosphere. A least-squares fitting procedure was used to compare the observed line profiles to four types of line profiles, including the Voigt function, two Dicke-narrowed profiles, and a speed-dependent Voigt profile. Clear deviations are shown between the observed profiles and the standard Voigt function. The other profiles all compare favorably with the observed lineshapes. Values of the line strengths and self-broadening coefficients, determined from least-squares fitting to the Galatry collisionally narrowed profile, are presented in tabular form. The distribution of line strengths is compared to expressions available in the literature. The self-broadening coefficients are compared with the measurements of several other investigators. Several lines have also been measured in air, and air broadening is compared with self-broadening.