Donald Rapp

Total Cross Sections for Ionization and Attachment in Gases by Electron Impact. I. Positive Ionization

The total ionization cross sections of He, Ne, Ar, Kr, Xe, H2, D2, N2, O2, CO, NO, CO2, N2O, and CH4 have been measured from threshold to 1000 eV in a total ionization tube. More limited measurements were performed in C2H4 and SF6. Great care was taken to assure complete collection of electron and ion currents, and the absence of spurious instrumental errors. A new method was devised for obtaining absolute cross sections of gases relative to H2, and a McLeod gauge was used to obtain the absolute cross section in H2. The cross sections in NO and O2 could not be obtained by this method, and an approximate correction to direct McLeod‐gauge readings was used for these gases. It is believed that the results are as accurate as is possible with the present method. It is difficult to explain the differences found between cross sections measured by various investigators. McLeod‐gauge errors appear to account for most of the difference in absolute magnitude.

Cross Sections for Dissociative Ionization of Molecules by Electron Impact

Cross sections for dissociative ionization have been measured as a function of electron energy from threshold to 1000 eV in nine gases (H2, D2, N2, CO, NO, O2, CO2, N2O, and CH4) by collecting those ions reaching the ion collector after passing through a 0.25‐V retarding potential in a total‐ionization tube. Approximate correction is made for the effective solid angle subtended by the ion collector at the electron beam. The results are reported as the fraction of total ionization, and as absolute cross sections for dissociative ionization. At moderately high electron energies (>70 eV), the fraction of total ionization that is dissociated ions with kinetic energy in excess of 0.25 eV, ranges from ∼7% in H2 and D2 to ∼35% in N2O, with other gases intermediate.

COLLINEAR COLLISIONS OF AN ATOM AND HARMONIC OSCILLATOR

A comparison is made between quantum, semiclassical, and classical treatments of collinear collisions, with exponential repulsive potential, between an atom and a harmonic oscillator. The quantum calculations used for comparison are those of Secrest and Johnson. The semiclassical treatment, which we call ITFITS, gives analytic transition probabilities in the form of a quantum forced oscillator whose energy transfer is determined separately for each combination of initial and final states by a “refined impulsive” classical approximation symmetrized over initial and final states. Detailed balance is obeyed. The classical treatment is phase averaged, the energy transfer, calculated by numerical integration of the equations of motion, being averaged over the initial phase of the oscillator. The quantum transition probabilities are very well matched for both single and multiple quantum jumps by the semiclassical ITFITS approximation. The quantum average energy transfer is closely approximated both by the semic...

Resonant and Near‐Resonant Vibrational—Vibrational Energy Transfer between Molecules in Collisions

A semiclassical calculation of the probabilities of resonant and near‐resonant vibrational energy interchange in molecular collisions is accomplished by means of a collision model similar to that used in vibrational—translational energy transfer. The results indicate that transition probabilities are of the order of ½ in resonant and near‐resonant processes at room temperature.

Complete Classical Theory of Vibrational Energy Exchange

By using purely classical mechanics, the amount of energy ΔEvib transferred to an harmonic oscillator molecule in a head‐on molecular collision of velocity v0 is calculated. In the classical limit for small transition probabilities, the quantum‐mechanical probability per collision of going from the ground state to the first excited state is given by P0→1=(ΔEvib/ℏω), where ω is the frequency of the oscillator, and ΔEvib is the energy classically transferred to the oscillator in one collision. This transition probability is integrated over a normalized distribution of collision velocities to give an average probability for all collisions 〈P0→1〉. Finally, 〈P1→0〉 is calculated from the law of microscopic reversibility. The result turns out to be the same as that obtained by Herzfeld,1 who used a quantum‐mechanical perturbation treatment and went to the classical limit by assuming that the de Broglie wavelength of the molecule colliding with the oscillator is small compared to the range of the intermolecular f...

Vibrational–Vibrational–Translational Energy Transfer between Two Diatomic Molecules

A semiclassical calculation of transition probabilities for vibrational–vibrational–translational energy transfer in a collision of two diatomic molecules is presented. The collision model is approximate, utilizing a collinear collision of harmonic oscillators with an exponential repulsion between center atoms. The method of Kerner and Treanor is used to solve the Schrodinger equation with linearized potential in the oscillator coordinates. Our procedure is a logical extension of the Treanor method to diatomic–diatomic collisions. Closed form analytical results are obtained for this model. The general magnitudes and trends of the probabilities are expected to be indicative of the behavior of real molecules. General formulas for the probabilities of processes of the type AB(n1) + BA(n2) → AB(n1′) + BA(n2′) as a function of collision velocity are presented. Special attention is given to “resonant” energy transfer where n1′ + n2′ = n1 + n2.

Theoretical and experimental studies of stratified thermocline storage of hot water

Abstract A theoretical calculation of the degradation of heat in stratified thermocline storage has been carried out based on a conduction model. Since this neglects mixing, eddy currents and other degradation mechanisms, it provides an upper limit to the performance of a stratified thermocline storage tank. The calculation can be carried out for any selection of dimensions, temperatures, and choice of insulation. The results indicate that heat conduction through the insulation to the ambient can be a larger loss mechanism than conduction across the thermocline, except in large diameter tanks with very heavy insulation. With a properly designed tank (length/diameter > 10, diameter > 1.5 ft, insulation resistance > 20 hr ft2 °F/B.t.u.) efficient storage of heat through a daily cycle should be routinely simple based on conduction. Experiments were carried out in static and dynamic modes. In the static experiments, a fixed thermocline was established, and temperatures were monitored at spatial intervals above and below the thermocline. Some mixing occurred during formation of the thermocline, which caused an initial broadening not present in the calculations. Aside from this, it was found that the spreading of the thermocline was only slightly faster than predicted by conduction theory. If a thinner wall tank had been available, agreement between experiment and theory probably would have been closer. Dynamic experiments were conducted with a moving thermocline (both upward and downward). The results indicate preservation of the initial thermocline was excellent at linear flow rates below about 0.2 ft/min. It is believed that stratified thermocline storage has been shown to be technically viable.

Interchange of Charge between Gaseous Molecules

The theoretical methods for calculation of charge‐exchange cross sections of Gurnee and Magee [J. Chem. Phys. 26, 1237 (1957)] have been applied to the reactions of H atoms with H+, O+, and N+. The agreement with experiment [Fite, et al., Phys. Rev. 119, 663 (1960); Hummer, et al., Phys. Rev. 119, 668 (1960)] is excellent considering the approximations involved in the theory.

Nitric Oxide‐Fluorine Dilute Diffusion Flame

The dilute diffusion flame method for measuring the rates of fast gas reactions has been used to study the reaction 2NO+F2=2ONF. The reaction proceeds with the emission of visible light, and photographic methods were used to obtain concentration profiles in space. The results were interpreted in terms of the mechanism [Complex chemical formula] The interpretation of results is somewhat ambiguous. The observed rate may be that for the first step, in which case the rate constant has a pre‐exponential factor of 6×1011 cc/mole‐sec and an activation energy of 1.5±1.0 kcal between room temperature and dry ice temperature. Alternatively the observed rate may be a composite of at least four of the elementary steps given above. With a reasonable assignment of rate constants for the succeeding steps, the first alternative is favored, although the margin of safety is not great.

Active structures for use in precision control of large optical systems

This paper discusses the application of active structures technology to the control of precision structures for future space-based astrophysics observatories. The state of the art in active structures is reviewed, and technology developments applicable to large optical systems are discussed.