The semiclassical theory developed in the preceding papers of this series is applied to the calculation of cross sections for the reaction ${\mathrm{C}}^{6+}-\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{C}}^{5+}\mathrm{}\left(n\right)+{\mathrm{H}}^{+}$, $n=3-6\mathrm{}$, over the energy range 0.05-30.0 keV/amu. Approximate variationally optimized translational factors, which generalize those of Bates and McCarroll, are employed in both adiabatic and diabatic representations. Cross sections obtained for a given basis, using the method of Piacentini and Salin or that of Bates and McCarroll, are compared with those from the new theory. The sensitivity of the cross sections to the choice of translational factor is explored and problems connected with the high-energy optimization of the translational factors are discussed. It is also shown that at the lowest energy the use of straight-line trajectory is incorrect. A new method to generate and store molecular-basis matrix elements with translational factors was developed to provide the essential input to the scattering program.

The origin and importance of electron-translation effects within a molecular description of electronic excitations in heavy-ion collisions is investigated. First, a fully consistent quantum-mechanical description of the scattering process is developed; the electrons are described by relativistic molecular orbitals, while the nuclear motion is approximated nonrelativistically. Leaving the quantum-mechanical level by using the semiclassical approximation for the nuclear motion, a set of coupled differential equations for the occupation amplitudes of the molecular orbitals is derived. In these coupled-channel equations the spurious asymptotic dynamical couplings are corrected for by additional matrix elements stemming from the electron translation. Hence, a molecular description of electronic excitations in heavy-ion scattering has been achieved, which is free from the spurious asymptotic couplings of the conventional perturbated stationary-state approach. The importance of electron-translation effects for continuum electrons and positrons is investigated. To this end an algorithm for the description of continuum electrons is proposed, which for the first time should allow for the calculation of angular distributions for $\delta$ electrons. Finally, the practical consequences of electron-translation effects are studied by calculating the corrected coupling matrix elements for the Pb-Cm system and comparing the corresponding $K$-vacancy probabilities with conventional calculations. We critically discuss conventional methods for cutting off the coupling matrix elements in coupled-channel calculations.

Experimental cross sections for single-electron capture for medium- to high-energy, highly charged oxygen and gold ions colliding with helium atoms are presented. Simple estimates based on the classical cross sections introduced by Bohr and Lindhard for multiply charged ions are shown to lead to good first approximations of the absolute magnitude of the cross sections for any target atom. Furthermore, these estimates suggest a universal scaling of the capture cross sections with ion and target-atom parameters. The experimental results of this work as well as those obtained by other groups are shown to be in accordance with the suggested scaling laws, which are also supported by the results of the few more-refined theoretical treatments that have been published.

Absolute and relative cross sections $Q$ were obtained for the charge-transfer reaction H${\mathrm{Cl}}^{+}$ + Xe→HCl + ${\mathrm{Xe}}^{+}$. The reactants and products are in their ground electronic states, but H${\mathrm{Cl}}^{+}$ and HCl may be vibrationally and rotationally excited. The studies were made by a merging-beams technique for a relative kinetic energy $W$ of the reactants from nominally 0.01 to 870 eV. Relative $Q$ and laboratory-energy distributions of ${\mathrm{Xe}}^{+}$ indicate that (a) near-resonant charge transfer preceded by a capture, or orbiting, collision occurs for 0.01≤W≲0.6 eV, (b) near-resonant charge transfer without capture occurs for $0.6\lesssim W\lesssim 200$ eV, and (c) nonresonant charge transfer is dominant for $W\gtrsim 400$ eV. The near-resonant charge transfer is apprarently fostered by the matching of electronic-vibrational-rotational energy levels of the entrance and exit channels. This results in the conversion of internal energy of H${\mathrm{Cl}}^{+}$ into internal energy of HCl.

We describe the techniques and the approximations used in extensive calculations for cross sections and reaction-rate parameters for electron-impact excitation of a number of heliumlike ions. All transitions involving the ground state and the $n=2\mathrm{}$ states are considered. Calculations are made in the distorted-wave approximation using configuration-interaction wave functions to represent the target states. Autoionizing resonances in the scattering cross sections are included through bound-channel correlation-type functions and through quantum-defect-theory analysis of the reactance matrices. The resonances are shown to make considerable contributions to the cross sections and thereby, in many cases, to enhance the excitation-rate coefficients by a significant factor. This should have important consequences for practical applications in the analysis of laboratory and astrophysical plasmas. The accuracy of our approximations is also discussed.

We describe in detail a hybrid method for calculation of electron-polar-molecule scattering in which (1) low-$l$ $S$-matrix elements are calculated in the body frame using a potential which incorporates a realistic representation of the molecular core; (2) intermediate-$l$ elements are calculated in the body frame using an exact method with a point-dipole potential; and (3) high-$l$ elements are calculated in the laboratory frame using the first Born approximation with a point-dipole potential. By taking into account the dominant interactions of each $l$ range when choosing the coordinate frame, potential, and calculational method, this hybrid framework achieves an exceptionally high level of efficiency and economy of calculation without sacrifice of accuracy. Using this method, we have calculated integrated and momentum-transfer cross sections for $e$-LiF scattering from 1 to 20 eV (differential cross sections have been reported elsewhere). The integrated cross section is dominated (> 99%) by the $j=0\mathrm{}\to j^{\prime }=1\mathrm{}$ rotational transition, whereas the momentum-transfer cross section is composed of comparable contributions from transitions to final $j^{\prime }=0\mathrm{} \mathrm{through} 3$, owing to its deemphasis of small-angle scattering. Eigenphase sums show no sign of resonant activity in this energy range.

The exchange correction to the differential scattering cross section for the electron-hydrogen-molecule scattering is derived. In the independent scattering center and Glauber approximation our expressions do not agree with those used in the published literature. The overall agreement between the calculated and the measured cross sections improves at higher angles and lower incident electron energies, where the exchange contribution is important.

The effects of local polarization and absorption potentials on differential cross sections and angular correlation parameters are studied within the distorted-wave approximation for electron excitation of the $2{}_{}{}^1{}_{}{}^{}P$ state of helium. For examining the effect of local polarization, we have compared a recent numerical self-consistent adiabatic polarization potential for helium with the commonly used hydrogenic adiabatic polarization potential. Different radial regions for the polarization potential were studied to determine their contribution to the overall effect of polarization. Calculations are also presented which show the effects of different strengths for a local absorption potential.

The authors have measured relative populations of terms in N II, N III, and N IV, excited after the passage of ${\mathrm{N}}^{+}$ ions through a carbon foil, as a function of the ion energy [$0.3<E\left(\mathrm{MeV}\right)<\mathrm{}1.9\mathrm{}$]. These populations are obtained from the measurements of intensity of transitions emitted from these terms [$300<\mathrm{}\lambda \left(\AA \right)<\mathrm{}1800\mathrm{}$]. The variation of the ratio $R\left(E\right)\mathrm{}$ of the relative population $N_i$ ($i$ is the term excited in the ion of charge $q$) to the equilibrium charge-state fraction $P\left(q\right)\mathrm{}$ is studied as a function of the emergent beam energy. The grouping of the terms according to the number of electrons excited relative to the ground state shows that the $R\left(E\right)\mathrm{}$ functions are generally different for the different groups of terms. Within a given group of terms (singly or doubly excited terms), the slopes of the $R\left(E\right)\mathrm{}$ functions increase with the excitation energy of the term. These results are useful for classifying new lines observed in beam-foil spectroscopy.

Electron correlations in the alkaline-earth atoms and alkali negative ions, especially as manifested by photoabsorption experiments, are studied using a hyperspherical-coordinate approach. A prototype quantitative calculation of the Be photoabsorption spectrum near the $2s$ and $2p$ thresholds, allowing for nonadiabatic transitions between potential curves for the first time and hence for autoionization, shows the formation of the " + "-type and "-"-type eigenmodes in the two-electron wave function. This has strong implications for the spectra of Be and other atoms, and permits a unified interpretation of their discrete and continuum oscillator strength.

Equilibrium charge-state distributions have been measured for argon ions in thin carbon foils between 2 and 20 MeV. Equilibration takes place in foils at least as thin as 5 μg/${\mathrm{cm}}^2$. Our measurements link up smoothly with other work at lower and at higher energies. Several models have been applied to postdict the data. It was found that while the mean charge can be quite accurately determined from empirical models, such as the Gaussian one, or even from extrapolation on $Z$, serious discrepancies arise with respect to the distribution widths. As a result, charge fractions which are off the peaks of the distributions can be in error by factors of 2 or more, rendering their measurement essential for the purposes of the present study. Evidence of ionic $\mathrm{LM}$ shell structure has also been observed in this work.

A scattering amplitude for particle-atom collisions is developed in the eikonal approximation, taking into consideration the second-order term in the phase function of the $S$ matrix. A finite value of the average excitation energy of the atom in its intermediate states is retained in each order (except the first) of the perturbation series. For zero excitation energy the second-order phase function reduces to twice the second-order Wentzel-Kramers-Brillouin phase shift for a static potential. Our amplitude becomes the modified Glauber amplitude by putting the second-order phase function equal to zero. The new amplitude satisfies the unitarity theorem to all orders of the coupling constant. It is free of all the shortcomings of the conventional Glauber theory.

We calculate the spin polarization of $1s\sigma$ vacancies and emitted $\delta$ electrons induced by the strong magnetic field ($\left|B_{max}\right|\sim {10}^{16}$G) in collisions of very heavy ions ($Z_1+Z_2=178\mathrm{}$). The electron excitations are determined by the solution of coupled-channel equations within the quasimolecular basis states including the vector potential. The formulation is extended to the many-electron case. Spin polarizations of the order of 5-10% for impact energies below the Coulomb barrier are predicted.

The Glauber scattering amplitude for $1s-nlm$ excitations of hydrogen by charged particle impact is reduced to a form numerically computable for arbitrary values of $n$, $l$, and $m$. The increasing number of repeated parametric differentiations appearing in earlier methods with the increase of $n$ is replaced in our method by a single contour integration, which is especially useful for large-$n$ states. In addition, whereas the available closed-form expressions would involve the calculation of a large number of hypergeometric functions as $l$ and $m$ increase for a given $n$, the present integral form involves only one hypergeometric function for any $n$, $l$, and $m$. The asymptotic form of the $1s-nlm$ amplitude as $n\to \infty$ is also presented. The procedure is applied for studying the $1s\to \mathrm{ns}(n=3, 4, 10, \mathrm{and} \infty )$ and $1s\to \mathrm{np}(n=3, 4, \mathrm{and} \infty )$ excitations of hydrogen by electron and proton impact. Tabular results of the cross sections are presented for differential and integrated cross sections in $e^{-}$-H collisions and for integrated cross sections in ${\mathrm{H}}^{+}$-H collisions. The qualitative features observed earlier for low $\mathrm{ns}$ and $\mathrm{np}$ excitations are found to exist also for $n\ge 3$ excitations. The $1s\to \mathrm{ns}$ and $1s\to \mathrm{np}$ cross sections obey an $n^{-3\mathrm{}}$ law asymptotically as $n^{-2\mathrm{}}\to 0$, which is in conformity with the analytical results obtained quite generally for $1s\to \mathrm{nlm}$ excitations. For proton impact $1s\to 3p$ excitations, the Glauber results are in excellent agreement with a recent 34-state calculation. A unified graphical representation of various normalized cross sections above some specific energy is presented, whence a knowledge of the high-energy Born cross sections for any $1s\to \mathrm{ns}$ or $1s\to \mathrm{np}$ excitation suffices to determine the absolute Glauber cross sections for the process.

The scattering parameters for $e^{-}$-H scattering have been obtained in the energy range 0.136-13.6 eV. In our calculations, the adiabatic dipole polarization potential that appears in the polarized-orbital method of Temkin and Lamkin (Sloan) has been replaced by distortion potential as used by Callaway et al. The present scattering parameters are in good agreement with the measured values and theoretical predictions. It has been found that the effects of nonadiabatic potential in the direct channel and the exchange polarization are appreciable.

A detailed study of the differential cross section for the elastic scattering of electrons by helium at intermediate and high energies has been made. In this study a theoretical procedure, recently suggested by one of the authors (J.N.D.), has been followed. The calculated differential cross sections in the energy range 100-200 eV appear to be in very good agreement with experiment and better than the existing theoretical results. At higher energies, the present results are also better except at very small angles where the eikonal-Born-series results of Byron and Joachain are better. The scattering amplitudes obtained during this calculation have also been presented.

The two-state approximation is applied to positron-lithium-atom collisions considering only the elastic scattering and the ground-state positronium formation. Taking the effect of the adiabatic polarization potential into account in both the direct and rearrangement channels, results for the differential, total, and momentum-transfer cross sections are computed at incident positron energies 0.5-10 eV. While for the elastic scattering the present data show satisfactory agreement with other available calculations, for positronium formation the present results are quite new and give us an idea of the order of the cross section. It is found that the differential cross section for both the elastic scattering and positronium formation shows a deep minimum at low energies of positron impact in agreement with available earlier findings.

The $X\alpha$ scattered-wave (XASW) technique is applied to the trimer of potassium, and the appearance of the high-field electron-spin-resonance (ESR) spectrum is predicted. Contact spin densities, including core-polarization contributions, are calculated for several different structures; the resulting model hyperfine patterns strongly reflect the assumed geometrical configuration of the atoms. Comparison of these model spectra with experimental results is discussed.

The spectrum of copperlike Br VII has been observed between 35 and 80 nm by the method of fast-ion spectroscopy. Nine new transitions have been classified and six new excited-state energies have been determined within the $n=4\mathrm{}$ and $n=5\mathrm{}$ shells. The excited-state energies and fine structures are compared with recent relativistic Hartree-Fock calculations for this single-valence-electron atomic system.

It is proved that to a first approximation it is impossible to exchange significant amounts of energy with an ensemble of particles having wave functions with random phases. Possible applications are outlined.