M. R. Flannery

Tables of transport collision integrals for (n, 6, 4) ion-neutral potentials☆

Transport collision integrals are tabulated for the (n, 6, 4) model of ion-neutral-molecule interactions as functions of effective ion temperature for eight values of n and several values of a parameter γ that measures the relative strengths of the r−6 and r−4 attraction terms. The ions can have any charge and the neutral entities can be either atoms or spherically symmetric molecules. The accuracy of the calculations is estimated to be a few parts in 104. The tables can be used to estimate ion-neutral potentials by comparison with experimental ion mobility data or conversely can be used to estimate ion mobilities and diffusion coefficients as functions of gas temperature and electric field strength from fragmentary information.

Molecular charge transfer. II. Experimental and theoretical investigation of the role of incident‐ion vibrational states in O2+–O2 and NO+–NO collisions

Charge‐transfer cross sections are measured for the O2+–O2 and NO+–NO systems and are compared with those calculated from a theoretical multistate impact parameter model for which the resulting coupled first‐order differential equations are solved numerically. Convergence in the theoretical total cross sections is achieved by the systematic introduction of as many as 54 product states to the wavefunction expansion for the total system. At high kinetic energies (∼2 keV) the computed cross sections are controlled predominantly by the magnitude of the vibrational overlaps between the reactant and product states, and multiquantum transitions do occur with high efficiency. At lower energies, the energy defects and vibrational overlaps of the various product channels tend to control the reaction pathways. Total charge‐transfer cross sections measured as a function of reactant ion vibrational and translational energy are found to be in general accord with the computed multistate cross sections. In the low veloci...

Ionic recombination of rare‐gas atomic ions X+ with F− in a dense‐gas X

Rates for the recombination processes X++F−+X→XF*+X, (X≡He, Ne, Ar, Kr, Xe) at 300 K are calculated for pressures of the background gas X in the range ∼0.1–50 atm. Rates as high as (2–7) ×10−6 cm3 sec−1 are obtained for pressures 1–5 atm of Xe→He, and in general decrease with increasing ionic mass, except at low gas densities.

Molecular charge transfer. III. The role of incident‐ion vibrational states in H+2–H2 and D+2–D2 collisions

Charge transfer cross sections for the H+2–H2 and D+2–D2 systems have been computed and compared with experimental measurements in the 1 eV to 5000 eV kinetic energy range. Cross sections have been calculated using a multistate impact parameter treatment of charge transfer in which the set of first order coupled differential equations resulting from the time dependent Schrodinger equation are solved numerically. At low kinetic energies the inclusion of a comparatively small number of product states results in converged cross sections. However, as the ion kinetic energy is increased, it becomes necessary to include as many as ∼100 final vibrational states in the wavefunction expansion of the system. Both the energy defects and vibrational overlaps of the different product channels have a strong influence on reactions at low kinetic energies but as the ion energy is increased the vibrational overlaps exert a relatively more important role in controlling the product state distribution. Vibrational overlaps h...

The enigma of nonholonomic constraints

The problems associated with the modification of Hamilton’s principle to cover nonholonomic constraints by the application of the multiplier theorem of variational calculus are discussed. The reason for the problems is subtle and is discussed, together with the reason why the proper account of nonholonomic constraints is outside the scope of Hamilton’s variational principle. However, linear velocity constraints remain within the scope of D’Alembert’s principle. A careful and comprehensive analysis facilitates the resolution of the puzzling features of nonholonomic constraints.

Three-Body Recombination of Positive and Negative Ions. II. General Third Body

A quasi-equilibrium statistical theory is used to investigate the low density limit to the rate of the three body ionic recombination process X+ + Yˉ + Z → [XY] + Z, the interaction between the third body and an ion being taken to be of the Langevin form. It is shown that the recombination coefficient α is, to a close approximation, equal to the sum of two partial recombination coefficients, α13 and α23 the former describing recombination due only to X+ — Z collisions and the latter describing recombination due only to Yˉ — Z collisions. Results are presented which enable α to be found for a wide range of values of the temperature, the masses of the three species involved, the two Langevin hard-sphere radii and the polarizability of the third body. In the case of equal masses (for which it was designed) the well-known theory of Thomson is remarkably successful with regard to its predictions on the dependence of α on the temperature and on the interactions.

New semiclassical treatments of rotational and vibrational transitions in heavy‐particle collisions. I. H–H2 and He–H2 collisions

Two new semiclassical methods—the multistate orbital treatment and the multichannel eikonal treatment—are proposed for the description of rotational and vibrational excitation in heavy‐particle collisions. The first method includes appropriate trajectories determined from a certain optical potential designed to couple the response of the internal structure, which is described by a quantal multistate expansion, to the orbit for the relative motion and vice versa. While this approach is, in general, valid when the quantal imprecision in the classical trajectories is small (as for heavy particles) the second method based on the use of a straight‐line eikonal for the relative motion, of different local momenta in the various channels and of a multistate expansion for the internal motions, is valid for scattering mainly about the forward direction. These procedures are applied to representative rotational transitions in H–H2 and He–H2 collisions at 0.25–1.5 eV and yield angular distributions and integral cross...

Mobility, diffusion, and clustering of K+ ions in gases

We have measured, with a drift tube mass spectrometer, the mobilities and longitudinal diffusion coefficients of K+ ions in nitrogen and carbon monoxide at 300°K. The measurements were made over a range of E/N extending from thermal values up to 636 × 10−17 V·cm2. Here E is the drift field intensity and N is the gas number density. The zero‐field reduced mobilities of K+ ions in N2 and CO were determined to be (2.54 ± 0.05) and (2.30 ± 0.04) cm2/V · sec, respectively. The low‐field diffusion coefficients are in excellent agreement with the values calculated by the Einstein equation from the experimental zero‐field mobilities. The experimental diffusion coefficients are compared with the predictions of an equation developed by Wannier on the assumption that the ion‐molecule interaction consists of only the attractive polarization force, of which a constant mean free time between collisions is a consequence. Comparison is also made with a modified version of this equation which contains the ionic drift velo...

Vibrational deactivation of oxygen ions in low velocity 02+(X2Πg,υ=1)+02(X 3Σg−,υ=0) collisions

The deactivation of 02+(X 2Πg, υ=1) ions in collisions with 02(X 3Σg−,υ=0) molecules has been examined using multistate impact parameter eikonal and orbital treatments. Cross sections for the formation of various product states in the charge exchange and direct scattering channels have been computed for ions with 0.5 to 8.0 eV c.m. kinetic energies. The relative probabilities for forming products in given vibrational states at the higher kinetic energies are similar for the eikonal and orbital approaches. At energies below several eV it is necessary to employ the multistate orbital treatment which takes explicit account of the strong ion–molecule scattering. Cross sections for reaction channels leading to de‐excitation and/or excitation of the product 02+(X 2Πg,v=1) ions have been computed for both charge exchange and direct scattering processes. The channels leading to vibrationally deactivated 02+(X 2Πg, v=0) product ions are strongly favored at low velocities over the excitation processes in the charge...

Photoionization of metastable rare‐gas atoms (He*,Ne*,Ar*,Kr*,Xe*)

Cross sections σ for the photoionization of metastable rare‐gas atoms (He*‐Xe*) over a wide range of photon energies are presented. In marked contrast to that found for He* where σ∼10−18 cm2 and decreases monotonically with photon energy, the cross sections σ for Ne*‐Xe* are much smaller ∼10−19 cm2 and exhibit optical windows within the wavelength range 2000–3000 A of current laser interest.