Velocity-changing Collisions Research Articles

Effects of velocity changing collisions on line shapes of HF in Ar

The generalized Hess method (GHM) gives a line shape expression which is formally equivalent to the Rautian–Sobel’man hard collision model of Dicke narrowing, but differs radically in the definition of one of the relaxation terms. The relaxation term leading to pressure broadening is the same, but the term leading to Dicke narrowing and ultimately to Doppler line shapes at zero density differs in certain important respects: (1) in GHM it is a weighted sum of the pressure broadening coefficient and an optical diffusion coefficient and (2) there is no sharp distinction between ‘‘velocity changing’’ and ‘‘phase changing’’ collisions. The Dicke narrowing term should thus be understood as including both collision types irretrievably intermixed, with GHM providing a prescription for both relaxation terms. Applied to HF v=0→1, j→j±1 absorption spectra in a bath of Ar and using an accurate interaction potential obtained from spectra of the van der Waals complex and essentially exact close coupling scattering S matrices, GHM provides a rather good description of recently measured line shapes.

Thermalization of velocity-selected excited-state populations by resonance exchange collisions and radiation trapping.

Populations of excited atoms that all have the same z component of velocity can be produced by pumping a vapor with a narrow-band laser. This velocity-selected population is then thermalized by velocity-changing collisions. However, in a pure vapor, even at low densities where velocity-changing collisions can be ignored, the mechanisms of radiation trapping and resonance exchange collisions can still lead to substantial thermalization of excited-atom velocity distributions. In this paper, we present data demonstrating these effects. We compare our data with results from a simple model of these processes. The model is in qualitative agreement with the experimental results.

Theory of selective reflection spectroscopy

We present a calculation of selective reflection spectroscopy, in which the reflection coefficient of a light beam from the interface of a dielectric and an atomic vapor is evaluated as a function of the light frequency. It is shown that the reflection signal depends critically on the spatial attenuation pattern of the refracted field inside the vapor. In the linear case, where the incident laser power is below the saturation limit, we show the dependence of the peak- and center-frequencies of the reflectivity line shapes on the atomic number density. In particular, we show that our self-consistent solution leads to a previously unrecognized line shift. The effects related to saturation and velocity-changing collisions between vapor atoms are also analyzed.

Experimental study on methods minimizing the influence of velocity-changing collisions in Doppler-free saturation spectroscopy

A method based on homodyne mixing is described which facilitates the use of rf-modulation of the pump beam for laser saturation spectroscopy together with conventional kHz lock-in amplifiers yielding a substantial reduction of disturbing pedestals present due to collisions in an atomic vapour. The technique benefits also from the significant improvement in the signal to noise ratio when transferring the Doppler-free signal to a frequency domain of several MHz where the interfering laser noise is low. These experimental procedures allow measurements of high quality saturated absorption spectra in vapour cells of otherwise unfavourable high gas pressure such as in commercial see-through hollow-cathodes. In addition we report the detection of an optogalvanic signal at rf-modulation (3.3 MHz).

Theory of selective reflection spectroscopy

We present a calculation of selective reflection spectroscopy, in which the reflection coefficient of a light beam from the interface of a dielectric and an atomic vapor is evaluated as a function of the light frequency. It is shown that the reflection signal depends critically on the spatial attenuation pattern of the refracted field inside the vapor. In the linear case, where the incident laser power is below the saturation limit, we show the dependence of the peak- and center-frequencies of the reflectivity line shapes on the atomic number density. In particular, we show that our self-consistent solution leads to a previously unrecognized line shift. The effects related to saturation and velocity-changing collisions between vapor atoms are also analyzed.

Direct measurement of velocity-changing collision cross sections by laser optical pumping.

We extend the theory of velocity-selective laser optical pumping in atomic vapors, allowing for arbitrarily rapid velocity-changing collisional rates. The results yield a simple relationship between the line-shape areas of narrow spectroscopic features present in optically pumped samples. This relationship gives directly the ground- and excited-state velocity-changing collision rates and cross sections. We use the results to analyze the data from a laser optical-pumping experiment in [sup 6]Li vapor perturbed by Ar buffer gas.

Collisional effects in gas lasers.

The effects of phase-interrupting and velocity-changing collisions between active and perturber atoms on the spectral profile of a gas laser are studied. Exact analytical results for the density matrix are presented for the case of strong collisions in a unidirectional ring laser, and the laser intensity is then evaluated in the Doppler limit under the condition of self-consistency. The washout of the hole burning in the steady-state population difference and the broadening of the laser line shape are discussed. The results of the third-order perturbation theory are compared with the exact calculations valid for an arbitrarily intense pump.

Flame temperature measurement using picosecond transient grating experiments

Picosecond transient grating experiments were performed on a sodium-seeded methane/air flame at very small fringe spacings ( < 1 μm). At these fringe spacings, the grating signal decay occurs on a time scale fast compared to that of velocity changing collisions. The form of the decay is determined by the Maxwell-Boltzmann velocity distribution of the Na atoms. The data is fit with one adjustable parameter, the temperature. These experiments demonstrate a potentially useful approach for the non-invasive measurement of flame temperatures in small regions of a flame.

Light-shift optical coherent averaging in rubidium vapors.

The sublevel time-domain magnetic-resonance signal is calculated for $^{85}\mathrm{Rb}$ atoms subjected to static or coherently modulated light-shift fields. We predict and experimentally confirm that the observed light shift may be scaled down by coherent light-shift modulation. We submit that the inhomogeneous light-shift broadening may be removed by this purely optical form of coherent averaging, which is referred to as the ``light-shift concertina.'' Our expressions also indicate that the velocity-changing collisions of atoms in a static light-shift field can cause narrowing of the magnetic-resonance line shape in a manner analogous to the effect of electronic exchange or molecular motion.

Line shapes of saturated absorption spectra in hollow cathode discharges

The saturated absorption line shapes of sputtered uranium atoms in hollow cathode discharges have been investigated using a single axial mode tunable CW laser. The spectral profiles observed under specific experimental conditions exhibit a marked deviation from the usual saturated absorption line shape function. These new features appear under the low velocity changing collision rate, high quenching rate and in the regime of strong pump saturation. A generalized line shape function based on population dynamics along with quenching mechanisms is derived and used to discuss the observed spectra. Our results suggest that the additional features in the observed spectra may be attributed to coherent effects which are manifested under suitable experimental conditions.

Effect of Ion-ion Coulomb Scattering in Plasma on the Photon Echo Decay

The extra photon echo decay due to ion-ion, velocity-changing collisions is computed. The strong velocity dependence of the collision frequency is shown to decrease the decay constant by 30%.

Interatomic potentials from velocity-changing collision kernels.

Measurements of velocity-changing collision kernels have recently been reported. Here we describe the results of calculations which demonstrate that interatomic potentials can accurately be derived from such data. It is important to analyze the kernel directly in terms of an interatomic potential and not in terms of a traditional energy-averaged differential cross section. We use experimental results to determine the Rb-He potential and compare it to calculated potentials.

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.

Scattering angle resolution in measurements of velocity-changing collision kernels.

A Comment on the Letter by A. J. McCaffery et al., Phys. Rev. Lett. 61, 2085 (1988).Received 14 September 1990DOI:https://doi.org/10.1103/PhysRevLett.67.1936©1991 American Physical Society

The spectra of radiation redistribution in the presence of velocity-changing collisions

The authors present an approach that allows the study of the influence of velocity-changing collisions (VCC) on the spectrum of resonance fluorescence. They give a theoretical framework yielding general, though quite complicated results. Working in the dressed-atom basis and describing the VCC by a strong-collision model, they focus their attention on the particular case of well separated spectral lines, which leads to relatively simple expressions. The results allow the authors to compare the effects of Doppler shifts and VCC on the profiles of the central line and on the spectra sidebands. They predict that VCC cause a narrowing of the spectral lines, which they attribute to Dicke narrowing. This prediction is also confirmed by numerical results. The adopted method of dealing with VCC in terms of collision operators can be applied to a larger class of collision models than just the strong-collision model used here.

Exchange collision kernel.

In the analysis of laser-spectroscopic line shapes, velocity-changing collisions are accounted for by adding to the density-matrix equations-of-motion terms involving the direct collision kernel. The direct collision kernel is the probability density per unit time that an atom has a specific velocity after a collision, as a function of its velocity before the collision. If the collision partner's velocity distribution is not thermal, however, the direct collision kernel alone does not completely characterize the effect of collisions. In such cases it is necessary to include terms involving the exchange collision kernel. The exchange kernel is the conditional probability density per unit time that the atom has a specific velocity after the collision as a function of its collision partner's velocity before the collision. Both the direct and the exchange collision kernels are obtained from the linearized Boltzmann equation. We derive an expression for the exchange kernel in terms of the colliding-pair scattering cross section, and calculate the exchange kernel for hard-sphere collisions. Moreover, we propose a phenomenological exchange kernel similar to the Keilson-Storer direct kernel [J. Keilson and K. E. Storer, J. Appl. Math. 10, 243 (1952)] and compare it with the hard-sphere kernel. In an earlier paper [P. R. Berman, J. E. M. Haverkort, and J. P. Woerdman, Phys. Rev. A 34, 4647 (1986)], a connection was made between the collision kernels of laser spectroscopy and the collision integrals of classical transport theory. We expand on this earlier work by including the exchange collision kernel, and indicate how results from classical transport theory might be used in setting the parameters appearing in the phenomenological exchange kernel. We interpret an excitation-transfer experiment in terms of the exchange kernel.

Measurements of velocity-changing collision kernels.

Measurements of velocity-changing collision (VCC) kernels are obtained using velocity-selective optical pumping. This is the first measurement of the shape of an elastic VCC kernel over the full thermal range of velocity changes. Since ground-state collisions are studied (5${\mathit{s}}_{1/2}$ Rb and He, Ne, Ar, Kr, or Xe), very low buffer-gas pressures can be used, and therefore pressure broadening (dephasing collisions) does not obscure the effects of VCC's. The data are deconvolved to eliminate the effects of the natural linewidth and are then extrapolated with respect to buffer-gas pressure to determine the single-collision limit. For small initial velocities, the measured kernels are consistent with a hard-sphere model for large velocity changes, but differ significantly for small velocity changes. The measured VCC kernels for large initial velocities and large velocity changes do not exhibit this agreement with the hard-sphere kernel. This implies that information about the inter- atomic potential can be obtained from a measurement of VCC kernels. We also show the inadequacy of the much-used Keilson-Storer kernel [J. Appl. Math. 10, 243 (1952)].

Effects of saturation and velocity-changing collisions on nonlinear mixing in resonant systems.

We study the effects of velocity-changing collisions (VCC's) on nearly degenerate forward four-wave mixing (FWM) in the presence of a strong pump. The calculations include the effects of both VCC's and phase-interrupting collisions. Explicit calculations and results for FWM in two-level systems for the case of strong collisions are presented in the Doppler limit. Effects of saturation on VCC-induced narrowing and those of VCC's on strong-field-induced resonances are discussed in detail.

Study of collisional effects on band shapes of the ν1/2ν2 Fermi dyad in CO2 gas with stimulated Raman spectroscopy. II. Simultaneous line mixing and Dicke narrowing in the ν1 band

An experimental (SRS) and theoretical analysis for the ν1 component of the ν1/2ν2 Fermi dyad of CO2 has been performed for densities lying from 0.01 to 50 amagat at 295 K, and from 0.01 to 20 amagat at 500 K. At subatmospheric pressure, both line mixing and Dicke narrowing take place for this component due to the very weak Q line spacings. A simple method to account for both diffusional narrowing (due to velocity changing collisions) and collisional narrowing (due to energy transfers) on isotropic Raman Q-branch profile is proposed. This method is based on the transformation of the collapsed Q-branch profile as a sum of individual Lorentzian plus dispersive components whose parameters are density-dependent. Such an exact transformation permits to easily introduce the averaging effect of velocity changing collisions on each component, and then on the collapsed Q-branch itself. In the present study, the Galatry soft collision model is used to define a generalized complete profile for each Lorentzian plus dispersive component. Such a procedure allows us to take into account the velocity changing collision’s effects not only on isolated lines (the well-known Dicke narrowing) but also on the line couplings resulting from collisionally induced rotational energy transfers. The present analysis permits an accurate description of the observed modifications on the SRS profile of the ν1 band of CO2 (1388 cm−1) as a function of density. The straightforward extension to other spectroscopies (linear and nonlinear) is suggested.

Light-induced drift of Na in molecular buffer gases

Conventional light-induced drift is based on purely elastic velocity-changing collisions. The authors discuss qualitatively the potentialities of light-induced drift originating from inelastic velocity-changing collisions, which may occur in a molecular buffer gas. In such collisions a large fraction of the electronic excitation energy of the absorbing particle may be transformed into kinetic energy thus affecting light-induced drift. The authors report experiments on light-induced drift of Na in various molecular buffer gases and compare these with their predictions.