Kinetic Cross Sections Research Articles

Diffusion processes in the relaxed cross section for the reaction 107, 109Ag+ 20Ne

The fragments emitted in the reaction 107,109Ag+ 20Ne at 175 and 252 MeV bombarding energy have been identified in charge up to Z = 32. Kinetic energy distributions, cross sections and angular distributions have been measured for each Z. The kinetic energy spectra show the two usual components: the quasielastic component and the relaxed component. The Z-distribution of the latter is fairly flat, slowly decreasing up to Z ≈ 15 and then rising again up to Z = 30. The variations in the Z-distribution are more pronounced at the lower bombarding energy. The angular distributions associated with the relaxed component are forward peaked for Z-values close to that of the projectile and behave like 1 sinθ for larger Z-values. The forward peaking is very substantial for Z < 10. For Z > 10 the forward peaking in excess of 1 sinθ disappears around Z = 15. These features are interpreted in terms of a diffusion process along the asymmetry coordinate of a short-lived intermediate complex.

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.

Definitions and properties of generalized collision cross sections

A unified classification of binary collision cross sections is presented. This is accomplished with the aid of a collision superoperator, in terms of which both differential and kinetic theory cross sections are defined. Connections and comparisons are then made with standard expressions for chemical reaction cross sections and with those ’’spectral’’ cross sections describing collisional widths, shifts and overlapping of spectral lines. A detailed treatment of rotational invariance is included. Finally, it is shown how this general framework encompasses the more complicated cross sections that arise in the study of the field dependence of gas transport coefficients.

Formal and Approximate Evaluations of a Number of Collision Integrals for Diatomic Molecules

Expressions which are exact in the distorted wave Born approximation are derived for a number of kinetic theory collision cross sections, viz. This is done for a number of nonspherical potentials, namely for single-P1 , single-P2, dipole-dipole, dipolequadrupole and quadrupole-quadrupole interactions. A number of additional approximations is used to obtain approximate relations between some of these cross sections and to derive a approximate law of corresponding states. A simple model is described which makes the approximate evaluation of collision cross sections for multipole-multipole interactions very straightforward.

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.

Ultrasonic determination of the volume viscosity of N 2, CO, CH 4 and CD 4 between 77 and 300 K

Results are reported for the frequency-independent volume viscosity in N 2, CO, CH 4 and CD 4 at temperatures ranging from 77 to 300 K as determined from sound-absorption measurements. The closely related rotational relaxation times and the appropriate kinetic cross sections are derived.

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.

Formal Kinetic Theory of the Senftleben Effects

A formal theory for the magnetic field changes induced in the transport properties of paramagnetic gases (the Senftleben effects) is developed. In order to illustrate the formal theory, it is applied to a calculation of the low-pressure Senftleben effects for molecular oxygen. The calculated results are compared with experiment and quite good agreement is shown to exist. All kinetic collision cross sections relevant to these effects have been extracted and listed. One conclusion arising from this analysis is that O2 has a slightly more nonspherical intermolecular interaction potential than N2.

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.

Statistical Model for the Vibrational Deactivation of Molecular by Atomic Oxygen

A theoretical investigation is performed of the transfer of vibrational energy from a highly excited diatomic molecule to a free atom at thermal velocities under the special condition of a deep attractive minimum in the intermolecular potential. The model utilizes a Monte Carlo statistical analysis of classical particle trajectories, with calculations performed for selected semiempirical forms of the interaction potential. Data relevant to the ozone stable configuration are applied to the O–O2 system, with primary emphasis upon the role of the latter in atmospheric reactions which produce the OH airglow emission. A deep attractive potential well is found to be the principal parameter leading to rapid vibrational deactivation of O2, with cross sections of the same order as kinetic cross sections and with the direct collision process of an importance comparable to the atom-interchange mechanism. The fundamental concept of the “intermediate complex” is favored to best describe the details of similar reaction processes which are associated with such strong attractive forces.

Near-Resonant Vibrational Energy Transfer Among Isotopes of CO2

Quantitative calculations are presented which show that large (approximately gas kinetic) cross sections observed for vibrational-vibrational energy transfer between isotopes of C${\mathrm{O}}_{2}$ are due to long-range forces. The mechanism involved in the transfer of a quantum of asymmetric stretch vibration from ${\mathrm{C}}^{12}$${\mathrm{O}}_{2}^{16}$ to ${\mathrm{C}}^{12}$${\mathrm{O}}_{2}^{16}$ and ${\mathrm{O}}^{16}$${\mathrm{C}}^{12}$${\mathrm{O}}^{18}$ can be described in terms of dipole-dipole coupling. However, dipole-dipole coupling is too weak to describe the energy transfer to ${\mathrm{C}}^{13}$${\mathrm{O}}_{2}^{16}$. It is shown that in this case dipole-octupole coupling is expected to be stronger than dipole-dipole coupling. The room-temperature results are reproduced by assuming a value of 1 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}67}$ stat ${\mathrm{C}}^{2}$ ${\mathrm{cm}}^{6}$ for the square of matrix element for the vibrational transition. Temperature dependence of the rate constant is calculated to put this hypothesis to test.

Electron Spin Relaxation in Gases. I. Bis(perfluoromethyl) Nitroxide

The ESR spectra of the relatively large bis (perfluoromethyl) nitroxide (BFMN) radical has been studied in the gas phase. At low pressures, i.e., below 0.1 atm, the spectrum consists of a 480-G-wide Gaussian line which presumably arises from the unresolved nuclear hyperfine and spin–rotational lines. (The rootmean-square spin–rotational coupling constant is about 3.7 G.) As the pressure is increased by adding more radical or a diluant diamagnetic gas, the line narrows and becomes more Lorentzian. At total pressures, of radical plus diluant, above 10 atm the lines are Lorentzian and their widths vary as the inverse total pressure. This behavior can be explained semiquantitatively by assuming that the angular momentum, and hence the spin–rotational interaction, is relaxed by intermolecular collisions which can be understood in terms of a simple kinetic model. The cross sections for the relaxation of the angular momentum of the BFMN radical have been measured and the ratios, eJ, of these cross sections to the kinetic or van der Waals cross sections were determined. Approximate values of eJ are 0.28, 0.45, 0.70, and 0.84 for BFMN with N2, CF4, CF3H, and BFMN, respectively. As expected, eJ increases as the size and polarity of the colliding molecule increases. At high total pressures and low radical partial pressures the spin–rotational interactions are quenched and the nuclear hyperfine splitting is observed. At high total pressure and relatively high radical partial pressures (above 0.25 atm) the hyperfine splitting is coalesced into a single-exchange narrowed line. The cross section for spin exchange between BFMN radicals is about 0.04 of the kinetic cross section; the amount of exchange is, of course, proportional to the BFMN partial pressure.

Fluorescence and Phosphorescence of SO2 Vapor

Stern–Volmer constants for SO2 fluorescence [Ã(1B1)→X̃1A1] for six optically exciting wavelengths (3130, 3020, 2960, 2850, 2750, and 2650 Å) show a regular decrease in going to shorter exciting wavelengths in the pressure range 1–1000 μ Hg. Due to earlier work by Douglas, it is inferred that the principal change is occurring in the fluorescence lifetime, which decreases accordingly. If electronic quenching takes place at every gas–kinetic collision, then any amount of vibrational relaxation which occurs prior to emission has a larger-than-gas–kinetic cross section. The fluorescence yields (Qf)λ go to unity at zero pressure, within liberal error limits, for all exciting wavelengths. The phosphorescence [ã(3B1)→X̃1A1] essentially disappears at pressures below 10 μ and does not originate from vibrationally excited triplet levels even at low pressures. The phosphorescence yields (Qp)λ pass through a minimum at an exciting wavelength of 2850 Å, and the corresponding values at the exciting wavelength extreme are about the same.

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.

Nonresonant Microwave Absorption and Electric Dipole Moment of NO in the Gaseous State

The microwave absorption in NO has been measured by a resonant cavity method at frequencies near 9 and 23 kMc/sec and at pressures in the range 3 to 27 atmos. The major part of the absorption is due to direct Λ-type doublet transitions, although at the higher pressures, a significant contribution also comes from the low frequency wings of the pure rotational spectrum. Since the Λ-doublet separation is much smaller than the applied frequency for all significant transitions, the resulting spectrum has the nonresonant or Debye shape. From the intensity of this spectrum, the electric dipole moment was found to be 0.148±0.002 debye. The effective collision cross section for random spacial reorientation of the molecules is approximately twice the kinetic collision cross section.

Reactions of Gaseous Molecule Ions with Gaseous Molecules. IV. Experimental Method and Results

This paper is concerned with a detailed description of quantitative studies of certain secondary reactions involving simple molecules and ions that occur in the ion source of a mass spectrometer. It is found that the phenomenological reaction cross sections for reactions of the type P++R→S++···are independent of the temperature of the gas in the ion source, and vary inversely with the square root of the product of the ion repeller field strength and the reduced mass of the reactant ion-reactant molecule pair. For the reactant ion (P+) a rare gas, hydrogen, nitrogen, or carbon monoxide, and the resultant molecule (R) hydrogen, the cross sections for formation of the secondary ion, S+=PH+, are found to be one or two orders of magnitude greater than the ordinary, kinetic theory collision cross sections for similar atoms and molecules.

Resonance Fluorescence of Benzene. II

Further study of the resonance fluorescence of benzene with an improved technique is described and the analysis of the spectrum given some time ago by Kistiakowsky and Nelles is amplified and corrected. The new assignment shows that, upon absorption of the 2536A mercury line, only the changes of the quantum number of one (ν1; ω = 990 cm—1) vibration of the nonexcited benzene molecule are unrestricted in fluorescence. In other vibrations the changes of the quantum numbers are not larger than unity (or two when required by selection rules). This interpretation of the resonance spectrum accounts for most of the line groups measured on the new plates. Five frequencies, besides ν1, or their multiples can be tentatively identified; they are: 432; 791; 1542; 2557 and 3174 cm—1. The fluorescence of hexadeuterobenzene has also been studied and the spectrum interpreted in the same manner but not as completely as that of benzene. The frequencies observed are: 944 (Δν unrestricted); 2460. The quenching of the resonance fluorescence of benzene has been investigated with five different gases. This fluorescence is quenched by being changed into high pressure fluorescence. There is very little, if any, loss of electronic excitation energy by benzene molecules on collisions. The quenching action is quite unspecific and appears to increase as the kinetic cross section of the foreign gas molecules. Some new high pressure fluorescence bands have been observed in benzene in the presence of foreign gases. These bands support V. Henri's analysis of the absorption spectrum as consisting of two close electronic levels of the excited molecule. Attempts to excite resonance fluorescence of benzene derivatives have, on the whole, been unsuccessful. Fluorobenzene and toluene, even at 0.01 mm pressure, emit spectra which, by using a spectrograph with a resolving power of better than 25,000, appear nearly continuous. Other derivatives tried have too little fluorescence to study it at low pressures.