Relaxation Cross Sections Research Articles

Laboratory study of rotationally inelastic collisions of CO2 at low temperatures.

The rotational relaxation of CO2 by inelastic collisions has been studied in three supersonic jets. The jets were probed by means of Raman spectroscopy with high spectral and spatial resolutions, measuring the rotational populations and the total number density. The time evolution of the rotational populations was analyzed by means of a kinetic master equation, with the help of the energy-corrected sudden power law to relate the numerous state-to-state rate (STS rates) coefficients. In the thermal range investigated, 60-260 K, the STS rates decrease with increasing temperature and with increasing change in the rotational quantum number. Other quantities of interest for fluid dynamics, such as the rotational collision number, the relaxation cross section, and the bulk viscosity, have been derived from the STS rates.

A Rigid Bender Study of the Bending Relaxation of H2O and D2O by Collisions with Ar.

The bending relaxation of H2O and D2O by collisions with Ar is studied at the Close Coupling level. Two new 4D PES are developed for these two systems. They are tested by performing rigid rotor calculations as well as by computing the D2O-Ar bound states. The results are compared with available theoretical and experimental data. Propensity rules for the dynamics are discussed and compared to those of H2O colliding with Ne or He. The bending relaxation cross sections and rates are then calculated for these two systems. The results are analysed and compared with available experimental data.

Low-Temperature Gas-Phase Kinetics of Ethanol-Methanol Heterodimer Formation.

The structures of gas-phase noncovalently bound clusters have long been studied in supersonic expansions. This method of study, while providing a wealth of information about the nature of noncovalent bonds, precludes observation of the formation of the cluster, as the clusters form just after the orifice of the pulsed valve. Here, we directly observe formation of ethanol-methanol dimers via microwave spectroscopy in a controlled cryogenic environment. Time profiles of the concentration of reagents in the cell yielded gas-phase reaction rate constants of kMe-g = (2.8 ± 1.4) × 10-13 cm3 molecule-1 s-1 and kMe-t = (1.6 ± 0.8) × 10-13 cm3 molecule-1 s-1 for the pseudo-second-order ethanol-methanol dimerization reaction at 8 K. The relaxation cross section between the gauche and trans conformers of ethanol was also measured using the same technique. In addition, thermodynamic relaxation between conformers of ethanol over time allowed for selection of conformer stoichiometry in the ethanol-methanol dimerization reaction, but no change in the ratio of dimer conformers was observed with changing ethanol monomer stoichiometry.

Fine-structure transitions of Si and S induced by collisions with atomic hydrogen

ABSTRACT Using a quantum-mechanical close-coupling method, we calculate cross-sections for fine-structure excitation and relaxation of Si and S atoms in collisions with atomic hydrogen. Rate coefficients are calculated over a range of temperatures for astrophysical applications. We determine the temperature-dependent critical densities for the relaxation of Si and S in collisions with H and compare these to the critical densities for collisions with electrons. The present calculations should be useful in modelling environments exhibiting the [S i] 25 μm and [S i] 57 μm far-infrared emission lines or where cooling of S and Si by collisions with H is of interest.

Fine-structure transitions of the carbon isoelectronic sequence C, N+, and O2 + induced by collisions with atomic hydrogen

ABSTRACT Fine-structure transitions can be involved in various processes including photon absorption, charge transfer, and inelastic collisions between ions, electrons, and neutral atoms. We present fine-structure excitation and relaxation cross-sections for the collisions of the first few members of the carbon isoelectronic sequence (C, N+ and O2 +) with atomic hydrogen calculated using quantum-mechanical methods. For C, the scattering theory and computational approach is verified by comparison with previous calculations. The rate coefficients for the collisional processes are obtained. For N+ and O2 +, the transitions correspond to the lines [O iii] 52 μm, [O iii] 88 μm, [N ii] 122 μm, and [N ii] 205 μm, observed in the far-infrared in the local universe and more recently in high-redshift galaxies using radio interferometry. The influence of different potentials on the cross-sections and rate coefficients are demonstrated.

Total angular momentum representation for state-to-state quantum scattering of cold molecules in a magnetic field.

We show that the integral cross sections for state-to-state quantum scattering of cold molecules in a magnetic field can be efficiently computed using the total angular momentum representation despite the presence of unphysical Zeeman states in the eigenspectrum of the asymptotic Hamiltonian. We demonstrate that the unphysical states arise due to the incompleteness of the space-fixed total angular momentum basis caused by using a fixed cutoff value Jmax for the total angular momentum of the collision complex J. As a result, certain orbital angular momentum (l) basis states lack the full range of J values required by the angular momentum addition rules, resulting in the appearance of unphysical states. We find that by augmenting the basis with a full range of J-states for every l, it is possible to completely eliminate the unphysical states from quantum scattering calculations on molecular collisions in external magnetic fields. To illustrate the procedure, we use the augmented basis sets to calculate the state-to-state cross sections for rotational and spin relaxation in cold collisions of 40CaH(X2Σ+, v = 0, N = 1, MN = 1, MS = 1/2) molecules with 4He atoms in a magnetic field. We find excellent agreement with benchmark calculations, validating our proposed procedure. We find that N-conserving spin relaxation from the highest-energy to the lowest-energy Zeeman state of the N = 1 manifold, |1112〉→|1-1-12〉 is nearly completely suppressed due to the lack of spin-rotation coupling between the fully spin-stretched Zeeman states. Our results demonstrate the possibility of rigorous, computationally efficient, and unphysical state-free quantum calculations on cold molecular collisions and on near-threshold energy levels of strongly anisotropic atom-molecule collision complexes in an external magnetic field.

Vibrational state-specific model for dissociation and recombination of the O2( 3Σg -)+O( 3P) system in DSMC.

A vibrational state-specific model for dissociation and recombination reactions within the direct simulation Monte Carlo method is introduced to study the energy level dynamics of the O2 + O system. The state-resolved cross sections for vibrational relaxation and dissociation reactions are obtained from a rotationally averaged quasi-classical trajectory database based on the Varandas and Pais O2( 3Σg -)+O( 3P) potential energy surface. A two-step binary collision framework is outlined to characterize the vibrational state-resolved recombination probabilities, which are constrained by detailed balance for orbiting pair formation, and microscopic reversibility applied to the dissociation cross sections for orbiting pair stabilization. The vibrational state-to-state (STS) model is compared to the phenomenological total collision energy (TCE) and quantum kinetic (QK) models through a series of 0-d non-equilibrium relaxation calculations. A quasi-steady state (QSS) region is established in the vibrational temperature profiles of the TCE, QK, and STS models under non-equilibrium heating. This QSS region is a result of the competition between vibrational relaxation by vibrational-translational (VT) transitions and O2 dissociation. The duration of QSS predicted by the STS model is approximately ten and four times that of the TCE and QK model predictions, respectively, and the total time to reach equilibrium is approximately 3.5 times that of the TCE model and 1.5 times that of the QK model. A distinct QSS region is not observed in the non-equilibrium cooling case. This is attributed to the relatively rapid VT transitions that work to equilibrate the vibrational energy distribution upon recombination, which is comparatively slow. The total time to reach equilibrium by the STS model in the non-equilibrium cooling case is five times and three times greater than those of the QK and TCE models, respectively.

Kinetics of two-pulsed photon echo formed on the 0–1 transition: isotropic and anisotropic collisions

The photon echo formed at the intercombination (6s2) 1S0 (6s6p) 3P1 (type 0–1) transition of ytterbium atoms 174Yb by two pulses of resonance radiation was investigated as a function of the time delay between exciting pulses (the photon echo kinetics). For exciting radiation pulses of the same linear polarization in the delay region 70–250 ns, the photon echo kinetics is close to the exponential one both in pure ytterbium and in its mixtures with buffer gases Ar and Xe. The relaxation cross sections were determined for all three cases, taking into account the isotopic composition of xenon and ytterbium. For the first time, the complex nonmonotonous kinetics of the collision-induced photon echo was observed in the same mixtures for the forming pulses of linear mutually orthogonal polarization. The relative efficiency of buffer atoms Yb (other isotopes than 174Yb), Xe and Ar in the collision-induced photon echo formation was obtained.

Quantitative study of optical pumping in the presence of spin-exchange relaxation

We have performed quantitative measurements of the variation of the on-resonance absorption coefficients ${\ensuremath{\kappa}}_{0}$ of the four hyperfine components of the Cs ${D}_{1}$ transition as a function of laser power $P$, for pumping with linearly and with circularly polarized light. Sublevel populations derived from rate equations assuming isotropic population relaxation (at a rate ${\ensuremath{\gamma}}_{1}$) yield algebraic ${\ensuremath{\kappa}}_{0}(P)$ dependences that do not reproduce the experimental findings from Cs vapor in a paraffin-coated cell. However, numerical results that consider spin-exchange relaxation (at a rate ${\ensuremath{\gamma}}_{\mathrm{se}}$) and isotropic relaxation fit the experimental data perfectly well. The fit parameters, viz., the absolute value of ${\ensuremath{\kappa}}_{0}$, the optical pumping saturation power ${P}_{\mathrm{sat}}$, and the ratio ${\ensuremath{\gamma}}_{\mathrm{se}}/{\ensuremath{\gamma}}_{1}$, are well described by the experimental conditions and yield absolute values for ${\ensuremath{\gamma}}_{1}$ and ${\ensuremath{\gamma}}_{\mathrm{se}}$. The latter is consistent with the previously published Cs-Cs spin-exchange relaxation cross section.

Spatially Resolved Measurements of Crosslinking in UV-Curable Coatings Using Single-Sided NMR

The UV-driven photocuring of coatings results in a crosslinked polymeric network. The degree of crosslinking in these coatings is typically assessed via optical spectroscopy; unfortunately, optical methods are typically limited in their maximum depth access. Alternatively, single-sided nuclear magnetic resonance (NMR) can be used to probe the crosslinking of UV-curable coatings in a spatially sensitive manner. Relaxation measurements, which correlate with crosslinking, can be done with a spatial resolution on the order of microns throughout the depth dimension of the coating, regardless of optical transparency of the material. These results can be visualized via a relaxation cross-section that shows the depth at which a particular relaxation value is observed. These measurements are used to probe the effect of a scavenger molecule that is added to the coating mixture, allowing for efficient crosslinking despite the presence of atmospheric oxygen. This method may find purchase in evaluating systems whose crosslinking properties are intentionally varied throughout its thickness; using NMR, these systems, up to approximately one hundred microns thick, can be measured without repositioning or rastering.

Rotational energy transfer in collisions between CO and Ar at temperatures from 293 to 30 K

Experimental measurements and theoretical calculations are reported for rotational energy transfer in the Ar-CO system. Experiments were performed in cold uniform supersonic flows of Ar, using an infrared – vacuum ultraviolet double resonance technique to measure absolute state-to-state rate constants and total relaxation cross sections for rotational energy transfer within the (v=2) vibrational state of CO in collision with Ar at temperatures from 30.5 to 293K. Close-coupling calculations were also performed using a recent potential energy surface (Sumiyoshi and Endo, 2015). Very good agreement is obtained between measured and calculated values.

Quantum close coupling calculation of transport and relaxation properties for Hg-H2 system

Quantum mechanical close coupling calculation of the state-to-state transport and relaxation cross sections have been done for Hg-H2 molecular system using a high-level ab initio potential energy surface. Rotationally averaged cross sections were also calculated to obtain the energy dependent Senftleben-Beenakker cross sections at the energy range of 0.005–25,000cm−1. Boltzmann averaging of the energy dependent Senftleben-Beenakker cross sections showed the temperature dependency over a wide temperature range of 50–2500K. Interaction viscosity and diffusion coefficients were also calculated using close coupling cross sections and full classical Mason-Monchick approximation. The results were compared with each other and with the available experimental data. It was found that Mason-Monchick approximation for viscosity is more reliable than diffusion coefficient. Furthermore, from the comparison of the experimental diffusion coefficients with the result of the close coupling and Mason-Monchick approximation, it was found that the Hg-H2 potential energy surface used in this work can reliably predict diffusion coefficient data.

Development of a two-dimensional binning model for N2–N relaxation in hypersonic shock conditions

A high fidelity internal energy relaxation model for N2–N suitable for use in direct simulation Monte Carlo (DSMC) modeling of chemically reacting flows is proposed. A novel two-dimensional binning approach with variable bin energy resolutions in the rotational and vibrational modes is developed for treating the internal mode of N2. Both bin-to-bin and state-specific relaxation cross sections are obtained using the molecular dynamics/quasi-classical trajectory (MD/QCT) method with two potential energy surfaces as well as the state-specific database of Jaffe et al. The MD/QCT simulations of inelastic energy exchange between N2 and N show that there is a strong forward-preferential scattering behavior at high collision velocities. The 99 bin model is used in homogeneous DSMC relaxation simulations and is found to be able to recover the state-specific master equation results of Panesi et al. when the Jaffe state-specific cross sections are used. Rotational relaxation energy profiles and relaxation times obtained using the ReaxFF and Jaffe potential energy surfaces (PESs) are in general agreement but there are larger differences between the vibrational relaxation times. These differences become smaller as the translational temperature increases because the difference in the PES energy barrier becomes less important.

Direct Time‐Domain Observation of Conformational Relaxation in Gas‐Phase Cold Collisions

AbstractCooling molecules in the gas phase is important for precision spectroscopy, cold molecule physics, and physical chemistry. Measurements of conformational relaxation cross sections shed important light on potential energy surfaces and energy flow within a molecule. However, gas‐phase conformational cooling has not been previously observed directly. In this work, we directly observe conformational dynamics of 1,2‐propanediol in cold (6 K) collisions with atomic helium using microwave spectroscopy and buffer‐gas cooling. Precise knowledge and control of the collisional environment in the buffer‐gas allows us to measure the absolute collision cross‐section for conformational relaxation. Several conformers of 1,2‐propanediol are investigated and found to have relaxation cross‐sections with He ranging from σ=4.7(3.0)×10−18 cm2 to σ>5×10−16 cm2. Our method is applicable to a broad class of molecules and could be used to provide information about the potential energy surfaces of previously uninvestigated molecules.

Direct Time-Domain Observation of Conformational Relaxation in Gas-Phase Cold Collisions.

Cooling molecules in the gas phase is important for precision spectroscopy, cold molecule physics, and physical chemistry. Measurements of conformational relaxation cross sections shed important light on potential energy surfaces and energy flow within a molecule. However, gas-phase conformational cooling has not been previously observed directly. In this work, we directly observe conformational dynamics of 1,2-propanediol in cold (6 K) collisions with atomic helium using microwave spectroscopy and buffer-gas cooling. Precise knowledge and control of the collisional environment in the buffer-gas allows us to measure the absolute collision cross-section for conformational relaxation. Several conformers of 1,2-propanediol are investigated and found to have relaxation cross-sections with He ranging from σ=4.7(3.0)×10(-18) cm(2) to σ>5×10(-16) cm(2). Our method is applicable to a broad class of molecules and could be used to provide information about the potential energy surfaces of previously uninvestigated molecules.

Quasi-bound complexes in collisions of different linear molecules: Classical trajectory study of their manifestations in rotational relaxation and spectral line broadening

Stable bimolecular complexes (tightly bound dimers) in the gas phase are usually created during third body stabilization of their unstable precursors-quasi-bound complexes (QCs). The latter can arise under the condition that at least one of the colliding partners has an internal degree of freedom. In this article, the principal difference between "orbitings" and QCs is demonstrated in the classical nonreactive scattering picture. Additionally, fractions of QCs in binary collisions of different linear molecules are compared. Also in the article the influence of QCs on rotational R-T relaxation and on vibration–rotational spectral line broadening is discussed. Explicit formulae shedding light on the QCs contribution to the R-T relaxation cross section and the line width and shift are presented. The obtained results emphasize the need for including QCs in every theoretical modeling of spectroscopic manifestation of intermolecular interactions. Besides the topics above, the possible manifestation of non-impact effects in the central regions of spectral lines due to QCs is stated. And finally, special consideration is given to the problem of adequate simulation of QCs formation at different pressures.

Broadband transient absorption spectroscopy with 1- and 2-photon excitations: Relaxation paths and cross sections of a triphenylamine dye in solution.

1-photon (382 nm) and 2-photon (752 nm) excitations to the S1 state are applied to record and compare transient absorption spectra of a push-pull triphenylamine (TrP) dye in solution. After 1-photon excitation, ultrafast vibrational and structural molecular relaxations are detected on a 0.1 ps time scale in nonpolar hexane, while in polar acetonitrile, the spectral evolution is dominated by dipolar solvation. Upon 2-photon excitation, transient spectra in hexane reveal an unexpected growth of stimulated emission (SE) and excited-state absorption (ESA) bands. The behavior is explained by strong population transfer S1 → Sn due to resonant absorption of a third pump photon. Subsequent Sn → S1 internal conversion (with τ1 = 1 ps) prepares a very hot S1 state which cools down with τ2 = 13 ps. The pump pulse energy dependence proves the 2-photon origin of the bleach signal. At the same time, SE and ESA are strongly affected by higher-order pump absorptions that should be taken into account in nonlinear fluorescence applications. The 2-photon excitation cross sections σ(2) = 32 ⋅ 10(-50) cm(4) s at 752 nm are evaluated from the bleach signal.

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.

Theoretical investigation of the relaxation of the bending mode of CH₂(X̃) by collisions with helium.

We have earlier determined the dependence on the bending angle of the interaction of the methylene radical (CH2) in its X̃³B₁ state with He [L. Ma, P. J. Dagdigian, and M. H. Alexander, J. Chem. Phys. 136, 224306 (2012)]. By integration over products of the bending vibrational wave function, in a quantum close-coupled treatment we have calculated cross sections for the ro-vibrational relaxation of CH 2(X̃). Specifically, we find that cross sections for a loss of one vibrational quantum (v(b) = 2 → 1 and 1 → 0) are roughly two orders of magnitude smaller, and those for a loss of two vibrational quanta (v(b) = 2 → 0) four orders of magnitude smaller, than those for pure rotational relaxation. In addition, no clear cut dependence on the energy gap is seen.

Properties of the ground3F2state and the excited3P0state of atomic thorium in cold collisions withHe3

Inelastic cross sections for collisions between thorium (Th) and helium ($^{3}\mathrm{He}$) are measured. For Th[${}^{3}{F}_{2}$]--$^{3}\mathrm{He}$, we determine the ratio of momentum transfer to Zeeman relaxation cross sections to be $\ensuremath{\gamma}\ensuremath{\sim}500$ at 800 mK. For Th[${}^{3}{P}_{0}$]--$^{3}\mathrm{He}$, we find no quenching of this metastable state during ${10}^{6}$ collisions. We measure the radiative lifetime of Th[${}^{3}P{}_{0}$] to be $\ensuremath{\tau}>130$ ms. The observed stability of Th[${}^{3}{P}_{0}$] opens up the possibility of trapping this metastable species.