We have studied the deexcitation of ${\mathrm{He}}^{+}$ ions in the $2S$ metastable state by collision with eleven different target gases. These include noble gases, symmetric linear molecules, water, and ammonia. From our data we extract velocity-averaged total deexcitation-rate constants $〈\sigma v〉$ ranging from 1.65(17) × ${10}^{-9\mathrm{}}$ to 20.9(21) × ${10}^{-9\mathrm{}}$ ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$ for helium and ammonia, respectively. In all cases the mean energy of the ${\mathrm{He}}^{+}$ ions was ≃0.23 eV and the target gases had a 300 °K Maxwell-Boltzmann distribution of velocities. The results are consistent with collision-induced Lyman $\alpha$ emission being a prominent deexcitation mechanism.

Recently developed analytic methods, which reduce the Glauber amplitude for charged-particle-neutral-atom collisions to a one-dimensional integral representation involving modified Lommel functions, are used to evaluate the cross sections for the direct excitation of the $2{}_{}{}^1{}_{}{}^{}P$ state of helium by electron impact with incident energies from 55.5 to 900 eV. The theoretical results for the differential and total excitation cross sections are in good agreement with the experimental data. In particular, the Glauber theory predicts a peak value for the total excitation cross sections around 80 eV which is consistent with the existing experimental findings, whereas other theoretical models give monotonically increasing values with decreasing energy below 100 eV.

Upper and lower bounds for transition probabilities in multichannel collision theory are derived, with numerical applications. The approach provides a general scheme for bounding a unitary matrix which depends on a parameter. Particular choices of the parameter include the radial approach coordinate of the colliding systems, with application to close-coupling expansions (both quantum mechanical and semiclassical); the strength parameter of the potential, with applications to the exponential approximation; the time, with applications to transitions induced by a time-dependent potential (a case previously treated by Spruch); and, in general, any parameter in the interaction potential. The method is based on two key steps: (i) the derivation of an integral equation for the dependence of the scattering matrix on the parameter, which can then be bounded, and (ii) the use of the matrix H (all whose elements are unity) as the initial upper bound for the (absolute value of the) scattering matrix. This initial bound is then improved by iterating the integral equation. Computational examples for rotational excitation in an atom-rotor collision are provided.

The photoionization cross section of helium is calculated by a numerical analytic continuation of the frequency-dependent polarizability. Approximate values of the polarizability are obtained by an application of the equations-of-motion method. The entire calculation is performed without the use of continuum basis functions. The calculated cross sections agree well with the observed values.

Hydrogenlike and heliumlike states in oxygen and fluorine projectiles produced in single collisions in various gas targets have been studied via $K$ x-ray emission. Data have been taken for oxygen beams of charge states +6, +7, and +8 incident on neon and argon and for fluorine beams of charge states 7+, 8+, and 9+ incident on helium and neon. The relative x-ray intensities corrected for detector efficiency have been obtained. The production of transitions in hydrogenlike systems following electron capture by fully stripped projectile (bare nuclei) differs somewhat from predictions based on a simple Brinkman-Kramers theory for the capture process and an inclusion of cascade effects. Excitation of the few-electron projectiles and electron exchange between projectile and target are also indicated by the data.

Calculations are made of the total energy lost to inelastic channels when a fast ion or atom is stopped in a gas. Contributions to this energy loss by sufficiently energetic recoil atoms are included, using a scheme of successive approximations, which reveals the relative importance of successive generations of recoils. The electronic energy losses resulting from a single collision are computed according to the theories of Lindhard and of Firsov, which are modified by the presence of a threshold function. It is shown that such a threshold is essential to calculations employing physically reasonable interaction potentials. Energy losses associated with the nuclear motion are treated as classical elastic scattering, and the sensitivity of the calculations to the assumed potential is demonstrated. The relative accuracy of approximations to the deflection function computed for several potentials is investigated.

Measurements of single and double electron-loss cross sections for He atoms in the gases ${\mathrm{H}}_2$, He, ${\mathrm{N}}_2$, Ar, and Kr are reported in the energy range from 0.1 to 4 MeV. The cross sections are determined by the initial-growth method, and the neutral beam is formed by charge transfer neutralization of ${\mathrm{He}}^{+}$ in a He gas. The results on single electron loss in ${\mathrm{H}}_2$ and He targets have been discussed in an earlier paper and compared with theoretical Born-approximation calculations. The present results are compared with those from other experiments and with available theoretical estimates.

Resonant enhancement of optical third-harmonic generation in cesium vapor has been observed when twice the energy of the fundamental photon becomes equal to the energy difference between the $9d{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}$ level and the ground state of the cesium atom. The measured, effective coefficient is ${10}^{-30\mathrm{}}$ esu/atom, which is more than a factor ${10}^8$ larger than the corresponding coefficient for the helium atom. An effective coefficient is synthesized by first calculating the coefficient for a single cesium atom at rest and then including the effects of Doppler broadening and the fundamental laser spectrum. The calculated value is in satisfactory agreement with experiment.

The technique of photoelectron spectroscopy has been used to obtain the relative continuum transition probabilities of atomic oxygen at 584 Å for transitions from the ${}_{}{}^3{}_{}{}^{}P$ ground state into the ${}_{}{}^4{}_{}{}^{}S$, ${}_{}{}^2{}_{}{}^{}D$, and ${}_{}{}^2{}_{}{}^{}P$ states of the ion. The ratio of the transition probabilities for the ${}_{}{}^2{}_{}{}^{}D$ and ${}_{}{}^2{}_{}{}^{}P$ states relative to the ${}_{}{}^4{}_{}{}^{}S$ state of the ion are 1.57 ± 0.14 and 0.82 ± 0.07, respectively. In addition, transitions from the excited ${\mathrm{O}}_2\left(a{}_{}{}^1{}_{}{}^{}\Delta _g^{}{}_{}{}^{}\right)$ state into the $\mathrm{O}_2^{}{}_{}{}^{+}\left({}_{}{}^2{}_{}{}^{}\Phi _u^{}{}_{}{}^{} \mathrm{and} {}_{}{}^2{}_{}{}^{}\Delta _g^{}{}_{}{}^{}\right)$ states were observed. The adiabatic ionization potential of $\mathrm{O}_2^{}{}_{}{}^{+}\left({}_{}{}^2{}_{}{}^{}\Delta _g^{}{}_{}{}^{}\right)$ was measured as 18.803 ± 0.006 eV.

Theoretical calculations of the angular distribution of photoelectrons ejected from the $2p$ subshell of atomic oxygen for photoelectron kinetic energies $0\le \epsilon \le 30$ Ry are presented using both Hartree-Fock (HF) and Herman-Skillman (HS) wave functions. Owing to the weakness of anisotropic electron-ion interactions, as evidenced by small differences between HF photoelectron phase shifts for alternative outgoing channels, the simple HS calculation of the angular-distribution asymmetry parameter is found to agree to within ≲ 0.1 with the HF calculations. Photoionization cross sections and photoelectron branching ratios have also beem computed in both the HF and HS approximation for the $2p$ subshell of atomic oxygen in the wavelength range $910\le \lambda \le 100$ ÅA. Comparison is made with other theoretical calculations and with the experimental branching-ratio measurements of Samson and Petrosky at $\lambda =584.3\mathrm{}$ ÅA.

Titanium atoms are excited by light from a nitrogen laser from the $a{}_{}{}^3{}_{}{}^{}F_4^{}{}_{}{}^{}$ state, near the ground state, through the $x{}_{}{}^3{}_{}{}^{}G_5^{}{}_{}{}^{}$ state, to become ${}_{}{}^4{}_{}{}^{}F$ ions plus free electrons. The angular distribution of photoelectrons from the process gives limits on the ratio of amplitudes for transitions from the intermediate $4p$ orbital to the final continuum $s$ and $d$ channels. The total number of photoelectrons indicates that the total ionization cross section for the ${}_{}{}^3{}_{}{}^{}G_5^{}{}_{}{}^{}$ state is 1×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$. While the method can, in principle, provide relaxation times for angular momentum reorientation (an application of the methods of perturbed angular correlations in atomic processes), the present measurements have been carried out under conditions in which no relaxation occurs.

Extensive Kohn calculations by Schwartz demonstrated the power of the method but also the presence of anomalies involving spurious rapid variations in $tan\eta$. Nesbet showed that anomalies result from the vanishing of a denominator, and he and others have proposed anomaly-free methods. Anomalies are analyzed herein by parametrizing the normalization of long-range expansion terms such that conventional direct and inverse Kohn methods are special cases. The functional dependence of the parametrized estimate on the normalization parameter is found to be of simple algebraic form. By appropriately averaging over this parameter, we obtain a generalized variational method which is anomaly free. Calculations for a simple model problem are used to test and illustrate properties of the several variational methods which are considered.

Two independent anticrossings have been observed between singlet and triplet levels in the He atom, one between the $7{}_{}{}^1{}_{}{}^{}D$ and $7{}_{}{}^3{}_{}{}^{}D$ states, the other between the $8{}_{}{}^1{}_{}{}^{}D$ and $8{}_{}{}^3{}_{}{}^{}D$ states. The states are excited by electron bombardment. Compensatory changes in the luminosity of the singlet and triplet states are detected as the levels are tuned through the anticrossing points by a magnetic field. The positions of the anticrossings have been analyzed to provide new values for these singlet-triplet separations accurate to ∼0.03 GHz. These results show the previous best optical determinations for the separations to be in error by over a GHz. The widths of the anticrossings are analyzed to provide the most direct measures of the spin-orbit coupling constant between a singlet and a triplet state yet obtained for any system. The measured values of these coupling constants are found to be several times larger than their corresponding diagonal value in the $7{}_{}{}^3{}_{}{}^{}D$ and $8{}_{}{}^3{}_{}{}^{}D$ states.

Absolute detachment cross sections for 200-eV to 10-keV ${\mathrm{H}}^{-}$ on He, Ar, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and ${\mathrm{O}}_2$ were measured to an accuracy of 7% using the beam-attenuation method. The cross sections, approximately (5-25) × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$, all increase slowly with increasing collision energy, except for ${\mathrm{O}}_2$, in which case the cross section decreases with increasing impact energies up to 4 keV. The present results are compared with previous measurements. A semiempirical theory based on low-energy-electron scattering predicts the detachment cross sections with some success.

Estimates have been made of the total ionization cross sections for the collision of high-energy electrons with neon, argon, and xenon atoms and all of their ground-state ions. The cross sections were computed within the framework of the Bethe-Born high-energy-approximation theory using the semiclassical projection-operator technique of Hahn and Watson and the independent-particle model for atoms of Green, Sellin, and Zachor. Both direct continuum ionization and inner-shell excitation followed by Auger transitions were taken into account. Multiple-ionization cross sections were also estimated using experimental data on electron emission following ejection of inner-shell electrons in the various rare-gas atoms and a simplified model of Auger-vacancy cascading in ions. The computed cross-section values were then used in calculations of the cumulative ionization produced by a relativistic electron-ring beam interacting initially with pressure pulses of the various gases. The results obtained, taken together with previous computations for krypton, indicate a progressive increase in the relative importance of Auger processes with increase in $Z$ such that for xenon (and presumably for higher-$Z$ target atoms), Auger ionization dominates the production rates of most of the multicharged ions formed in such a system.

Absolute cross sections, differential in electron energy and emission angle, have been measured for ejection of electrons from xenon by 0.3- to 2.0-MeV protons. Electron-energy distributions are presented for ten angles between 20° and 130°. Angular distributions are found to be more nearly isotropic than results for targets of lower atomic number. Cross sections differential in electron energy obtained by integration with respect to emission angle, are found to be in relatively good agreement with calculations based on binary-encounter theory. Auger electrons resulting from initial vacancies in the $M$ and $N$ shells of xenon are discussed. Estimates of total $M$- and $N$-shell ionization cross sections for fast protons are presented.

The differential inelastic energy loss $Q$ has been determined for keV atomic collisions between ${\mathrm{Na}}^{+}$, ${\mathrm{Ne}}^{+}$, ${\mathrm{Ne}}^{++}$, ${\mathrm{F}}^{+}$, ${\mathrm{O}}^{+}$, and ${\mathrm{N}}^{+}$ projectiles and Ne, ${\mathrm{N}}_2$, and N${\mathrm{H}}_3$ targets for scattering angles between 2° and 15°. The data, which have been obtained under single-collision conditions, determine the probability of producing a $K$ vacancy and the corresponding $K$-excitation energy for specified charge states of the projectile before and after the collision. The production of a $K$ vacancy has been shown to take place preferentially in the low-$Z$ collision partner with a probability depending on the collision's distance of closest approach and the projectile velocity. The data suggest that rotational coupling between the $2p\sigma$ molecular orbital (MO) and the $2p\pi$ MO produces the $K$ vacancy. The $K$-excitation probability is shown to depend strongly on the outer-shell ($2p$), precollisional configuration of the high-$Z$ collision partner. For ${\mathrm{N}}^{+}$-N${\mathrm{H}}_3$, ${\mathrm{Ne}}^{+}$-Ne, ${\mathrm{Ne}}^{++}$-Ne, and ${\mathrm{Na}}^{+}$-Ne collisions, the maximum $K$-excitation probabilities are 35%, (10-15)%, 20%, and ≤ 1%, respectively. These observations are in accord with the Fano-Lichten model. For ${\mathrm{N}}^{+}$ and ${\mathrm{O}}^{+}$ projectiles incident on ${\mathrm{N}}_2$ and N${\mathrm{H}}_3$ targets, triple-peaked $Q$ spectra occur, indicating a fair probability of the production of two $K$ vacancies. For asymmetric collision systems such as ${\mathrm{O}}^{+}$-N${\mathrm{H}}_3$, the two $K$ vacancies are produced preferentially in the low-$Z$ collision partner.

An approximate theory is given for calculating the cross sections for single-electron excitation and transfer from a neutral alkali-metal atom $M$ colliding with atomic oxygen. The trajectories of the colliding atoms are computed classically, and the electron is treated by the time-dependent Schrödinger equation in two- and three-state approximations. The three states considered are the ground and first-excited states $M$ and $M^{*}$ of the incident atom and the single bound state of ${\mathrm{O}}^{-}$. Numerical calculations are carried out for energies between 10 and 10 000 eV (laboratory energies of the alkali-metal atoms). Comparison of results obtained with the two- and three-state approximations shows that the charge-transfer cross sections are almost unaffected by the presence of the alkali-metal-atom excited state. The excitation cross sections, on the other hand, are considerably increased by the presence of the ionic channel. This evidence indicates that excitation can occur as a two-step process in which the electron is exchanged between the colliding partners. The numerical values of the electron-transfer cross section generally agree with those calculated by van den Bos for Cs-O collisions (based on the Landau-Zener-Stückelberg theory and suitably corrected by a statistical weight factor) and the recent experimental data of Woodward. At low velocities ($v<\mathrm{}0.01\mathrm{}$ a.u.), however, we find a steeper decrease with decreasing velocity than the Landau-Zener-Stückelberg results. At high velocities the results agree with the Born approximation.

Crossed beams of ${\mathrm{N}}_2^{+}$ and electrons were used to measure the absolute cross sections for the excitation, $\mathrm{N}_2^{}{}_{}{}^{+}(X{}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}, v=0)+e\to \mathrm{N}_2^{}{}_{}{}^{+}(B{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}, v=0)+e$, over an electron energy range from below threshold (3.17 eV) to 91 eV. Absolute emissions of the 391.4-nm band were measured from impact of electrons on ${\mathrm{N}}_2^{+}$ ions in various state mixtures. Corrections were made to the data to account for state mixtures and other effects to obtain the cross section for the above process. The cross section falls from its finite threshold value of 3.0 × ${10}^{-16\mathrm{}}$ to 0.30 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at 91 eV. The present values are more than an order of magnitude smaller than either the 1968 values of Lee and Carleton or the 1973 value of Daschenko et al. At threshold the Gaunt-factor formula of Seaton predicts a value only 45% of that measured, but at the highest energy, the predictions of the Seaton formula have converged to within 20% of the present values of the cross section. Rate coefficients calculated from the present measurements are consistent with the recent rate-coefficient measurements of McLean et al. Total uncertainty at high confidence is about 18%, taken as the quadrature sum of random uncertainty (15% at 98% confidence level) with systematic uncertainties (about 8% at high confidence). The analysis leading to interpretation of the emission cross section in terms of an excitation cross section between specific states is subject to uncertainties which are not well defined, and are not included in the stated uncertainty.

Differential cross sections for the elastic scattering of electrons from atomic hydrogen have been measured at 9.4, 12, and 20eV. The data at 9.4 eV are shown to agree with a previous measurement and to agree with the prediction of the close-coupling approximation even at the smaller scattering angles of the present experiment. The data at 12 eV agree very well with the six-state close-coupling calculation. The data at 20 eV agree well with a three-state calculation except at the most forward angles.