Collisional Relaxation Research Articles

Broadband ultrafast photoprotection by oxybenzone across the UVB and UVC spectral regions.

Recent studies have shed light on the energy dissipation mechanism of oxybenzone, a common ingredient in commercial sunscreens. After UVA photoexcitation, the dissipation mechanism may be understood in terms of an initial ultrafast excited state enol → keto tautomerisation, followed by nonadiabatic transfer to the ground electronic state and subsequent collisional relaxation to the starting enol tautomer. We expand on these studies using femtosecond transient electronic absorption spectroscopy to understand the non-radiative relaxation pathways of oxybenzone in cyclohexane and in methanol after UVB and UVC excitation. We find that the relaxation pathway may be understood in the same way as when exciting in the UVA region, concluding that oxybenzone displays proficient broadband non-radiative photoprotection, and thus photophysically justifying its inclusion in sunscreen mixtures.

Kinetic theory of phase space plateaux in a non-thermal energetic particle distribution

The transformation of kinetically unstable plasma eigenmodes into hole-clump pairs with temporally evolving carrier frequencies was recently attributed to the emergence of an intermediate stage in the mode evolution cycle, that of an unmodulated plateau in the phase space distribution of fast particles. The role of the plateau as the hole-clump breeding ground is further substantiated in this article via consideration of its linear and nonlinear stability in the presence of fast particle collisions and sources, which are known to affect the production rates and subsequent frequency sweeping of holes and clumps. In particular, collisional relaxation, as mediated by e.g. velocity space diffusion or even simple Krook-type collisions, is found to inhibit hole-clump generation and detachment from the plateau, as it should. On the other hand, slowing down of the fast particles turns out to have an asymmetrically destabilizing/stabilizing effect, which explains the well-known result that collisional drag enhances holes and their sweeping rates but suppresses clumps. It is further demonstrated that relaxation of the plateau edge gradients has only a minor quantitative effect and does not change the plateau stability qualitatively, unless the edge region extends far into the plateau shelf and the corresponding Landau pole needs to be taken into account.

The collisional relaxation of electrons in hot flaring plasma and inferring the properties of solar flare accelerated electrons from X-ray observations.

X-ray observations are a direct diagnostic of fast electrons produced in solar flares, energized during the energy release process and directed towards the Sun. Since the properties of accelerated electrons can be substantially changed during their transport and interaction with the background plasma, a model must ultimately be applied to X-ray observations in order to understand the mechanism responsible for their acceleration. A cold thick target model is ubiquitously used for this task, since it provides a simple analytic relationship between the accelerated electron spectrum and the emitting electron spectrum in the X-ray source, with the latter quantity readily obtained from X-ray observations. However, such a model is inappropriate for the majority of solar flares in which the electrons propagate in a hot megaKelvin plasma, because it does not take into account the physics of thermalization of fast electrons. The use of a more realistic model, properly accounting for the properties of the background plasma, and the collisional diffusion and thermalization of electrons, can alleviate or even remove many of the traditional problems associated with the cold thick target model and the deduction of the accelerated electron spectrum from X-ray spectroscopy, such as the number problem and the need to impose an ad hoc low energy cut-off.

Improved collision operator for plasma kinetic simulations with multi-species ions and electrons

A linearized collision operator, which preserves the conservation properties of particles, momentum, and energy, and the self-adjointness relation (H-theorem) for arbitrary particle species, is applied to Eulerian kinetic simulations of multi-species ions and electrons. Velocity-space grid number scans clarify that numerical errors in like-particle and unlike-ion collisions are sufficiently small under turbulence-simulation relevant resolutions. For electron–ion/ion–electron collisions, it is identified that highly steep and localized nature in the velocity-space leads to relatively larger conservation errors in the standard implementation without error corrections. In order to resolve such numerical difficulties, a modified field-particle operator based on the original one is newly constructed, so that the conservation properties are improved to achieve the round-off error levels. It is confirmed that the modified collision operator successfully reproduces the collisional relaxation of multi-species ions and electrons towards their equilibrium distributions satisfying the H-theorem.

Time-resolved UV–IR pump-stimulated emission pump spectroscopy to probe collisional relaxation of the 8p2P3/2 state of Cs I

We describe and use a time-resolved pump-stimulated emission pump spectroscopic technique to measure collisional relaxation in a high-lying energy level of atomic cesium. Aligned 8p2P3/2 cesium atoms were produced by a pump laser. A second laser, the stimulated emission pump, promoted the population exclusively to the 5d2D5/2 level. The intensity of the 5dD5/22→6sS1/22 cascade fluorescence at 852.12nm was monitored. The linear polarization dependence of the 6sS1/22→8pP3/22→5dS5/22 transition was measured in the presence of argon gas at various pressures. From the measurement, we obtained the disalignment cross sectional value for the 8p2P3/2 level due to collisions with ground-level argon atoms.

THE FINAL-PARSEC PROBLEM IN THE COLLISIONLESS LIMIT

A binary supermassive black hole loses energy via ejection of stars in a galactic nucleus, until emission of gravitational waves becomes strong enough to induce rapid coalescence. Evolution via the gravitational slingshot requires that stars be continuously supplied to the binary, and it is known that in spherical galaxies the reservoir of such stars is quickly depleted, leading to stalling of the binary at parsec-scale separations. Recent N-body simulations of galaxy mergers and isolated nonspherical galaxies suggest that this stalling may not occur in less idealized systems. However, it remains unclear to what degree these conclusions are affected by collisional relaxation, which is much stronger in the numerical simulations than in real galaxies. In this study, we present a novel Monte Carlo method that can efficiently deal with both collisional and collisionless dynamics, and with galaxy models having arbitrary shapes. We show that without relaxation, the final-parsec problem may be overcome only in triaxial galaxies. Axisymmetry is not enough, but even a moderate departure from axisymmetry is sufficient to keep the binary shrinking. We find that the binary hardening rate is always substantially lower than the maximum possible, "full-loss-cone" rate, and that it decreases with time, but that stellar-dynamical interactions are nevertheless able to drive the binary to coalescence on a timescale <=1 Gyr in any triaxial galaxy.

Collective modes of chiral kinetic theory in a magnetic field

We study collective excitations in systems described by chiral kinetic theory in external magnetic field. We consider high-temperature weak-coupling plasma, as well as high-density Landau Fermi liquid with interaction not restricted to be weak. We show that chiral magnetic wave (CMW) emerges in hydrodynamic regime (at frequencies smaller than collision relaxation rate) and the CMW velocity is determined by thermodynamic properties only. We find that in a plasma of opposite chiralities, at frequencies smaller than the chirality-flipping rate, the CMW excitation turns into a vector-like diffusion mode. In the interacting Fermi liquid, the CMW turns into the Landau zero sound mode in the high-frequency collisionless regime.

Backward mapping solutions of the Boltzmann equation in cylindrically symmetric, uniformly charged auroral ionosphere

By applying a backward mapping technique, we solve the Boltzmann equation to investigate the effects of ion-neutral collisions on the ion velocity distribution and related transport properties in cylindrically symmetric, uniformly charged auroral ionosphere. Such a charge geometry introduces a radial electric field which increases linearly with distance from the axis of symmetry. In order to obtain complete analytical solutions for gaining physical insights into more complicated problems, we have substituted a relaxation collision model for the Boltzmann collision integral in the Boltzmann equation. Our calculations show that collisions drive the velocity distribution to a “horseshoe” shape after a few collision times. This feature extends to all radial positions as long as the electric field keeps increasing linearly versus radius. If the electric field is introduced suddenly, there is a transition from the collision-free pulsating Maxwellian distributions obtained in previous work (Ma and St.-Maurice, J. Geophys. Res., 113:A05312, 2008) to the “horseshoe” shapes on a time scale of within the few collision times. We also show how the transport properties evolve in a similar fashion, from oscillating to a non-oscillating features over the same time interval.

Monte Carlo simulation of electron detachment properties for ions in oxygen and oxygen:nitrogen mixtures

Electron detachment properties of ions in pure oxygen and oxygen:nitrogen mixtures have been studied by a Monte Carlo technique for the reduced electric fields up to 350 Td (1 Td = 10−17 V·cm2). Swarm parameters were calculated for unexcited and vibrationally excited ions taking into account vibrational transfer and relaxation, charge transfer and electron detachment. The cross sections for vibrational transfer and relaxation in collisions between ions and O2 molecules were calculated on the basis of the statistical approach that had been successfully used in our previous work to simulate the effect of vibrational excitation and the effect of electric field on electron detachment. Good agreement between the calculated detachment rate and available measurements in oxygen were obtained over a wide range of reduced electric fields without using adjusted parameters. The method was used to calculate detachment rates in air and in some other oxygen:nitrogen mixtures and to study the effect of gas temperature on electron detachment.

State-resolved collisional relaxation of highly vibrationally excited CsH by CO2

Quenching of highly vibrationally excited CsH(X1Σ+, v=15–23) by collisions with CO2 was investigated. A significant fraction of the initial population of highly vibrationally excited CsH(v=22) was relaxed to a low vibrational level (Δv=−5). The near-resonant 5–1 vibration-to-vibration (V–V) energy was efficiently exchanged. The rate constants for the rotational levels of CO2(0000) [J=36–60] and CO2(0001) [J=5–31] from the collisions with excited CsH were determined. The experiments revealed that the collisions resulting in CO2(0000) were accompanied by substantial excitation in rotation and translation. The vibrationally excited CO2(0001) state exhibited rotational and translational energy distributions near those of the initial state. The total quenching rates relative to the probed state of excited CsH were determined for both CO2 states. The corresponding data indicated that the gains in the rotational and translational energies in CO2 were sensitive to the collisional depletion of excited CsH.

Collisional relaxation of vibrational states of SrOH with He at 2 K

Vibrational relaxation of strontium monohydroxide (SrOH) molecules in collisions with helium (He) at 2 K is studied. We find the diffusion cross section of SrOH at 2.2 K to be and the vibrational quenching cross section for the (100) Sr–O stretching mode to be . The resulting ratio is more than an order of magnitude smaller than for previously studied few-atom radicals (Au et al 2014 Phys. Rev. A 90 032703 ). We also determine the Franck–Condon factor for SrOH () to be .

Combined effect of small- and large-angle scattering collisions on a spectral line shape

Algebraic approximations for line profiles calculated on the basis of quantum-mechanical collision integral kernels for dipole–dipole, dipole–quadrupole, and quadrupole–quadrupole intermolecular interaction potentials were obtained. In derivation of the profiles velocity-changing collisions of molecules with scattering on small and large angles also with the speed-dependence of collision relaxation constants have been taken into account. It was shown that the relative contribution of small-angle collisions into the frequency of elastic velocity-changing collisions is much more pronounced for long-range potentials. A sensitive criterion for analysis of a line narrowing was proposed and tested.

Relaxation mechanisms affecting magneto-optical resonances in an extremely thin cell: Experiment and theory for the cesiumD1line

We have measured magneto-optical signals obtained by exciting the ${D}_{1}$ line of cesium atoms confined to an extremely thin cell (ETC), whose walls are separated by less than $1\ensuremath{\mu}\text{m}$, and developed an improved theoretical model to describe these signals with experimental precision. The theoretical model was based on the optical Bloch equations and included all neighboring hyperfine transitions, the mixing of the magnetic sublevels in an external magnetic field, and the Doppler effect, as in previous studies. However, in order to model the extreme conditions in the ETC more realistically, the model was extended to include a unified treatment of transit relaxation and wall collisions with relaxation rates that were obtained directly from the thermal velocities of the atoms and the length scales involved. Furthermore, the interactions of the atoms with different regions of the laser beam were modeled separately to account for the varying laser beam intensity over the beam profile as well as saturation effects that become important near the center of the beam at the relatively high laser intensities used during the experiments in order to obtain measurable signals. The model described the experimentally measured signals for laser intensities for magnetic fields up to 55 G and laser intensities up to $1{\text{W/cm}}^{2}$ with excellent agreement.

Hypocoercivity for linear kinetic equations conserving mass

We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted L 2 L^2 norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed.

Determining the relaxation constants of a molecular gas in a continuous laser field

The processes of collisional relaxation in 13CH3F polar gas are considered, and the nonmonotonous character of the dependence of the signal of delayed optical nutations on the duration of the Stark field is explained. A damping constant is introduced for the matrix of optical coherence.

First accurate experimental study of Mu reactivity from a state-selected reactant in the gas phase: the Mu + H2{1} reaction rate at 300 K

This paper reports on the experimental background and methodology leading to recent results on the first accurate measurement of the reaction rate of the muonium (Mu) atom from a state-selected reactant in the gas phase: the Mu + H2 MuH + H reaction at 300 K, and its comparison with rigorous quantum rate theory, Bakule et al (2012 J. Phys. Chem. Lett. 3 2755). Stimulated Raman pumping, induced by 532 nm light from the 2nd harmonic of a Nd:YAG laser, was used to produce H2 in its first vibrational (v = 1) state, H, in a single Raman/reaction cell. A pulsed muon beam (from ‘ISIS’, at 50 Hz) matched the 25 Hz repetition rate of the laser, allowing data taking in equal ‘Laser-On/Laser-Off’ modes of operation. The signal to noise was improved by over an order of magnitude in comparison with an earlier proof-of-principle experiment. The success of the present experiment also relied on optimizing the overlap of the laser profile with the extended stopping distribution of the muon beam at 50 bar H2 pressure, in which Monte Carlo simulations played a central role. The rate constant, found from the analysis of three separate measurements, which includes a correction for the loss of concentration due to collisional relaxation with unpumped H2 during the time of each measurement, is = 9.9[(−1.4)(+1.7)] × 10−13 cm3 s−1 at 300 K. This is in good to excellent agreement with rigorous quantum rate calculations on the complete configuration interaction/Born–Huang surface, as reported earlier by Bakule et al, and which are also briefly commented on herein.

Experimental determination of the rate of V-V collisional relaxation in (14)N2 in its ground (X(1)Σ(g)(+)) electronic state between 77 and 300 K.

We propose new values for the V-V collisional energy transfer rate constant of (14)N2 (X(1)Σg(+)) at different temperatures in collisions between molecules in the v = 1 and v = 0 vibrational states. The values were obtained experimentally by means of a time-resolved double resonance pump-probe stimulated Raman setup in which the stimulated Raman technique was used for both the pump and the probe stage. The main feature of the experiment is the fact that population pumping is done with rotational (and thus spin) selectivity, that is, only molecules belonging to the ortho spin variety of (14)N2 are promoted to v = 1. The probe stage is then used to monitor the decay of this ortho rotational population placed in v = 1 and the emergence of a para population in that same vibrational level. Since the only possible mechanism for the arrival of para population to v = 1 is collisional V-V energy transfer, the evolution of the ortho/para ratio in v = 1 is used to quantify the rate constant of the process. The measurements were conducted at 77, 136, 226 and 300 K. The 300 K value had been measured and calculated before by other authors, but a spread larger than an order of magnitude existed between their results. Our proposed value is more precise than previous ones and lies near the mid-point of that interval. The low-temperature values of the rate constant are reported here for the first time. The availability of data at several temperatures has allowed us to unequivocally determine the existence of a strong negative temperature dependence of the rate constant between 77 and 300 K that exhibits a linear behavior in a Landau-Teller plot in this temperature interval.

Collisional relaxation of apocarotenals: identifying the S* state with vibrationally excited molecules in the ground electronic state S(0)*.

In recent work, we demonstrated that the S* signal of β-carotene observed in transient pump-supercontinuum probe absorption experiments agrees well with the independently measured steady-state difference absorption spectrum of vibrationally hot ground state molecules S0* in solution, recorded at elevated temperatures (Oum et al., Phys. Chem. Chem. Phys., 2010, 12, 8832). Here, we extend our support for this "vibrationally hot ground state model" of S* by experiments for the three terminally aldehyde-substituted carotenes β-apo-12'-carotenal, β-apo-4'-carotenal and 3',4'-didehydro-β,ψ-caroten-16'-al ("torularhodinaldehyde") which were investigated by ultrafast pump-supercontinuum probe spectroscopy in the range 350-770 nm. The apocarotenals feature an increasing conjugation length, resulting in a systematically shorter S1 lifetime of 192, 4.9 and 1.2 ps, respectively, in the solvent n-hexane. Consequently, for torularhodinaldehyde a large population of highly vibrationally excited molecules in the ground electronic state is quickly generated by internal conversion (IC) from S1 already within the first picosecond of relaxation. As a result, a clear S* signal is visible which exhibits the same spectral characteristics as in the aforementioned study of β-carotene: a pronounced S0 → S2 red-edge absorption and a "finger-type" structure in the S0 → S2 bleach region. The cooling process is described in a simplified way by assuming an initially formed vibrationally very hot species S0** which subsequently decays with a time constant of 3.4 ps to form a still hot S0* species which relaxes with a time constant of 10.5 ps to form S0 molecules at 298 K. β-Apo-4'-carotenal behaves in a quite similar way. Here, a single vibrationally hot S0* species is sufficient in the kinetic modeling procedure. S0* relaxes with a time constant of 12.1 ps to form cold S0. Finally, no S0* features are visible for β-apo-12'-carotenal. In that case, the S1 → S0 IC process is expected to be roughly 20 times slower than S0* relaxation. As a result, no spectral features of S0* can be found, because there is no chance that a detectable concentration of vibrationally hot molecules is accumulated.

A parallel Runge–Kutta discontinuous Galerkin solver for rarefied gas flows based on 2D Boltzmann kinetic equations

The high-order Runge–Kutta Discontinuous Galerkin (RKDG) method is applied to solve the 2D Boltzmann kinetic equations. A conservative DG type discretization of the non-linear collision relaxation term is formulated for both the Bhatnagar–Gross–Krook and the ellipsoidal statistical kinetic models. Verification is carried out for a steady and an unsteady oscillatory 1D Couette flows, a 2D conduction problem as well as for a 2D long microchannel flow by comparison with the DSMC and analytical solutions. The computational performance of the RKDG method is compared with a widely used second-order finite volume method. The RKDG method has up to 3rd-order spatial accuracy and up to 4th-order time accuracy and is more efficient than the finite volume approach. The parallelization by domain decomposition in physical space is implemented and parallel performance is evaluated. It is shown that 2nd order RKDG is over 15 times faster than the 2nd-order FVM method for the Couette flow test case. The high-order RKDG method is especially attractive for solution of low-speed and unsteady rarefied flows.

Ultracold Fermi gases with emergent SU(N) symmetry

We review recent experimental and theoretical progress on ultracold alkaline-earth Fermi gases with emergent SU(N) symmetry. Emphasis is placed on describing the ground-breaking experimental achievements of recent years. The latter include (1) the cooling to below quantum degeneracy of various isotopes of ytterbium and strontium, (2) the demonstration of optical Feshbach resonances and the optical Stern–Gerlach effect, (3) the realization of a Mott insulator of 173Yb atoms, (4) the creation of various kinds of Fermi–Bose mixtures and (5) the observation of many-body physics in optical lattice clocks. On the theory side, we survey the zoo of phases that have been predicted for both gases in a trap and loaded into an optical lattice, focusing on two and three dimensional systems. We also discuss some of the challenges that lie ahead for the realization of such phases such as reaching the temperature scale required to observe magnetic and more exotic quantum orders. The challenge of dealing with collisional relaxation of excited electronic levels is also discussed.