The trapped-electron method is applied to the excitation by electron impact of the $\left(2\mathrm{}{p}^2\right){}_{}{}^3{}_{}{}^{}P$ state, the lowest doubly excited state of helium which is stable against auto-ionization. The energy of this state, 59.64±0.08 eV, is in good agreement with theory. An estimate of the slope of the total cross section for excitation of the $\left(2\mathrm{}{p}^2\right){}_{}{}^3{}_{}{}^{}P$ state at threshold gives a value of 4 × ${10}^{-20\mathrm{}}$ ${\mathrm{cm}}^2$/eV.

The charge-exchange reactions between ${\mathrm{Ar}}^{+}$ or ${\mathrm{Kr}}^{+}$ and several molecules have been studied spectroscopically. Light emission is observed from the molecular ions, indicating near-resonant charge exchange. Measurements on mixtures of gases provide relative cross sections for the formation of electronically excited ions. The cross sections are largest for the smallest energy defect, in agreement with the theory of Rapp and Francis. The Franck-Condon principle is not a dominant factor in determining the populations of different vibrational levels of diatomic ions, but it may be important for triatomic ions.

The scattering of ${\mathrm{He}}^{+}$ projectiles by impact on the noble gases He, Ne, and Ar was investigated in the energy range 120-830 keV under single-collision conditions. Specifically, the experiment measured, as a function of angle in the range 1° -8°, the total differential scattering cross section as well as the differential cross sections for scattering without change of charge, for scattering with charge transfer, and for scattering with electron stripping. The total differential scattering cross section was found to be in agreement with a theoretical differential scattering cross section calculated classically using a screened Coulomb potential. Thus, the scattering of the particles in these close encounters is determined primarily by the mutual nuclear repulsion and may be adequately described by classical mechanics. The fraction of particles in a particular charge state was independent of the scattering angle, a result consistent with theory and with previous experiments at slightly lower energies. For the resonant case ${\mathrm{He}}^{+}$ + He, it was found that the fraction of scattered particles which had picked up an electron during the collision could be prediced by a semiempirical equation. Good agreement was also found when comparing relative charge-state populations with the predictions of a statistical theory.

Excited-state population ratios for atomic hydrogen have been measured for energetic hydrogen ions neutralized by charge exchange with a number of different metallic vapors and permanent gases. Electric field ionization techniques were used to determine excitation ratios. Detection of the energetic ions and neutrals was accomplished using partially depleted surface-barrier detectors. Counting, using phase-detection techniques in which an add-subtract scaler was phased to the signal, provided an improved signal-to-noise ratio. Two methods were used to provide desired targets. Metallic vapor and permanent-gas thin targets of the order of ${10}^{-5\mathrm{}}$ mTorr cm were produced as chopped neutral beams, using conventional crossed-beam techniques. Gas cells were used to extend these measurements with permanent gases to targets up to seven orders of magnitude thicker. In the latter case, the ion beam was interrupted electrically. Targets investigated were magnesium, potassium, barium, hydrogen, nitrogen, thallium, Freon, water vapor, ammonia, and perfluorodimethylcyclohexane (${\mathrm{C}}_8$${\mathrm{F}}_{16}$).

The trapped-electron method is applied to a study of vibrational excitation by low-energy (0-1-eV) electrons on ${\mathrm{O}}_2$. It is found that the dominant feature of the vibrational cross section consists of spikes, spaced about 0.11 eV apart. This spacing is characteristic of the spacing of the vibrational levels of the $\mathrm{O}_2^{}{}_{}{}^{-}$ system which serves as a compound state and which is also measured in the present study. It is found that one of the levels of the compound system ($\mathrm{O}_2^{}{}_{}{}^{-}$) is coincident with the $v=3\mathrm{}$ level of ${\mathrm{O}}_2$. When the measured anharmonicity of the $\mathrm{O}_2^{}{}_{}{}^{-}$ system (3 ± 0.5 mV per level) is taken into account, the spacing of the lowest vibrational states ($v^{\prime }=0\mathrm{}\to v^{\prime }=1\mathrm{}$) of $\mathrm{O}_2^{}{}_{}{}^{-}$ becomes 132 mV, provided that the Pack-Phelps value of 0.43 eV is used for the electron affinity of ${\mathrm{O}}_2$. The spacing of the $v^{\prime }=0\mathrm{}\to v^{\prime }=1\mathrm{}$ vibrational states obtained in the present experiment is in excellent agreement with the values obtained by Raman spectroscopy of alkali-halide crystals in which $\mathrm{O}_2^{}{}_{}{}^{-}$ is trapped (135 mV). The magnitudes of the cross sections of the spikes, integrated over the electron energy distribution, are given and the branching ratio for the decay of $\mathrm{O}_2^{}{}_{}{}^{-}$ states is discussed.

Faddeev equations together with the Coulomb $t$ matrix have been used to determine the asymptotic amplitude for electron capture from neutral hydrogen by fast protons. The results show that in the high-energy limit the capture cross section should go down as $v^{-11\mathrm{}}$, where $v$ is the velocity of the incident proton. The capture amplitude is identical to Drisko's second-Born-approximation calculation except for a complex energy-dependent phase factor which ultimately approaches unity with sufficiently high incident energy. The major contribution to the three-body capture amplitude can be shown to come from the on-energy-shell two-body $t$ matrix, in agreement with general theorems concerning scattering from complex systems. At high incident energies, the on-energy-shell contribution to the capture amplitude (not the cross section) will decrease as $v^{-5\mathrm{}}$, while the off-energy-shell continuum contribution will decrease as $v^{-6\mathrm{}}$. The contributions from the sum of the infinite number of two-body bound-state poles can be shown to converge, and the sum can be explicitly performed at high enough incident energies in all except the forward direction. The bound-state contributions to the capture amplitude go down as $v^{-11\mathrm{}}$, which is much less than the continuum contributions.

Unpolarized and spin-exchange differential-scattering cross sections of Na-Cs are calculated using our phenomenological potentials for $r<\mathrm{}14\mathrm{}$ a. u. and the difference potential of Dalgarno and Rudge for $r\ge 14$ a. u. The calculated results are in good agreement with the experimental results.

A survey has shown that light emission from low-energy (< 1 keV) ion-molecule reactions is a common occurrence. ${\mathrm{Ar}}^{+}$ and $\mathrm{N}_2^{}{}_{}{}^{+}$ were used with target gases of Ar, ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, CO, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, NO, ${\mathrm{N}}_2$O, C${\mathrm{O}}_2$, C${\mathrm{H}}_4$, and ${\mathrm{C}}_2$${\mathrm{H}}_2$; in addition, He, Ne, and Kr were used as $\mathrm{N}_2^{}{}_{}{}^{+}$ targets. Electronically excited states were produced by charge transfer and ionization with simultaneous excitation, conversion of translational to electronic energy of the incident ion or target, and dissociation with simultaneous excitation. For several collision partners, more than one of these reactions was seen. In general, charge-transfer reactions had the largest cross sections, to 2 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$, for ion laboratory energies of several hundred eV. Cross sections for the strongest features in the other types of reactions were about (1-5) × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$.

The mean excitation potential of liquid hydrogen has been determined to be 20.4 ± 0.9 eV. This value was obtained from measurement in a hydrogen bubble chamber of (i) the range of monoenergetic muons and (ii) the range and momentum of protons which stop in the chamber.

The classical-path approximation reduces the problem of pressure broadening of spectral lines to the evaluation of matrix elements of the scattering operator. If the intermolecular potential is long range and the interaction volume is large, the broadening is caused by distant or weak collisions. In this case, the scattering operator can be approximated by a second-order expansion, and the perturber trajectories can be taken to be straight paths. For neutral atoms or molecules, the intermolecular potential is short range and broadening arises from close or "strong" collisions. In this paper it is shown how classical trajectories, determined by a "scalar interaction" (i.e., one that does not depend upon the state of the radiator), can be used to expand the scattering operator in the sum of operators characteristic of the radiator's internal states.

The problem of electron-atom scattering in the energy range where both high- and low-energy methods are unreliable is considered. A previously proposed equation is made tractable by a separable approximation on the electron-electron correlation function. This results in a pair of coupled equations in which all inelastic channels are lumped into one effective one. The equations are then reduced to a tractable form by some drastic approximations and solved by an eikonal approximation. The results are good in a restricted angular range, and the restrictions are shown to be due to the "drastic approximations" and the eikonal approximation, neither of which is really necessary.

Total cross sections for single-electron capture by ${\mathrm{C}}^{4+}$ from the target gases He, Ne, and Ar were measured at laboratory energies between 400 eV and 40 keV. The fast-collision products that scattered less than 1° were charge analyzed after single collision in a gas cell. Experimental results are interpreted in terms of pseudocrossings of the adiabatic potential curves for the initial and final states. The cross sections for ${\mathrm{C}}^{4+}$ + He and ${\mathrm{C}}^{4+}$ + Ne are consistent with the second maximum predicted for distant pseudocrossings by a numerical solution of the two-state semiclassical approximation by Bates, Johnson, and Stewart. Electron capture with an Auger-type ionization of the target is exothermic for ${\mathrm{C}}^{4+}$ + Ne and ${\mathrm{C}}^{4+}$ + Ar and is considered as the explanation of the large (50 ${\mathrm{\AA }}^2$) and slowly varying cross section measured for ${\mathrm{C}}^{4+}$ + Ar.

The theory of generalized variational bounds is applied to two-channel collisions of positrons on hydrogen leading to positronium formation. The formalism is developed in detail for this problem, and the zero partial-wave solution is obtained in the coupled-static approximation. The nonlocal coupling kernels and the behavior of the wave functions are exhibited in detail. Eigenphase shifts and coupling parameters, and the stripping and pickup cross sections, as well as the elastic amplitudes for positron-hydrogen and positronium-proton collisions, are studied as functions of scattering energies. The unitarity limits are exhibited, one of which is nearly saturated in the $\mathrm{P}\mathrm{s}-p$ channel. A useful iteration procedure for solving the coupled equations with large coupling kernels is developed.

A discussion of the inelastic scattering of high-energy electrons from atomic systems using linear-response theory is presented. Following Van Hove, an expression for the differential scattering cross section within the Born approximation is derived. The relationship of this expression to the linear-response function is demonstrated and a practical procedure for its computation using the so-called random-phase approximation is given. Finally, explicit results for the excitation of the lowest singlet $S$ and singlet $P$ state of helium by 500-eV electrons are given.

Beams of hydrogen atoms in the ($2S$) metastable state and ground state were passed through an iodine vapor target at energies between 0.2 and 2.5 keV. Measurements of the positive-ion current after the iodine target indicate that the cross section for ionization of the metastable atoms by iodine is much larger than the cross section for ionization of ground-state atoms, especially at the lower energies. The results indicate that this reaction can be effectively used for production of polarized protons in a Lamb-shift polarized-ion source.

The results of an experiment measuring the charge states of 1.5-, 3.0-, 6.0-, and 12.0- MeV iodine ions scattered through angles between 2.5° and 8.0° by single collisions with xenon atoms are reported. The charge states measured range from 9 to 27, and the charge-state distributions showed average values from 11 to 23. The variation of these average values with the collision's distance of closest approach shows the influence of the $M$ and $L$ shells of the colliding ions.

The shift and broadening of the ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ 0-0 line (frequency 6.8 GHz) due to collisions with Kr atoms have been studied in the pressure range 0.2-10 Torr. The shift versus pressure has been found to be linear and equal to -542 ± 10 Hz/Torr. The linewidth results from the super-position of several effects which are analyzed, one of the most important being the relaxation due to the spin-orbit interaction experienced by Rb atoms while temporarily bound in van der Waals Rb-Kr molecules.

The coupled equations of collision theory are examined in the projection-operator formulation of Feshbach. It is shown that the separate treatments of the open and closed channels provide distinct numerical advantages over the conventional methods. As an illustrative example, the phase shift and resonances for the ($e$, H) system are calculated.

The angular distribution of ${\mathrm{O}}^{-}$ produced by electron bombardment of ${\mathrm{O}}_2$ has been measured in the electron energy range 5.75-8.40 eV. The results show a strong energy dependence and are consistent with the theory of O'Malley and Taylor if the final $\mathrm{O}_2^{}{}_{}{}^{-}$ repulsive resonance state is assumed to have the symmetry ${}_{}{}^2{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, and if only the first two allowed partial waves of the incident electron corresponding to $L=1\mathrm{}$ and $L=3\mathrm{}$ contribute. The results indicate that the $L=3\mathrm{}$ term becomes more important as energy increases and thereby demonstrate that the single-term approximation for the angular distribution does not apply for this process.

Absolute measurements of cross sections for electron-impact scattering in helium at an angle of 5° have been made for elastic scattering and excitation of the $2{}_{}{}^1{}_{}{}^{}P$ and $2{}_{}{}^1{}_{}{}^{}S$ states and for incident energies of 50-400 eV. Cross-section values of $\sigma (2\mathrm{}{}_{}{}^1{}_{}{}^{}P,5^{\circ })$ are found to be lower than theoretical Born values by (9.5 ± 5.4)% at 400 eV, (31.5 ± 4.6)% at 100 eV, and (62.5 ± 3.4)% at 50 eV. Deduced values of total $2{}_{}{}^1{}_{}{}^{}P$ excitation cross sections ($E\ge 100$ eV) are in agreement with other experimental values. Our measurements for elastic scattering agree well with recent theoretical calculations.