Collisional Relaxation Rates Research Articles

Collective modes in interacting two-dimensional tomographic Fermi liquids

We develop an analytically solvable model for interacting two-dimensional Fermi liquids with separate collisional relaxation rates for parity-odd and parity-even Fermi surface deformations. Such a disparity of collisional lifetimes exists whenever scattering is restricted to inversion-symmetric Fermi surfaces, and should thus be a generic feature of two-dimensional Fermi liquids. It implies an additional unanticipated "tomographic" transport regime (in between the standard collisionless and hydrodynamic regimes) in which even-parity modes are overdamped while odd-parity modes are collisionless. We derive expressions for both the longitudinal and the transverse conductivity and discuss the collective mode spectrum along the collisionless-tomographic-hydrodynamic crossover. Longitudinal modes cross over from zero sound in the collisionless regime to hydrodynamic first sound in the tomographic and hydrodynamic regime, where odd-parity damping appears as a subleading correction to the lifetime. In charged Fermi liquids with long-range Coulomb coupling, these modes reduce to plasmons with a strongly suppressed odd-parity correction to the damping. The transverse response, by contrast, has a specific tomographic transport regime with two imaginary odd-parity modes, one of which requires a finite repulsive interaction, distinct from both the shear sound in the collisionless regime and an overdamped diffusive current mode in the hydrodynamic limit. Our work demonstrates that there are deep many-body aspects of interacting Fermi liquids, which are often thought to be well understood theoretically, remaining unexplored.

The CH4 abundance in Jupiter’s upper atmosphere

Hydrocarbon species, and in particular CH4, play a key role in the stratosphere-thermosphere boundary of Jupiter, which occurs around the μ-bar pressure level. Previous analyses of solar occultation, He and Ly-α airglow, and ISO/SWS measurements of the radiance around 3.3 μm have inferred significantly different methane concentrations. Here we aim to accurately model the CH4 radiance at 3.3 μm measured by ISO/SWS by using a comprehensive non-local thermodynamic equilibrium model and the most recent collisional rates measured in the laboratory for CH4 to shed new light onto the methane concentration in the upper atmosphere of Jupiter. These emission bands have been shown to present a peak contribution precisely at the μ-bar level, hence directly probing the region of interest. We find that a high CH4 concentration is necessary to explain the data, in contrast with the most recent analyses, and that the observations favour the lower limit of the latest laboratory measurements of the CH4 collisional relaxation rates. Our results provide precise constraints on the composition and dynamics of the lower atmosphere of Jupiter.

Vibrational self-quenching rates of CO(v=1,2) measured via transient diode laser absorption spectroscopy

New laboratory measurements of the rate coefficients for the vibrational relaxation of CO(v=1) and CO(v=2) through collisions with CO have been performed. The experimental approach involved creating a temperature-jump in an equilibrium mixture of CO and bath gases by photolyzing a trace amount of O3 in the mixture with a pulsed UV laser. This shifted a small fraction of the CO population to excited vibrational states. Transient diode laser absorption spectroscopy was then used to observe the evolving vibrational state populations as a function of time. Rate coefficients were deduced from the change in collisional relaxation rate with quencher concentration. This work was motivated by the need for a robust non-LTE model to describe Titan's upper atmosphere. Because the gas collision frequencies are not sufficient to reach thermal equilibrium in a non-LTE environment, the distribution of states is not easily predicted. To properly model such a region, all contributing vibrational energy transfer mechanisms must be thoroughly characterized. Despite their importance, the uncertainties associated with several CO quenching rate parameters in the literature are large. In this work, the rate coefficient for CO(v=2) self-quenching was measured to be (2.7 ± 0.6) x 10−12 cm3 molecule−1 s−1and the overall rate coefficient for CO(v=1) self-quenching was measured to be (1.8 ± 0.3) x 10−12 cm3 molecule−1 s−1. Each represents a significant decrease in uncertainty compared with values being used in current Titan non-LTE models.

The collisional relaxation rate of kappa-distributed plasma with multiple components

The kappa-distributed fully ionized plasma with collisional interaction is investigated. The Fokker-Planck equation with Rosenbluth potential is employed to describe such a physical system. The results show that the kappa distribution is not a stationary distribution unless the parameter kappa tends to infinity. The general expressions of collisional relaxation rate of multiple-component plasma with kappa distribution are derived and discussed in specific cases in details. For the purpose of visual illustration, we also give those results numerically in figures. All the results show that the parameter kappa plays a significant role in relaxation rate.

Modeling of a dual-wavelength pumped metastable argon laser

Optically pumped metastable argon laser is an attractive research topic of innovative gas lasers, but the slow collisional relaxation rates of 1s4–1s5 (in Paschen notation) may form a bottleneck on the cycling of active atoms and decrease the laser output at room temperature. Here, by employing a method of a dual-wavelength pump, we demonstrate the removal of accumulation on the 1s4 level and the improvement of output power in the simulation. The simulated results show that a large increase in laser output is possible with a relatively weak assistant pump intensity. This method offers a feasible way to scale the laser to higher gain.

Nuclear Spin Conversion in CH4: A Multichannel Relaxation Mechanism.

Experiments on nuclear spin interconversion of ortho, para, and meta nuclear spin isomers of the methane molecule have been undertaken in gas phase and cryomatrices. Only the latter environment has led to the observation of the nuclear spin conversion. In this study, a quantitative explanation is given for the first time by considering the coupling of three relaxation paths: meta ⇔ para, meta ⇔ ortho, and ortho ⇔ para. The global evolution of the three populations of spin isomers is thus described by two characteristic times, which have been calculated using the best values of the energy levels for the vibrational ground state, of the intramolecular magnetic interactions, and of the collisional relaxation rates, and for different pressure and temperature conditions. Such calculations also provide an indication for the proper choice of reliable scenarios for experimental separation of the spin isomers of methane.

Effect of optical-lattice heating on the momentum distribution of a one-dimensional Bose gas

We theoretically study how excitations due to spontaneous emission and trap fluctuations combine with elastic collisions to change the momentum distribution of a trapped non-degenerate one-dimensional (1D) Bose gas. Using calculated collisional relaxation rates, we first present a semi-analytical model for the momentum distribution evolution to get insight into the main processes responsible for the system dynamics. We then present a Monte-Carlo simulation that includes features that cannot be handled analytically, and compare its results to experimental data. These calculations provide a baseline for how integrable 1D Bose gases evolve due to heating processes in the absence of diffractive collisions that might thermalize the gases.

Experimental test of the quadratic approximation in the partially correlated speed-dependent hard-collision profile

We report on the outcomes of a specific study on the quadratic approximation in the partially correlated speed-dependent hard-collision (pC-SDHC) model, which is currently the recommended profile to replace the Voigt convolution for the shape of an isolated line, when perturbed by neutral gas-phase molecules. In particular, we compared the quadratic approximation with the hypergeometric dependence of the collisional relaxation rate on the absorber velocity by using high-quality ${\mathrm{H}}_{2}^{18}\mathrm{O}$ absorption spectra, in coincidence with three vibration-rotation transitions of the ${\ensuremath{\nu}}_{1}+{\ensuremath{\nu}}_{3}$ band, at 1.39 $\ensuremath{\mu}$m, also by looking for possible differences in the retrieved parameters. The pC-SDHC profile was found to be quite robust, regardless of the choice of the particular speed dependence. The pressure broadening and shifting parameters, retrieved by using the quadratic and hypergeometric versions, were found to be fully consistent, provided that the velocity-changing collision frequency ${\ensuremath{\nu}}_{\text{vc}}$ was considered as a free parameter. Similarly, the integrated absorbance was found to be completely unaffected by the choice of the speed dependence, in the entire pressure range we have explored. It must be noted, however, that the velocity-changing collision frequency resulted to be largely overestimated compared to the expected one when using the quadratic approximation. Moreover, the ${\ensuremath{\nu}}_{\text{vc}}$ values from the quadratic approximation are always significantly larger than those of the hypergeometric model.

Study of collisional deactivation of O2(b 1Σ g + ) molecules in a hydrogen-oxygen mixture at high temperatures using laser-induced gratings

Collisional deactivation of O2(b 1Σ g + ) molecules resonantly excited by a 10 ns pulse of laser radiation with a wavelength of 762 nm in H2/O2 mixtures is experimentally studied. The radiation intensity and hence the molecule excitation efficiency have a spatially periodic modulation that leads to the formation of laser-induced gratings (LIGs) of the refractive index. The study of LIG temporal evolution allows collisional relaxation rates of molecular excited states and gas temperature to be determined. In this work, the b 1Σ g + state of O2 molecules deactivation rates are measured in a 4.3 vol % H2 mixture at the number density of 2 amg in the temperature range 291–850 K. The physical deactivation is shown to dominate in the collisions of H2 with O2(b 1Σ g + ) and O2(a 1Δ g ) up to temperatures of 780–790 K at time delays up to 10 μs after the excitation pulse. The parameters of the obtained temperature dependence of the (b 1Σ g + state deactivation rate agree well with the data of independent measurements performed earlier at lower temperatures (200–400 K). Tunable diode laser absorption spectroscopy is used to measure the temperature dependence of the number density of the H2O molecules which appear as the mixture, as the result of the dark gross reaction with O2 molecules in the ground state, O2 + 2H2 → 2H2O. The measurements show that this reaction results in complete transformation of H2 into H2O at temperatures of 790–810 K.

Isotropic inelastic and superelastic collisional rates in a multiterm atom

The spectral line polarization of the radiation emerging from a magnetized astrophysical plasma depends on the state of the atoms within the medium, whose determination requires considering the interactions between the atoms and the magnetic field, between the atoms and photons (radiative transitions), and between the atoms and other material particles (collisional transitions). In applications within the framework of the multiterm model atom (which accounts for quantum interference between magnetic sublevels pertaining either to the same J-level or to different J-levels within the same term) collisional processes are generally neglected when solving the master equation for the atomic density matrix. This is partly due to the lack of experimental data and/or of approximate theoretical expressions for calculating the collisional transfer and relaxation rates (in particular the rates for interference between sublevels pertaining to different J-levels, and the depolarizing rates due to elastic collisions). In this paper we formally define and investigate the transfer and relaxation rates due to isotropic inelastic and superelastic collisions that enter the statistical equilibrium equations of a multiterm atom. Under the hypothesis that the atom-collider interaction can be described by a dipolar operator, we provide expressions that relate the collisional rates for interference between different J-levels to the usual collisional rates for J-level populations. Finally, we apply the general equations to the case of a two-term atom with unpolarized lower term, illustrating the impact of inelastic and superelastic collisions on scattering polarization through radiative transfer calculations in a slab of stellar atmospheric plasma anisotropically illuminated by the photospheric radiation field.

Nuclear spin conversion in H2O

Nuclear spin conversion (NSC) in water molecules has often been investigated in the gas or solid phase. It has not been observed in the former yet because of the difficulty in producing an efficient disequilibrium of the spin isomer populations. Another, again failed, attempt at such an experiment is presented based on the supposed spin-selective adsorption ability of nanoporous materials. To explain the reason for so many failures, the NSC rate has been calculated in the framework of the quantum relaxation model, using the best available values of the energy levels of the vibrational ground state, the intramolecular magnetic interactions, and the collisional relaxation rates. The characteristic time of NSC in the gas phase is of the order of 1 s at ambient temperature. As NSC is observed in low-temperature matrices, the quantum relaxation model can be adapted to estimate the rate in such environments. Finally, some recent experimental results devoted to astrophysical problems are discussed.

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).

OODR-LIF on N2(A3Σ u + in dielectric barrier discharges

We report on the application of Optical-Optical Double Resonance (OODR)LIF to the detection of N2(A3Σ u + in a dielectric barrier discharge (DBD) along two research lines. At low pressure (1 ÷ 30 Torr) OODR-LIF is used to selectively excite N2(C3Πu, v = 1) and obtain, with a direct method, electronic quenching and, for the first time, the collisional vibrational relaxation rate coefficient (C, v = 1) → (C, v = 0). At high pressure OODR-LIF is used to measure, again for the first time, N2(A3Σ u + density with time and space resolution in an atmospheric pressure DBD, with the aid of a spectroscopic calibration method that relies upon the measurement of SPS and NO-γ emissions in the post-discharge.

The role of relaxation in the nuclear spin conversion process

The nuclear spin conversion rate depends on the collisions, which break the coherence created by magnetic intramolecular interactions between pairs of quasi degenerate levels belonging to the different spin isomers. The collisions act similarly to break the coherence created by a radiation field between two levels inducing pressure broadening of molecular transitions. Collisional relaxation rates have been extensively studied in this last situation using semi-classical approach and rectilign trajectory for collisional path. Taking advantage of the analogy, the present paper shows that calculations can be efficiently adapted for the collisional relaxation terms present in the ‘quantum relaxation’ model of nuclear spin conversion. For 13CH 3F, numerous experimental measurements of spin conversion rates in the presence of an electric field have allowed to derive directly relaxation rates. Our calculation appears to agree satisfactorily with these experimental values. For 12CH 3F, calculated relaxations rates are also given for the pairs involved in nuclear spin conversion.

Comparing continuous wave progressive saturation EPR and time domain saturation recovery EPR over the entire motional range of nitroxide spin labels

The measurement of spin–lattice relaxation rates from spin labels, such as nitroxides, in the presence and absence of spin relaxants provides information that is useful for determining biomolecular properties such as nucleic acid dynamics and the interaction of proteins with membranes. We compare X-band continuous wave (CW) and pulsed or time domain (TD) EPR methods for obtaining spin–lattice relaxation rates of spin labels across the entire range of rotational motion to which relaxation rates are sensitive. Model nitroxides and spin-labeled biological species are used to illustrate the potential complications that arise in extracting relaxation data under conditions typical to biological experiments. The effect of super hyperfine (SHF) structure is investigated for both CW and TD spectra. First and second harmonic absorption and dispersion CW spectra of the nitroxide spin label, TEMPOL, are all fit simultaneously to a model of SHF structure over a range of microwave amplitudes. The CW spectra are novel because all harmonics and microwave phases were acquired simultaneously using our homebuilt CW/TD spectrometer. The effect of the SHF structure on the pulsed free induction decay (FID) and pulsed saturation recovery spectrum is shown for both protonated and deuterated TEMPOL. We present novel pulsed saturation recovery measurements on biological molecules, including spin–lattice relaxation rates of spin-labeled proteins and spin-labeled double-stranded DNA. The impact of structure and dynamics on relaxation rates are discussed in the context of each of these examples. Collisional relaxation rates with oxygen and transition metal paramagnetic relaxants are extracted using both continuous wave and time domain methods. The extent of the errors inherent in the CW method and the advantages of pulsed methods for unambiguously measuring collisional relaxation rates are discussed. Spin–lattice relaxation rates, determined by both CW and pulsed methods, are used to determine the electrostatic potential on the surface of a protein.

Vibrational relaxation of NO(υ=1) by oxygen atoms

The rate constant kO(υ=1) for NO(υ=1) vibrational relaxation by O has been measured at room temperature using a laser photolysis-laser probe technique. Vibrationally excited NO and relaxer O atoms were formed using 355 nm laser photolysis of a dilute mixture of NO2 in argon bath gas. The time evolution of both the NO(υ=1) and the O atoms was monitored using laser-induced fluorescence (LIF). The required absolute O-atom densities were obtained through a comparison of O-atom LIF signals from the photolysis source and from a titrated cw microwave source. At early times the O atoms constitute the most important loss mechanism for the nascently produced NO(υ=1). Possible effects from NO(υ=1) vibrational ladder-climbing and from thermal expansion have been shown to be minimal. The rate constant kO(υ=1)=(2.4±0.5)×10−11 cm3 s−1 determined herein is a factor of 2 to 3 lower than the generally accepted value of kO(υ=1) used in thermospheric modeling. The present value for kO(υ=1) is the same, within the error bars, as the kO(υ=2,3) previously measured in this laboratory using an entirely different technique, resonant infrared laser excitation of NO(υ=0). This result suggests that the collisional relaxation rates are independent of υ. A recent quasiclassical trajectory calculation, in which both allowed NO–O surfaces have been explicitly considered, predicts a collisional relaxation rate which is in good agreement with the present result. The kO(υ=1) value, along with previously measured rate constants for NO–O high-pressure recombination (krec∞) and isotope exchange (kiso), can serve as a proxy for the rate coefficient kC describing the formation of a long-lived NO2* intermediate from O+NO collisions. The present value for kO(υ=1) is significantly lower, however, than a recent determination of krec∞ and also the value of kC derived from kiso. In the latter case the comparison is not as straightforward.

Experimental investigation of an optically pumped mid-infrared carbon monoxide laser

Results from a dual experimental/theoretical investigation of an optically pumped room-temperature carbon monoxide (CO) laser are discussed. Ro-vibrational transitions in the (2, 0) overtone of CO at 2.3 /spl mu/m were pumped with an optical parametric oscillator to generate lasing on (2, 1) band transitions near 4.7 /spl mu/m. During the build-up of the laser pulse, only rotational redistribution of the initial optically pumped population was observed in the resolved CO spectra. Calculations describing the CO laser pulse dynamics and collisional relaxation rates support this observation. The addition of helium and argon bath gases enhanced the rotational relaxation process. A pressure dependent loss mechanism that degrades optical efficiency has been identified and possible causes are discussed.

Amplification without inversion in a medium with collisional dephasing

Amplification without inversion in the presence of collisions in V and \ensuremath{\Lambda} systems is studied within the framework of density-matrix formalism. We show that while it is possible to achieve amplification without inversion close to Raman resonance in both systems, it is affected by collisions in a different way. In the V system, collisions enhance quantum interference, whereas in the \ensuremath{\Lambda} system they quench it. This effect depends crucially on the collision characteristics, essentially on the relative values of the collisional relaxation rates for the Raman coherence and for the optical coherences. For the \ensuremath{\Lambda} system, different incoherent pumping processes are studied: pumping via the upper level and direct pumping between the two low-energy levels. The direct pumping process is interesting for the frequency up-conversion of the coherent and incoherent pump fields. Furthermore, with direct pumping the gain always occurs without inversion.

State-to-state vibrational and rotational energy transfer in CO2 gas from time-resolved raman-infrared double resonance experiments

A time-resolved Raman–infrared double resonance technique was used to study collisional relaxation rates of vibrational and rotational energy levels in CO2 gas at 295 K. A pulsed Raman excitation populated a selected rovibrational initial state. Measurements of the rates of transfer from the pumped initial state into specific final states were carried out using time-resolved laser absorption spectroscopy. First, the transfer rates were determined for the five lower vibrational energy levels. In particular, it was confirmed that the rate of transfer between the two Fermi levels (1000) and (0200) is very small [(5.3±0.2)×104 Torr-1 s-1]. The rotational structure inside the (0200) vibrational level was also studied. A kinetic master equation was used to model energy transfer among rotational levels. The state-to-state rotational energy transfer rates were calculated by the fitting and scaling laws. The ability of different laws (ECS-P, ECS-EP, MEG) was then compared in order to reproduce the time-dependent population evolution. © 1998 John Wiley & Sons, Ltd.

The Infrared Diode Laser Spectroscopy of the ν2+ ν5− ν2Hot Band of Acetylene

The infrared diode laser spectrum of the ν2+ ν5− ν2hot band of acetylene has been observed within the discharge plasma of acetylene diluted in He. The concentration of acetylene in the ν2state was modulated by applying a few kHz of ac current, and the spectrum of the hot band was recorded selectively by the discharge modulation technique. In total, 46P,R, andQ-branch lines have been assigned to the ν2+ ν5− ν2hot band and molecular constants including the band origin 727.59318(27) cm−1were derived. The lifetime of acetylene in the ν2state was measured to be about 1 ms, proving that the ν2state is metastable. The collisional relaxation rate constant of acetylene in the ν2state by helium was measured to bek= 8.01 ± 0.19 × 10−14cm3molec−1s−1.