Diffusion theory is often employed to calculate the effects of wall destruction on the local concentration of an active species immersed in a scattering gas. In many situations the spatial dependence of the concentration is given to a good approximation by the fundamental diffusion mode, and the local loss frequency can be calculated using the container’s fundamental mode diffusion length Λ. The additional assumption that the density of the active species may be taken to be zero at the container boundaries gives a value of Λ=Λ0 which depends only on the container dimensions, but use of Λ0 can be seriously in error if the diffusion mean free path λm is comparable to the dimensions, or if the particle reflection coefficient R becomes of significance. An improved boundary condition may be written simply in terms of the linear extrapolation length λ, whose inverse is the logarithmic gradient of the particle density at the boundary. The equation λ=2(1+R)λm/3(1−R) allows the representation of the full range of possible values of the particle reflection coefficient, 0<R<1, and extends the usefulness of the diffusion approximation to low scatterer densities. In the collisionless limit, the predicted particle loss frequency is identical to that predicted from the average chord length. Using this boundary condition, the dependence of Λ on λ/Λ0 has been computed for a range of simple container shapes, by solving the transcendental equations involved. This has allowed the identification of a dimensionless scaling variable, l0λ/Λ20, where l0 is the ratio of the container volume to its surface area. For all cases considered the simple empirical approximation Λ2=(Λ20+l0λ) is accurate when λ is very large or very small compared to Λ0, and disagrees most with the numerical solutions in the region where λ and Λ0 are comparable, with the worst case error being 11%.

The distribution in center-of-mass energy caused by the thermal motion of the target gas molecules has been rigorously derived for the case of a monoenergetic particle beam interacting with target molecules having an isotropic Maxwellian velocity distribution corresponding to temperature T°K. Provided the nominal c.m. energy E0 exceeds a few kT, the distribution has a full width at half-maximum (FWHM) of W1/2=(11.1γk T E0)1/2. where γ=m/(m+M), m and M being the projectile and target masses. This is identical to the width derived previously in a one-dimensional approximate treatment by Bethe and Placzek. The exact and approximate distributions differ significantly, however, in shape and mean energy, particularly at low values of E0/γkT. The Doppler width, W1/2, is shown to significantly affect the appearance curve of the products of endothermic reactions involving heavy particles. Convolution integrals are derived for a number of idealized forms of the cross section for such reactions. In the extreme case of a step-function cross section the estimation of the threshold ET by the usual linear extrapolation technique gives a value which is too low by approximately 0.6W1/2 (ET), where W1/2 (ET) is the FWHM evaluated at E0=ET. The effect of the thermal velocities of the parent molecules from which the primary beam is formed is considered in the case of an accelerated beam with no kinetic energy imparted to the beam particles by the formation process, and in the case where the energy of the interacting particles is controlled only by the kinetic energy released in a resonant dissociative formation process. The latter situation is shown to be described exactly by the equations derived for the monoenergetic beam case provided an appropriately defined equivalent temperature is used in place of the true temperature of the target gas. The results of the present theory are applied to the experimental data of Berkowitz, Chupka, and Gutman on the reactions I−+O2→O2 −+I and I−+NO→NO−+I. In addition data on the reaction O−+O2→O2 −+O are presented and analyzed. The derived thresholds are consistent with A (O2)≥0.56±0.10 eV, A (NO)≥0.06±0.1 eV, and A (O2)≥0.50±0.1 eV, respectively. The experimental data of Maier on the reaction C++D2→CD++D is found to be consistent with a cross section which rises from threshold with approximately twice the slope of the cross section computed by Truhlar from statistical phase space theory.

The attachment of low-energy electrons (<4 eV) by the reaction e+N2O → O−+N2 has been studied as a function of gas temperature from approximately 160 to 1040°K. The ions produced by a monoenergetic electron beam are detected by total ion collection or by mass analysis. The kinetic energy distributions of the O− ions have also been measured and found to be relatively insensitive to the electron energy when the latter exceeds 1.5 eV, in which case the most probable ion energy is 0.38 eV. The shape and magnitude of the cross section below 2 eV is found to be sensitive to gas temperature throughout the range studied. The differences in shape and threshold observed by previous workers occur below 2 eV and to a large extent may be reconciled in terms of the differing gas temperatures employed. The temperature insensitive portion of the cross section is ascribed to electron capture into the highest-energy N2O− state connected to electronic ground state N2 + O−. The O− kinetic energy distributions arising therefrom are explained in terms of the N2O−* potential energy surface involved. It is argued that the strongly temperature sensitive portion of the cross section is due predominantly to excitation of the bending mode of vibration, and arises from the dependence on bond angle of the separation in energy of the electronic ground states of N2O and N2O−.

We have calculated α and η, the ionization and attachment coefficients, and (E/N) *, the limiting breakdown electric-field–to–gas-density ratio, in SF6 and SF6 mixtures by numerically solving the Boltzmann equation for the electron energy distribution. The calculations require a knowledge of several electron collision cross sections. Published momentum transfer and ionization cross sections for SF6 were used. We measured various attachment cross sections for SF6 using electron-beam techniques with mass spectrometric ion detection. We determined a total cross section for electronic excitation of SF6 by comparing the predicted values of α, η, and (E/N) * with our measured values obtained from spatial current growth experiments in SF6 in uniform fields over an extended range of E/N. With this self-consistent set of SF6 cross sections, together with published He and N2 cross sections, it was then possible to predict the dielectric properties of SF6-He and SF6-N2 mixtures. Published experimental values of α for the SF6-He mixtures lie between the values of α calculated with and without ionization of SF6 by excited He atoms. Published experimental values of (E/N) * agree with our calculations to within 5% in both the SF6-He and the SF6-N2 mixtures.

Production of SF−5 by dissociative attachment of very low energy electrons to SF6 is known from previously reported work to be strongly enhanced by increasing the gas temperature. Data on this effect is presented and analyzed to give an activation energy of εa=0.2 eV for the reaction. The expectation that this effect can be produced by direct optical excitation of the ν3 vibrational mode is confirmed by using a tunable cw CO2 laser focused collinearly with an electron beam inside a collision chamber. The product ions are monitored using a quadrupole mass filter. By chopping the laser beam and monitoring ion signals and electron current during the laser on, and laser off, periods it is possible to isolate the desired signals from the interfering effects of heating of the collision chamber and the electron gun filament, caused by the laser beam. The observed enhanced of the SF−5 signal by the radiation is strongly dependent on the laser wavelength, and is confined to the attachment peak at very low (<0.1 eV) electron energy. This is consistent with the thermal excitation data. The tuning curves for the production of 32SF−5 and 34SF−5 are well resolved and are separated by the known isotope shift of the ν3 SF6 absorption. Both peaks, however, are red shifted by 8 cm−1 from their respective room temperature small-signal absorption peaks. Possible reasons for this shift are discussed. They suggest that efficient promotion of the (SF−6) * dissociative decay channel requires a total of two or more vibrational quanta to be present in the SF6. The peak enhancement of 32SF−5 was found to occur at the P (28) CO2 laser line (936.85 cm−1). At this wavelength the enhancement effect was found to be linearly dependent on laser intensity. The interpretation that this implies single-photon absorption is rejected on the grounds that the laser fluence levels are too high for such conditions to prevail. The linearity remains unexplained, in common with similar observations by others on absorption effects in SF6 at similar fluence levels. Future measurements of the present type, in particular, of the dependence on laser fluence at other wavelengths should provide additional insight to this general problem of understanding the mechanisms contributing to the absorption of the first few photons in any multiple photon absorption process.