By measuring the radiative decay in flight of a foil-excited heliumlike fluorine beam, we have determined the lifetime of the metastable $2 {}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state of the two-electron ion ${\mathrm{F}}^{7+}$. Our data yield the singlet-triplet intercombination transition probability $A(1\mathrm{} {}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-2 {}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{})=(1.77\mathrm{}\pm 0.10)\times {10}^9$ ${\sec }^{-1\mathrm{}}$, which is in excellent agreement with theoretical calculations of a strongly $Z$-dependent spin-orbit-induced electric dipole decay, and extends our earlier measurements for ions in this isoelectronic sequence. Because this transition is observed in the solar spectrum for all abundant heliumlike ions from carbon to iron, we also discuss the relevance of this measurement to solar physics.

The structure in the total electron-impact ionization cross section in cesium can be partially accounted for by the mechanisms of autoionization and excitation ionization of $5p$ electrons. For electron energies above 17 eV a large fraction of the ions are metastable and can de detected by Auger emission from a metal surface. The experiment was performed in a cesium-atom—electron crossed-beam apparatus, and the metastable ions were counted with a channel electron multiplier. The metastable-ion count rate was a factor of 100 higher than that due to photons from atomic and ionic transitions. We have measured the over-all excitation function for a number of unresolved ${\mathrm{Cs}}^{+}$ metastable levels, the lowest being $5d\left\{\right[3\frac{1}{2}],3\}$ at 17.02 eV and $5d\left\{\right[\frac{1}{2}],1\}$ at 17.06 eV.

The quenching of hydrogenic metastables is formulated as a near-resonant photon-scattering problem, and a complete analysis of the polarization and angular distribution of the emitted radiation is presented. The contribution from $\mathrm{np}$ states with $n>\mathrm{}2\mathrm{}$ is calculated, and an alternative method of measuring the Lamb shift is suggested.

Measurement of a system's Compton profile makes possible, in principle, the calculation of its electronic radial momentum distribution. From this quantity, the expectation values $〈p^n〉$ and the total energy may be obtained. The feasibility of using Compton-scattering data in this way is examined in view of the limitations imposed by (i) random experimental errors on the measured profile, and (ii) restriction of the profile data to a finite range of momenta. It is concluded that while present techniques may be adequate for a few systems, improved experimental methods are required before Compton scattering becomes a useful source of atomic and molecular energies.

Three new autodetaching states of ${\mathrm{O}}^{-}$ have been found and an electron configuration has been assigned one of two previously observed transitions. This gives a total of five known autodetaching states of ${\mathrm{O}}^{-}$. Transitions from these states appear as peaks in the spectrum of electrons produced in collisions of ${\mathrm{O}}^{-}$ ions with a helium target. These peaks lie at 9.50, 10.11, 10.87, 12.12, and 13.71±0.02 eV. The electron spectrum produced by collisions of neutral O with helium shows four autoionizing series of oxygen lying just above the first ionization potential.

The cross section for charge-transfer excitation of the ${N_2}^{+}$ first negative 3914-Å band by protons (5-65 keV) has been measured using a photon-particle coincidence technique. The target ${\mathrm{N}}_2$ is collisionally excited to the ${{\mathrm{N}}_2}^{+} \left(B {}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\right)$ state and emits a 3914-Å photon in the (0,0) transition. This photon is detected in coincidence with the scattered particle, a proton or hydrogen atom, allowing separation of the two reactions which contribute to 3914-Å emission. The cross section for charge-transfer excitation indicates that charge transfer is the dominant contributor to 3914-Å excitation at energies below 10 keV, and that ionization with excitation becomes increasingly important with increasing energy. The by-product measurements, which include the cross section for charge transfer, the total cross section for 3914-Å emission, and the lifetime of the ${{\mathrm{N}}_2}^{+} \left(B {}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\right)$ state, agree well with those of other workers.

The construction of a semiclassical optical model for molecular collisions to consider explicitly the dynamics of more than a single nuclear degree of freedom is investigated. A sample model is developed for nonreactive systems as the direct multidegree analog of the semiclassical optical model for a single nuclear degree of freedom. In this model all nuclear degrees of freedom, moving in a complex potential, are treated explicitly through the integration of Hamilton's equations of motion in complex time and complex phase space. Calculations are performed for probabilities of elastic collinear collisions of an atom with a diatomic oscillator in its ground vibrational state with excited vibrational states energetically accessible. Agreement is obtained with exact quantum-mechanical results for just the real part of the potential, through variation of an adjustable parameter in the imaginary part of the potential. Extensions and variations of this model toward the simplification of more-complicated calculations on reactive and three-dimensional systems are discussed.

Investigations are made of the production of excited-state hydrogen neutrals using 10-keV proton or 20-keV $\mathrm{H}_2^{}{}_{}{}^{+}$ beams and a magnesium vapor cell. Optical measurements are used to determine the population of the $n=6\mathrm{}$ level as a function of target thickness and to determine the relative populations for $3\le n\le 8$. The cross section for capture into the $n=6\mathrm{}$ level for incident $\mathrm{H}_2^{}{}_{}{}^{+}$ is found to be about equal to that for incident protons. An approximate $\frac{1}{n^3}$ dependence of the excited-state populations is found for $n\ge 6$ with an assumed $2l+1$ weighted substate distribution.

Differential and integral cross sections for the electron-impact excitation of the $2 {}_{}{}^3{}_{}{}^{}S$, $2 {}_{}{}^1{}_{}{}^{}S$, and $2 {}_{}{}^3{}_{}{}^{}P$ states of He relative to the $2 {}_{}{}^1{}_{}{}^{}P$ state have been measured at 29.6- and 40.1-eV energies in the 3° to 138° angular range. The relative cross sections have been normalized to the absolute scale by utilizing the previously determined $2 {}_{}{}^1{}_{}{}^{}P$ cross sections [D. G. Truhlar, S. Trajmar, W. Williams, S. Ormonde, and B. Torres (unpublished)]. The differential cross section for the $2 {}_{}{}^1{}_{}{}^{}S$ state has a deep minimum at 50°; for the $2 {}_{}{}^3{}_{}{}^{}P$ state it is nearly isotropic, and for the $2 {}_{}{}^3{}_{}{}^{}S$ state it shows a complicated structure which has not been previously reported. The experimental cross sections are compared to the results of quantum-mechanical calculations performed by Truhlar, Yates, Tenney, Cartwright, Steelhammer, and Lipsky using the Born, Born-Ochkur-Rudge, and Glauber approximations for the $2 {}_{}{}^1{}_{}{}^{}S$ excitation and the Born-Oppenheimer and the Ochkur-Rudge approximations for the $2 {}_{}{}^3{}_{}{}^{}S$ and the $2 {}_{}{}^3{}_{}{}^{}P$ excitations. None of the first-order plane-wave calculations predict the observed differential cross sections for these optically forbidden transitions. It is interesting to note, however, that the Ochkur-Rudge model predicts the correct magnitude and approximate shape of the $2 {}_{}{}^3{}_{}{}^{}P$ differential cross sections in the whole angular range at these energies. The Glauber approximation shows considerable improvement compared to first-order plane-wave theories in predicting the cross sections for the $2 {}_{}{}^1{}_{}{}^{}S$ state. However, at large scattering angles, calculation and experiment differ significantly. It is clear from the present study that more refined calculations are needed to predict angular distributions for these optically forbidden excitations in the 30-40-eV energy region.

The behavior of scattering cross sections near an excitation threshold is examined for the case of long-range potentials. The theory is confirmed by computations of $e-\mathrm{L}\mathrm{i}$ scattering. Recent observations of threshold structure in $e-\mathrm{N}\mathrm{a}$ collisions are ascribed to a ${}_{}{}^1{}_{}{}^{}D$ resonance of ${\mathrm{Na}}^{-}$. A true cusp should occur only in the ${}_{}{}^1{}_{}{}^{}P$ partial cross section.

The energy dependence of the charge-exchange cross section in proton—hydrogen-atom collisions at very high energies, within the framework of the Schrödinger equation, has long been a subject of controversy. We attempt to determine the energy dependence of the forward-scattering cross section at very high energies in an arbitrary rearrangement collision involving two heavy particles of masses $M_a$ and $M_b$ and a light particle of mass $m$, with $m$ initially bound to $M_a$ and finally bound to $M_b$. In the limits $\frac{m}{M_a}$, $\frac{m}{M_b}\to 0$ the scattering is entirely in the forward direction and the cross section $\sigma$ for forward capture is given exactly by the impact-parameter treatment. A Born-type expansion is developed in the impact-parameter treatment for the forward-capture amplitude $A$. Thus, $A$ is written as a sum of a finite number of Born terms plus a remainder $R$. The Schwarz inequality can be used to bound $R$ since there are no non-normalizable plane-wave functions—the motion of $M_a$ and $M_b$ is treated classically. We can thereby show that for a certain class of nonsingular interactions the second Born term provides the dominant contribution to $\sigma$ at high energies, whether or not the Born series converges. (This may be the first example for which it has been shown that the second Born term dominates.) This result makes plausible the dominance of the second Born term in $p-\mathrm{H}$ forward charge exchange.

Previous Hylleraas calculations of $\mathcal{E}=<\mathrm{QHQ}>\mathrm{}$ for the lowest ${}_{}{}^1{}_{}{}^{}P$ autoionization state of helium are here supplemented by calculations of the shift ($\Delta$), width ($\Gamma$), and shape parameter ($q$) using a ($ls,2\mathrm{}\tilde{p}$) pseudostate nonresonant continuum function. The function is constructed to eliminate the dominant ($2s,2p$) configuration of the autoionization state, while at the same time containing three variationally determined radial functions. Both $\Delta$ and $q$ are also shown to contain contributions from the discrete part of the nonresonant spectrum, although quantitatively that contribution is found to be small. Final results change previous polarized-orbital results minimally, which means that the resonance position, $\mathcal{E}=\mathrm{E}+\Delta$, continues to be on the edge of the experimental error, and $q$ remains somewhat outside the experimental result. Further relativistic corrections are briefly discussed, but a simple argument indicates that they are not likely to explain the differences with experiment. It is concluded that more-accurate experiments should be carried out.

A variational treatment of the $R$ matrix method for multichannel scattering is given, in which basis functions used for expanding the wave function within a boundary radius $r_0$ need not satisfy specific boundary conditions at $r_0$. As an illustration, a simple basis set of monomial functions ($r^n,n=1,\dots ,N$) is used in a two-channel-model problem with long-range potentials. Excellent results are obtained with ten such functions in each channel.

Measurements have been made at two laboratories which indicate that the structure reported at 450-550eV in the electron spectrum from ${\mathrm{Ar}}^{+}$-Ar collisions by Ogurtsov, Flaks, and Avakyan is spurious. It is argued that the double $L$ vacancies which they invoke to explain the structure are more likely to decay by the two-step Auger process $L^{ 2}\to L{M}^{ 2}\to M^{ 4}$ than by the one-step process $L^{ 2}\to M^{ 3}$ suggested by these authors. Evidence supporting this is found in our electron spectra from ${\mathrm{P}}^{+}$-Ar collisions, where it is known from energy-loss and charge-state measurements that double $L$ vacancies are produced in phosphorus.

The transport equation for electron scattering through plane parallel targets has been solved by expanding the electron distribution function into spherical harmonics. The electron energy is assumed to be constant. No simplifying assumptions have been made concerning the scattering cross sections. In fact, a simple technique has been found for accurately determining the screening angle which plays an important role in multiple scattering. For small angles (≤ 10°) and thin targets, the emerging electron distribution agrees well with earlier theories. However, for larger angles the present theory predicts a greater probability of scattering than earlier theories. For thin targets it is well known that the earlier theories merge with the single-scattering distribution function at large angles. This difference at large angles between the present and earlier theories implies that the electron distribution predicted by the present calculations will not merge with the single-scattering distribution. For thick targets, as one would expect, the earlier theories are poor approximations of the emergent electron distribution function for all angles.

The eikonal approximation has been used to investigate $e^{\pm }-\mathrm{L}\mathrm{i}$ scattering in the energy region $E=0.8\mathrm{}$ to 500 eV. In addition to the static potential, the effect of the polarization potential has been included explicitly. Our results for the total cross section of $e^{-}-\mathrm{L}\mathrm{i}$ scattering in the energy region $4\le E\le 10$ eV are in close agreement with the recent experimental findings as well as with the theoretical results obtained by various authors using the close-coupling approximation. In the energy region $10<E\le 500$ eV, the present approach yields higher values than first Born approximation (FBA). Our results for the total cross section for $e^{+}-\mathrm{L}\mathrm{i}$ scattering in the eikonal approximation are displayed and compared with the corresponding polarized FBA results and the results obtained by the polarized-orbital method. Results for the differential cross sections for both the systems $e^{\pm }-\mathrm{L}\mathrm{i}$ in the eikonal approximation are also presented together with the corresponding polarized FBA results.

A theory of rearrangement collisions taking account of the nonorthogonality of initial and final states is presented. Detailed discussion of the range of validity of the theory is worked out. The method is applied to proton-hydrogen-atom charge exchange collisions. We find that at high energy the Jackson-Schiff results are obtained and that below 100 kev the cross section is raised significantly above the result of Jackson and Schiff. The new result is in better agreement with experimental results than the calculations based on the Jackson-Schiff formulation.

New analytic methods for reducing the Glauber amplitude for charged particle-neutral atom collisions to a one-dimensional integral representation involving modified Lommel functions are proposed. To illustrate these new methods, the reduction of the Glauber amplitude for $e^{-}$ + He elastic scattering, using a simple Hylleraas wave function for the He ground state, is described in detail, and the resulting integral for the amplitude is evaluated numerically. The Glauber-approximation-predicted elastic scattering amplitude previously calculated by Franco from a three-dimensional integral representation, with a more complex Hartree-Fock wave function for the ground state, is also recalculated using these new procedures; these results are in good agreement with those obtained by Franco. Thus, the utility and practicality of these new techniques are demonstrated. The application of these procedures to more general charged particle-neutral atom collisions is discussed.

In this paper we report new and improved theoretical electron-impact cross sections involving energy levels of different electronic configurations of atomic nitrogen and oxygen, and some of their ions. The results are expected to be improvements over previously published work, based on a single (ground-state) configuration approximation, because allowance has been made for additional distortion of the target system by the projectile by taking into account the effect of either virtual or real transitions to different terms of excited electronic configurations. The effect of coupling to excited configurations on the total elastic and forbidden cross sections among the ground-state terms of atomic nitrogen and of N IV is discussed in detail. Cross sections are also given for selected transitions to terms of excited configurations in O II, O III, N II, N III, and N IV. Some new autoionizing series in O II and N II are predicted and suggestions are made for their experimental verification. Also, qualitative agreement with recent observations of autodetaching states in atomic oxygen is obtained and the existence of other as yet unobserved states is suggested. The results indicate the need for additional experiments in oxygen and nitrogen and especially a careful measurement of the electron-nitrogen scattering in the energy range 0-5 eV.

Observed intensity fluctuations in the emission of Stark-perturbed $\mathrm{L}\mathrm{y}-\beta$ radiation, from hydrogen atoms formed by passage of hydrogen ions through carbon foils, are compared with theoretical calculations using a density-matrix formalism to yield information on the cross sections for creation into the various $l$ states. It is found, for beam energies between 250 and 500 keV/atom, that the $s$ states are preferentially populated by more than a factor of 4, compared to a statistical distribution. Similar results are also obtained for $\mathrm{L}\mathrm{y}-\alpha$ emission in electric and motional electric fields, in contrast with previous reports at lower energies. The effects of Zeeman splittings, hyperfine interaction, and fringing fields on the signal are investigated.