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A scaling law for energy transfer by inelastic electron-molecule collisions in mixtures

The equation governing the electron energy distribution in the presence of a spatially uniform electric field in a weakly ionized gas was reformulated into an integral equation for the logarithmic slope of the distribution function. For gas mixtures in which the dominant electron energy loss mechanism is by vibrational excitation of the molecules, this equation is suitable for approximate analysis and exact numerical solution by iteration. Superelastic collisions are easily included in this formulation, and do not seriously effect the convergence of the numerical scheme. The approximate analytical results are only qualitatively correct, but suggest appropriate parameters which correlate the exact numerical results very well. The distribution function as well as certain gross properties such as net energy transfer into vibration, mean energy, and drift velocity depend primarily on a single nondimensional parameter involving only E/N and the cross sections.

Bienkowski, G. K.↗

Vibrational and rotational transitions in low-energy electron-diatomic-molecule collisions. I - Close-coupling theory in the moving body-fixed frame. II - Hybrid theory and close-coupling theory: An /l subscript z-prime/-conserving close-coupling approximation

A detailed vibrational-rotational (V-R) close-coupling formulation of electron-diatomic-molecule scattering is developed in which the target molecular axis is chosen to be the z-axis and the resulting coupled differential equation is solved in the moving body-fixed frame throughout the entire interaction region. The coupled differential equation and asymptotic boundary conditions in the body-fixed frame are given for each parity, and procedures are outlined for evaluating V-R transition cross sections on the basis of the body-fixed transition and reactance matrix elements. Conditions are discussed for obtaining identical results from the space-fixed and body-fixed formulations in the case where a finite truncated basis set is used. The hybrid theory of Chandra and Temkin (1976) is then reformulated, relevant expressions and formulas for the simultaneous V-R transitions of the hybrid theory are obtained in the same forms as those of the V-R close-coupling theory, and distorted-wave Born-approximation expressions for the cross sections of the hybrid theory are presented. A close-coupling approximation that conserves the internuclear axis component of the incident electronic angular momentum (l subscript z-prime) is derived from the V-R close-coupling formulation in the moving body-fixed frame.

Choi, B. H.↗

Ion-quadrupole effects in ion-molecule collisions.

Ion-quadrupole effects are investigated via numerical calculations of capture cross sections and computer-plotter studies of ion trajectories in the quadrupole field. Capture cross sections are roughly equal to Langevin values for low rotational temperatures; a large fraction of multiple reflection captures are calculated corresponding to formation of ion-molecule complexes.

Dugan, J. V., Jr.↗

Ion-molecule collision frequencies in gases determined by phase coherent pulsed ICR.

The transient method considered is analogous to similar phase coherence experiments performed in NMR and plasma physics. Using a pulsed ion cyclotron resonance (ICR) spectrometer equipped with a trapped ion analyzer cell, gaseous ions are formed by a pulse of an electron beam and then trapped in the cell by the combined effects of the magnetic and electrostatic fields. The results obtained in the experiments indicate that the classical mobility treatment of Wannier (1953) is helpful in the understanding of collision frequencies under the considered conditions.

Lieder, C. A.↗

ICR study of nonreactive ion-molecule collision rate constants for Cl/-/ and Cr/CO/5/-/

Determination of experimental momentum transfer rate constants for systems of Cl(-) and Cr(CO)5(-) ions by means of an ion cyclotron resonance (ICR) line-broadening technique. It is found that in the pure polarization limit of small ion/large neutral collisions the Langevin ion mobility theory gives good agreement with experimental results. A comparison of isotropic and anisotropic neutral systems suggests that a correction for the anisotropic systems is necessary. Beyond the pure polarization limit the Langevin theory gives poor predictions for ion mobilities. The adjustable parameter, gamma, of the Mason-Schamp (12-6-4) potential function permits unique solution of the ion mobility for Cr(CO)5(-) in a wide range of neutral gases. The large values of gamma obtained for most of these systems imply, in terms of the Mason-Schamp theory, that the r to the minus 6th power contribution to the potential function is significant.

Dymerski, P. P.↗

Studies of electron-polyatomic-molecule collisions Applications to e-CH4

The first application of the Schwinger multichannel formulation to low-energy electron collisions with a nonlinear polyatomic target is reported. Integral and differential cross sections are obtained for e-CH4 collisions from 3 to 20 eV at the static-plus-exchange interaction level. In these studies, the exchange potential is directly evaluated and not approximated by local models. An interesting feature of the small-angle differential cross section is ascribed to polarization effects and not reproduced at the static-plus-exchange level. These differential cross sections are found to be in reasonable agreement with existing measurements at 7.5 eV and higher energies.

Lima, M. A. P.↗

Studies of electron-molecule collisions - Applications to e-H2O

Elastic differential and momentum transfer cross sections for the elastic scattering of electrons by H2O are reported for collision energies from 2 to 20 eV. These fixed-nuclei static-exchange cross sections were obtained using the Schwinger variational approach. In these studies the exchange potential is directly evaluated and not approximated by local models. The calculated differential cross sections, obtained with a basis set expansion of the scattering wave function, agree well with available experimental data at intermediate and larger angles. As used here, the results cannot adequately describe the divergent cross sections at small angles. An interesting feature of the calculated cross sections, particularly at 15 and 20 eV, is their significant backward peaking. This peaking occurs in the experimentally inaccessible region beyond a scattering angle of 120 deg. The implication of this feature for the determination of momentum transfer cross sections is described.

Brescansin, L. M.↗

Theoretical Study of Low-Energy Electron-Molecule Collisions

Polarized studies of electron collisions with carbon tetrafluoride and beryllium carbonyl are reported. In the e-CF4 study, the resonance structure between 8-9 eV is shown to be a superposition of the T2- and A1-symmetry shape resonances. The unequivocal assignment of this feature as a double-resonance structure clarifies certain discrepancies in previous attempts to ascribe the 8-9 eV feature to a shape resonance in one or another partial channel and explains the sensitivities found in the fragment ion production in the resonance region. The Be-CO system is chosen as a prototypical example of an absorbate-substrate interaction. To understand how bonding with the substrate affects the CO resonance, electron collision with two states of BeCO are studied, one with a very weak van der Waals bond and the other, with a normal chemical bond. It is shown that the nature of the Be-CO bond has strong effects on the cross section feature.

Huo, Winfred M.↗

Quantum-State-Controlled Collisions of Ultracold Polyatomic Molecules

Collisions between ultracold calcium monohydroxide (CaOH) molecules are realized and studied. Inelastic collision rate constants are measured for CaOH prepared in ground and excited vibrational states, and the electric field dependence of these rates is measured for molecules in single quantum states of the parity-doubled bending mode. Theoretical calculations of collision rate coefficients are performed and found to agree with measured values. The lowest collisional loss rates are for states with repulsive long-range potentials that shield ultracold molecules from loss channels at short distance. These results unveil the collisional behavior of parity-doublet molecules in the ultracold regime and lay the foundation for future experiments to evaporatively cool polyatomic molecules to quantum degeneracy.

Vilas, Nathaniel B. [Harvard University, Cambridge↗

Rotational excitation of hydrogen molecules by collisions with hydrogen atoms

Rate constants for rotational excitation of hydrogen molecules by collisions with hydrogen atoms have been obtained from quantum-mechanical calculations for kinetic temperatures between 100 and 5000 K. These calculations involve the rigid-rotator approximation, but other possible sources of error should be small. The calculations indicate that the early values of Nishimura are larger than accurate rigid-rotator values by about a factor of 20 or more.

Green, S.↗

The Schwinger Variational Method

Variational methods have proven invaluable in theoretical physics and chemistry, both for bound state problems and for the study of collision phenomena. The application of the Schwinger variational (SV) method to e-molecule collisions and molecular photoionization has been reviewed previously. The present chapter discusses the implementation of the SV method as applied to e-molecule collisions. Since this is not a review of cross section data, cross sections are presented only to server as illustrative examples. In the SV method, the correct boundary condition is automatically incorporated through the use of Green's function. Thus SV calculations can employ basis functions with arbitrary boundary conditions. The iterative Schwinger method has been used extensively to study molecular photoionization. For e-molecule collisions, it is used at the static exchange level to study elastic scattering and coupled with the distorted wave approximation to study electronically inelastic scattering.

Huo, Winifred M.↗