Gas Kinetic Cross Sections Research Articles

A hybrid mechanism of 3D optical trapping of particles immersed in a cold buffer gas

A novel mechanism of the formation of a deep optical superlattice (OSL) for three-dimensional (3D) trapping of resonant impurity atoms immersed in a transparent cold buffer gas is proposed and investigated theoretically. This mechanism is associated with the joint action of two factors of different physical nature: rectification effect of the gradient force of light pressure and effect of the light induced drift (LID) of atoms (a consequence of the difference in gas-kinetic cross sections of excited and unexcited atoms). Such a situation can be realised when a gas mixture is irradiated by a bichromatic combined light beam which is a special coaxial superposition of cosine-Gaussian optical beams. Here, the RcGF creates a periodic 1D array of deep potential wells (OSL) along the beam axes, and an effective force, causing LID, pulls resonant particles into the combined light beam and provides their transverse (with respect to the beam axes) confinement in OSL. As a result, there can occur a giant accumulation of impurity particles in the OSL cells, accompanied by a strong spatial particle localization far away from the walls of the reservoir, in which the gas mixture is located.

Diffusion and mobility of atomic particles in a liquid

The diffusion coefficient of a test atom or molecule in a liquid is determined for the mechanism where the displacement of the test molecule results from the vibrations and motion of liquid molecules surrounding the test molecule and of the test particle itself. This leads to a random change in the coordinate of the test molecule, which eventually results in the diffusion motion of the test particle in space. Two models parameters of interaction of a particle and a liquid are used to find the activation energy of the diffusion process under consideration: the gas-kinetic cross section for scattering of test molecules in the parent gas and the Wigner–Seitz radius for test molecules. In the context of this approach, we have calculated the diffusion coefficient of atoms and molecules in water, where based on experimental data, we have constructed the dependence of the activation energy for the diffusion of test molecules in water on the interaction parameter and the temperature dependence for diffusion coefficient of atoms or molecules in water within the models considered. The statistically averaged difference of the activation energies for the diffusion coefficients of different test molecules in water that we have calculated based on each of the presented models does not exceed 10% of the diffusion coefficient itself. We have considered the diffusion of clusters in water and present the dependence of the diffusion coefficient on the cluster size. The accuracy of the presented formulas for the diffusion coefficient of atomic particles in water is estimated to be 50%.

Broadening of a two-photon resonance in a zinc atom in collisions with CO2, CO, and NO molecules

The broadening of a two-photon resonance is studied experimentally at the 4s1S0−6s3S1 transition in a zinc atom upon absorption of two waves with a small detuning from an intermediate state in collisions with CO2, CO, and NO molecules. The measured absolute values of broadening cross sections greatly exceed gas-kinetic cross sections and are (9.4±2.4, 6.5±1.6, and 3.9±1.0)×10− 14cm2 for CO2, CO, and NO, respectively. Anomalously large rate constants and cross sections obtained in experiments are explained by the efficient resonance quenching of the excited states of zinc atoms in collisions with molecules accompanied by transfer of the energy of excited atoms to vibrational-rotational degrees of freedom of molecules.

NMR study of stable radicals in the gas phase

The temperature dependence of the NMR spectrum of methyl-substituted nitroxyl radical of the imidazoline series has been studied. The NMR signal induced by radicals in the gas phase has been observed. A shift of the lines of the NMR spectrum in the gas phase according to the Curie law is observed which allows one to determine the value of the hfi constant of the protons of different racial groups. The hfi constant for methyl-substituted radical within experimental accuracy coincides with those measured by other methods in the liquid phase. In the absorbed phase of the samples under study, a substantial contribution is made by the volumetric susceptibility of the liquid film. The diamagnetic contribution to the magnetic susceptibility of the radical in the liquid state has been measured (in the film of 2 × 10 −6). When the thickness of the adsorbed film is small, the molecular exchange between the liquid and gas phases becomes noticeable, causing a corresponding additional shift of the lines. The gas-kinetic cross section for the radical (120 Å 2) has been estimated from the temperature dependence of the line width in the gas phase.

Inelastic collisions and gas-kinetic effects of light.

Light can induce thermodynamic and hydrodynamic fluxes in a gas, which reflect the light-induced modifications of the velocity distribution of the gas particles. The common condition for these effects to occur is the combination of velocity-selective radiative excitation with state-dependent gas-kinetic cross sections. It has recently been suggested that gas-kinetic effects of light in a molecular gas can also arise without state-dependent total cross sections, due to rotational inelastic collisions. Standard gas-kinetic techniques are not directly applicable in this case, since the rapid processes do not drive the system to a steady state. We give a generalization of the standard formalism so as to encompass this case. We apply this generalized formalism in the simplest model case of three-state particles.

Collisional dynamics of the IF B 3Π(0+) state. III. Vibrational and rotational energy transfer

Rate constants at T=300 K for collision induced vibrational and rotational energy transfer within the IF B 3Π(0+) state have been determined using both cw and pulsed laser induced fluorescence. State-to-state vibrational energy transfer rate coefficients have been measured for IF(B; v′) collisions with He, Ne, Ar, Kr, Xe, N2, O2, and F2. Vibrational energy transfer has also been studied as a function of the initially excited vibrational level. Steady-state fluorescence emission from v′=3 has been analyzed to yield total rotational removal rate coefficients with the noble gases and N2 as collision partners. Vibrational energy transfer is generally inefficient; the thermally averaged cross sections for single quantum transfer (Δv=−1) from v′=3, σ(3,2), decrease from 1.2% to 0.3% of the gas kinetic cross sections, σg, for the periodic series He to Xe. For diatomic collision partners, the respective values of σ(3,2)/σg for N2, O2, and F2 are 0.014, 0.033, and 0.020. The Δv=−1 cross sections for the noble gases monotonically decrease with μ1/3 while no clear dependence on the collision reduced mass is observed with N2, F2, and O2. The vibrational transfer cross sections for the noble gases, N2, and O2 scale linearly with vibrational quantum number. The results also reveal that ‖Δv‖=1 transfer is at least an order of magnitude more probable than that for ‖Δv‖=2. Rotational energy transfer is the most efficient kinetic process in IF(B). The estimated efficiencies for total rotational energy transfer from J′=22 in v′=3 with the rare gases and N2 are typically 20 to 200 times greater than those for vibrational transfer. The rate coefficients range from (9.7±1.8)×10−11 cm3 molecule−1 s−1 for He to (1.1±0.1)×10−10 cm3 molecule−1 s−1 for Xe. The rotational transfer rate coefficients show a smooth dependence on both the collision reduced mass and the polarizability of the collision partner. The qualitative results of these experiments are discussed in relation to traditional energy transfer models.

Translational relaxation of a heavy molecule in a light rarefied gas

A study is made of the translational relaxation (in the sense of the loss of the original direction of the velocity) of a molecule of mass M injected into the flow field of a light gas (mass of a molecule m). It is shown that when the gas is sufficiently rarefied and M ≫ m the spreading of the wave packet of the heavy particle can mask the mean “classical” deviation of the heavy molecule from the original direction as a result of a collision with a light molecule. Therefore, not all the collisions determined by the gas-kinetic cross section are effective for the observed deflection of the heavy molecule. Some consequences of this behavior of heavy molecules are discussed. The obtained restrictions on classical theory must be taken into account when one is considering problems of the gas dynamics of rarefied mixtures.

On laser-induced harpooning reactions

Switching of chemical reactivity by a nonresonant laser field in simple gas-phase collisions of the type A+BC→AB+C is discussed in terms of a 2nd-order optical/collisional perturbation. A simple formula relating laser-induced harpooning cross sections to the laser power density is derived and applied to Hg/Cl2 collisions. Calculation shows that a gas-kinetic cross section for the reaction (Hg+Cl2+h/ω→HgCl*+Cl) may be achieved in the presence of an ArF laser at a power density of 109 W/cm2.

Self-quenching and electronic energy transfer of triplet molecules. The benzaldehyde-biacetyl system in the vapor phase

The triplet-triplet energy transfer from benzaldehyde to biacetyl and the competing self-quenching between triplets and ground state molecules of benzaldehyde were investigated in the dilute vapor phase by monitoring the phosphorescence (T1(nπ*)So) decay of benzaldehyde. Following excitation into the S1(nπ*)S0 absorption band, a triplet self-quenching rate constant of kSQ=(2.4±0.1) × 104 s−1 Torr−1, corresponding to a gas-kinetic cross section of σSQ=0.22 A2, was measured. The collision-free lifetime of the benzaldehyde triplet was found to be 2.3 ± 0.4 ms. Substitution of the aldehydic proton by deuterium reduces kSQ by a factor of two: complete deuteration of the molecule has no further effect. Under the same excitation conditions, the energy transfer rate to biacetyl is kET=(2.8 ± 0.1) × 106 s−1 Torr−1, with σET = 24 A2. This process is not influenced by deuteration.

A possible mechanism of relaxation over the rotational sublevels of molecules under conditions of saturation of a vibrational–rotational transition

An analysis is made of rotational relaxation in a molecular system under conditions of saturation of a vibrational--rotational transition. It is shown that for molecules having large dipole moments of vibrational transitions, the rotational relaxation is not due to an ''impact'' mechanism but to the dipole--dipole interaction between the colliding molecules. On the basis of qualitative concepts, it is established that under certain conditions the relaxation caused by the dipole--dipole interaction may be essentially nondiffusive. An estimate is made of the cross section of the elementary event using the proposed relaxation model for NF/sub 3/, CO/sub 2/, CF/sub 4/, SF/sub 6/, and UF/sub 6/ molecules. These cross sections are considerably larger than the gas-kinetic cross sections.

Validity of approximate methods in molecular scattering. III. Effective potential and coupled states approximations for differential and gas kinetic cross sections

Two dimensionality-reducing approximations, the jz-conserving coupled states (sometimes called the centrifugal decoupling) method and the effective potential method, were applied to collision calculations of He with CO and with HCl. The coupled states method was found to be sensitive to the interpretation of the centrifugal angular momentum quantum number in the body-fixed frame, but that choice leading to the original McGuire–Kouri expression for the scattering amplitude—and to the simplest formulas—proved to be quite successful in reproducing differential and gas kinetic cross sections. The computationally cheaper effective potential method was much less accurate.

Validity of approximate methods in molecular scattering: Thermal HCl–He collisions

Accurate close coupling scattering calculations are presented for thermal energy HCl–He collisions. The interaction potential is obtained from the Gordon–Kim electron gas model, adjusted to have the correct long-range multipole form. A variety of phenomenological cross sections are computed from the close coupling S matrix, and these are compared with results from several commonly employed approximate methods. In particular, it is found that the total integral, total differential, and gas kinetic cross sections are accurately predicted by the central field approximation which retains just the spherical average of the interaction. Integral inelastic cross sections are represented quite accurately by the coupled states approximation of McGuire and Kouri, but only qualitatively by the effective potential method of Rabitz. Pressure broadening cross sections from the close coupling calculation are in much better agreement with experiment than either Anderson theory calculations or the classical trajectory study of Gordon. NMR spin–lattice relaxation cross sections are also presented.

Vibrational relaxation by collisions of polyatomic molecules in excited states

Inelastic collisions leading to a degradation of the internal vibronic energy of an electronically excited molecule (β-naphthylamine) have been observed by direct timing of the fluorescence from the excited state as a function of pressure of added gases. The zero-pressure lifetime spectrum as a function of excitation energy was employed as the energy scale calibration for the lengthening of the fluorescence lifetime. These experiments were performed also as a function of excitation energy and the results interpreted in terms of a collisional inefficiency when compared to a gas-kinetic cross section and a statistical model of energy transfer. Principally helium, argon, and propylene were studied, but preliminary experiments with propane revealed results similar to those for propylene. Helium, as expected, was less efficient than argon which, in turn, due to its lack of internal degrees of freedom was much less efficient than propylene. When the statistical complexions resulting from these added degrees of freedom were computed, it was found that the remaining ``one-dimensional'' efficiency of propylene was quite similar to that of argon. In view of their similar mass this would lend support to a previously advanced model in which simple collision mechanics determine energy transfer in one dimension.

Quenching Rates for Metastable Oxygen Atoms(5S0)

Metastable O (3s 5S0) atoms were produced by rare gas sensitized decomposition of various oxygen containing compounds. The quenching rate constants of H2 , N2, O2 , NO, N2O, N2O4/NO2, CO, CO2, SO2 , SO3 , H2O and the noble gases for the 0 (5S) have been measured by absorption spectroscopy. The noble gases, except xenon, deactivate the metastable oxygen atom with low collision efficiency. Xenon and molecular gases, except hydrogen, deactivate this species efficiently, the cross section being of the order of gas kinetic cross sections.

Vibrational deactivation of HE in the H2-F2chain reaction

The population of the excited vibrational states <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\upsilon = 1</tex> through <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\upsilon = 6</tex> of hydrogen fluoride has been determined by spectroscopic measurements on a chain reacting mixture of hydrogen and fluorine dilute in helium. The reaction is initiated by partially dissociating the hydrogen molecules with an electric discharge prior to mixing with the fluorine. Mixing is accomplished with a specially designed laminar flow nozzle to provide an easily modeled reaction region. Typical experimental conditions are a mixture of 1:1:20 (H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> :F <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> :He) at a total pressure of 5 torr and a flow velocity of 100 m/s. Information on deactivation rates is obtained by making population measurements at various distances along the flow, which is equivalent to following the time development of the populations. Because there are a number of time dependent phenomena occurring simultaneously (e.g., reaction, diffusion, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\upsilon-\upsilon</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\upsilon-t</tex> processes) it is not possible to determine deactivation rates directly from the experimental data. Instead, the experimental data are compared with the predictions of a computer model of the reaction which treats all the significant processes and includes the best currently available reaction and deativation rates. The calculated populations for vibrational levels <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\upsilon = 4-6</tex> are consistently larger than the experimentally measured populations, particularly for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\upsilon = 6</tex> where the error approaches a factor of 10. The low populations imply a deactivation rate for the higher vibrational levels of HF which is significantly larger than the currently accepted values. A straightforward analysis based upon the known pumping rates and the known concentrations of deactivating species strongly suggests that deactivation by hydrogen atoms is responsible. The data do not provide sufficient information to choose between the two hydrogen atom reactions 1) H + HF* → HF + H 2) H + HF* → H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> + F as the cause of the deactivation. Computer calculations using reactions 1 and 2 separately produce better agreement, however, for the reverse "cold" reaction 2. The rate constant required to explain the low population of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\upsilon = 6</tex> is approximately <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2 \times 10^{-10}</tex> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> /molecule.s or an effective collision cross section 0.4 times the gas kinetic cross section.

Optical pumping of ions in buffer gases

Transient signals measured with a pulsed rf-optical pumping method are used to determine longitudinal relaxation rates for Sr+ ions (even isotopes) in noble gas buffers. Depolarization cross sections of the electronic spin in the Sr+52S1/2 ground state for binary collisions with rare gas atoms are deduced. The results for σ(Sr+52S1/2) in A2 are (at temperatures between 374 and 449 °K): 2·10−5(He),4·10−5(Ne), 5.7·10−3(Ar), 1.8·10−2(Kr), and 4.0·10−2(Xe). These cross sections for the Sr+ ion are about two to three orders of magnitude larger than the corresponding ones for the isoelectronic neutral Rb atom. The large increase of the Sr+ relaxation rates is explained with the relaxation mechanism of spin-orbit coupling, taking into account two “indirect” effects of the ionic charge: the increase in the gas kinetic cross sections and the more intimate collisions of the Sr+ ion with the noble gas atoms. The depolarization is shown to be predominantly due to short-range interactions. A contribution to the relaxation of the Sr+ ion from Sr+-noble gas molecule formation, induced by three-body or resonant two-body collisions, could not be established for applied pressuresp between 1.5 and 15 Torr of Ar, Kr, and Xe.

Resonant Transfer of Vibrational Energy in Molecular Collisions

The cross section for resonant vibration—vibration energy exchange between infrared-active molecules due to the long-range dipole potential is formulated. It is found that despite certain restrictions imposed by rotational selection rules, energy-exchange cross sections may be as much as 0.01 to 0.1 times as large as the molecular gas-kinetic cross section and are greater than those estimated using only an exponential repulsive interaction between molecules.

Inelastic Excitation Transfer in Helium

When the positive column of a helium glow discharge is irradiated with intense 5016 Å (21S−31P) light, the population of the 31P state can be markedly increased without affecting the discharge parameters. The resulting enhancement of radiation from the n=3 states allows an upper limit of 4×10−17 cm2 to be placed on the cross section for transfer of excitation by neutral collision in the reaction He(31P)+He→He(33P)+He. This is to be compared on the one hand to reported values ranging from 1.3 to 7.8 times the gas-kinetic cross section, 1.5×10−15 cm2, and on the other to a different interpretation of similar experimental results that does not require the above reaction with its violation of the Wigner spin-conservation rule.

Radiative and Collision-Induced Relaxation of Atomic States in the2p53pConfiguration of Neon

Application of techniques previously developed by the authors for the precise measurement of excited-state lifetimes has been made to radiative and collision-induced relaxation in the ten fine-structure levels of the $2{p}^{5}3p$ configuration of atomic neon. Lifetimes are determined as a function of pressure by studying the transient decay of isolated optical transitions from levels excited by short bursts of threshold-energy electrons. Measurements of the total radiative lifetimes have been made for these ten states within errors ranging from about 1 to 3%. The present work represents an improvement in the accuracy with which these lifetimes have been determined of at least an order of magnitude over previous experimental determinations. Discrepancies (which in some cases amount to an order of magnitude in the mean values) with previous lifetime studies are shown to be easily attributable to radiative cascade effects arising from nonthreshold excitation. The radiative lifetimes for these levels (Paschen notation) are, in nsec: $2{p}_{1}(14.4\ifmmode\pm\else\textpm\fi{}0.3)$; $2{p}_{2}(18.8\ifmmode\pm\else\textpm\fi{}0.3)$; $2{p}_{3}(17.6\ifmmode\pm\else\textpm\fi{}0.2)$; $2{p}_{4}(19.1\ifmmode\pm\else\textpm\fi{}0.3)$; $2{p}_{5}(19.9\ifmmode\pm\else\textpm\fi{}0.4)$; $2{p}_{6}(19.7\ifmmode\pm\else\textpm\fi{}0.2)$; $2{p}_{7}(19.9\ifmmode\pm\else\textpm\fi{}0.4)$; $2{p}_{8}(19.8\ifmmode\pm\else\textpm\fi{}0.2)$; $2{p}_{9}(19.4\ifmmode\pm\else\textpm\fi{}0.6)$; and $2{p}_{10}(24.8\ifmmode\pm\else\textpm\fi{}0.4)$. Variations \ensuremath{\approx} 5% in the radial part of the transition probability were encountered for different $3p\ensuremath{\rightarrow}3s$ transitions; these variations may be attributed to configuration interaction. Calculations of ${\ensuremath{\sigma}}^{2}$ from the Coulomb approximation agreed with the experimentally determined values within this spread. Cross sections for inelastic excitation transfer were encountered for the more closely spaced states which were comparable to gas kinetic cross sections, but which could not be determined in the present work to within much less than 50% error in most cases. The relationship of the present work to problems in the gas laser field is discussed.

Diffusion of Slow Electrons in Gases

The diffusion of slow electrons in hydrogen, nitrogen, carbon dioxide, methane, ethylene, and cyclopropane in uniform electric fields has been investigated for ratios of electric field to pressure from 0.2 to 5.0 (v/cm)/mm Hg. Such measurements lead to a determination of the ratio of electron drift velocity to diffusion coefficient. By assuming a distribution in velocity of the electrons in the swarm, the Townsend energy factor ${k}_{T}$ and the mean electron velocity can be computed as a function of $\frac{E}{P}$, where $E$ is the electric field and $P$ is the gas pressure. Where the electron drift velocity is also known, the mean free path at unit pressure, the average energy loss per collision, and the gas kinetic cross section can be calculated. The results are presented in tabular form.