Values of antishielding factor ${\gamma }_{\infty }$ have been obtained for Zn, Cd, In, ${\mathrm{Fe}}^{3+}$, and ${\mathrm{Zn}}^{2+}$ by solving the appropriate differential equations based on nonorthogonal Hartree-Fock perturbation theory. In the case of ${\mathrm{Fe}}^{3+}$ we have compared our value with that obtained earlier by Sternheimer. While the agreement in the total ${\gamma }_{\infty }$ is excellent, the individual shell contributions, namely ${\gamma }_{\infty }$ ($2p\to p$) and ${\gamma }_{\infty }$ ($3p\to p$), differ significantly. The reason for this discrepancy is discussed and is attributed to two compensating and exclusion-principle-violating contributions, namely ${\gamma }_{\infty }$ ($2p\to 3p$) and ${\gamma }_{\infty }$ ($3p\to 2p$), included in Sternheimer values, ${\gamma }_{\infty }(2p\to p) \mathrm{and} {\gamma }_{\infty }(3p\to p$), respectively.

The Bi $K\alpha$ lines observed in 460-MeV (lab) Xe + Bi encounters are significantly Doppler broadened. The x-ray line shapes can be calculated using theoretical models for the impact-parameter dependence $P\left(b\right)\mathrm{}$ of the probability of making $1s\sigma$ vacancies in Xe + Bi collisions. The measured line shapes are in good agreement with those derived from values of $P\left(b\right)\mathrm{}$ calculated by Betz et al.

The secondary-electron yield ${\gamma }_m$ for $\mathrm{O}\left({}_{}{}^5{}_{}{}^{}S\right)$ metastables on a Cu-Be-O multiplier surface was measured as a function of metastable kinetic energy from near thermal to several eV. This measurement, which seems to be the first of its kind, was made possible by the simultaneous detection of the metastables by secondary-electron emission from surfaces and in-flight radiative decay. Unlike the yield ${\gamma }_m$, the photon yield ${\gamma }_p$ for photons from radiative decay cannot depend on metastable velocity. The dependence of ${\gamma }_m$ on metastable kinetic energy was thus obtained by pulsing the metastable beam with a time-of-flight technique and comparing the time-of-flight distributions for direct particle detection and radiative decay. It was found that the yield ${\gamma }_m$ was constant to within 10% for metastable kinetic energies from about 0.05 to 3 eV. This range of available kinetic energies was determined by the process of dissociative excitation of $\mathrm{O}\left({}_{}{}^5{}_{}{}^{}S\right)$ metastables by electron impact on ${\mathrm{O}}_2$. According to theoretical arguments, constancy of the yield ${\gamma }_m$ may also apply to other metastable species and higher kinetic energies.

Absolute doubly differential cross sections for secondary electron production by electron impact have been measured for static gas targets of neon, argon, hydrogen, and nitrogen. Electron impact energies were from 100 to 500 eV. An electrostatic analyzer was used to analyze secondary electrons with energies between 4 eV and the primary electron energy minus the first ionization potential of the target. Angles of emission were 10° to 150°. The present data agree well with the data of Opal, Beaty, and Peterson at 90° but, as was observed previously for helium, the agreement becomes increasingly poorer for larger and smaller angles. This angular disagreement, which is independent of target gas and impact energy, is approximately given by $a+(1-a)\mathrm{}sin\theta$, where $a=0.10\mathrm{}\pm 0.12$. Previously we compared the experimental data of Opal, Beaty, and Peterson with calculations by Manson for helium and obtained a similar correction but with $a=0.53\mathrm{}$. Recent Born-approximation calculations of Manson are compared with our 500-eV argon data. The calculations reproduce the angular distributions of the measured cross sections quite well for small secondary-electron energies. For intermediate energies the agreement is still quite good near the momentum-conservation peak but poorer for large scattering angles.

Shifts of ion-scattering peaks from oxides indicate that the primary beam loses more energy than predicted by the scattering equation. The origin of these shifts is not clear but may be explained by inelastic-collision exchange processes between the noble-gas ion and oxygen on or near the surface. The phenomenon appears to be sensitive to matching energy levels and orbital symmetry of the ions with surface atoms. Other spectral features indicate that the ions penetrate the surface and lose energy in inelastic events beneath the surface. Large changes in relative scattering of the anion and cation in oxides may be caused by either geometric structural effects or selective sputtering phenomena.

Cross sections for single electron capture by ${\mathrm{Si}}^{q+}$ ($2\le q\le 9$) incident on atomic and molecular hydrogen have been measured in the relative-collision-velocity range (3.1-6.3)×${10}^8$ cm/s. All measured cross sections decrease monotonically with relative velocity and scale roughly as $q^N$. The values of $N$ needed to fit the data range from ∼2 to ∼3 and increase with velocity. Cross sections averaged over incident charge states $q$ for molecular hydrogen are larger than for atomic hydrogen, becoming twice as large for relative velocities greater than 4×${10}^8$ cm/s. For the limited cases where comparison was possible, we found the classical-trajectory Monte Carlo calculation to give a good account of the experimental results.

The energy-loss straggling of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ions incident at energies from 5 to 50 MeV on Al foils of thickness 100 to 500 μg/${\mathrm{cm}}^2$ has been measured. Although the collisional straggling at energies above 25 MeV is expected to be appropriately described by the Bethe-Livingston theory of straggling, the data give values about a factor of 2 greater than this theory. The uniformity of the foils was studied and the limits to systematic errors that arise from this source were found to be small. The difference between the Bethe-Livingston theory and experiment is interpreted in terms of charge-exchange fluctuations. Monte-Carlo calculations have been made for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ions at 40 MeV (where only two charge states predominate), and the charge-exchange cross sections (8×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$/atom for ${\sigma }_{7^{+}\to 8^{+}}$ and ${\sigma }_{8^{+}\to 7^{+}}$) required to produce a fit to the data are found to be similar in magnitude to those measured by Macdonald and Martin for 40-MeV ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ incident on ${\mathrm{N}}_2$ and Ar gas targets.

A three-mode microwave afterglow apparatus and high-speed grating spectrometer are used to study dissociative recombination in argon. The total rate coefficient may be represented by $\alpha \left[{\mathrm{Ar}}_2^{+}\right]=9.1\mathrm{}\times {10}^{-7\mathrm{}}\times {\left[\frac{300}{T_e\left(\mathrm{K}\right)}\right]}^{0.61}$ ${\mathrm{cm}}^3$/sec over the electron-temperature range $300\le T_e\le 8500$ K, with $T_{+}=T_{\mathrm{gas}}=300\mathrm{}$ K. The excited states produced by the dissociative recombination are determined at $T_e=300\mathrm{} \mathrm{and} 7200$ K. In both cases, the $4p$ and $4p^{\prime }$ states are found to be the most strongly populated.

We investigate the excitation of positive ions by charged-particle impact in the Coulomb Born approximation. We obtain closed-form expressions for the $1s-2s$ and $1s-2p$ amplitudes and present numerical results for the corresponding excitation cross sections. We also indicate how the matrix elements may be used to calculate excitation and ionization cross sections for many-electron ions.

The problem of electron transfer between neutral atoms and multiply charged ions is considered at low and medium energies. It is assumed that a large number of final states are available for the electron transition so that the electron-capture process is treated as a tunnel effect caused by the strong attractive Coulomb field of the multicharged ion. The electron transition probability is obtained in a closed form using the modified-comparison-equation method to solve the Schrödinger equation. An approximately linear dependence of the one-electron transfer cross section on the charge of multicharged ions is found. Cross-section calculations of a number of charge-exchange reactions are performed.

The mutual neutralization and ion-pair-formation reactions in alkali-hydrogen diatomic systems are investigated in the low-energy region. The ionic-covalent exchange interaction in these systems at the diabatic curve crossings is calculated by the Landau-Herring method. The cross sections and reaction-rate coefficients of these reactions are calculated using the Landau-Zener theory, modified to include the underbarrier transitions and the effects of the variation of coupling interaction within the transition zone. For Cs-H system, the calculated recombination and ion-pair-formation cross sections are compared with the existing theoretical calculations and experimental data.

The impact-parameter dependence of the $K$-vacancy production probability $P\left(b\right)\mathrm{}$ in the bombardment of a Ge solid target with 1.4-MeV/amu ${\mathrm{Kr}}^{24+}$ projectiles has been measured by recording coincidences between $K$ x rays and scattered ions. The range of impact parameters was always inside the $K$-shell radius of the united atom. The sum of the ionization probability for Kr and Ge and the vacancy-sharing ratio as a function of the impact parameter are compared to existing theoretical-model calculations. The two components corresponding to $\mathrm{KL}$ and $\mathrm{KM}$ transitions were resolved for both the Kr and Ge $K$ x rays, and variations in the relative intensities yield information about transitions in the outer shells of the collision systems.

In Na, the energy gap $\Delta E$ between the $n$, $d$ state and the $n$, $l>\mathrm{}2\mathrm{}$ states is ten times larger than $\Delta E$ between $n$, $f$ and the $n$, $l>\mathrm{}3\mathrm{}$ states. To investigate the effect of this difference on the $d$- and $f$-state $l$-mixing cross sections, ${\sigma }_d$ and ${\sigma }_f$, we have recently carried out experiments to measure ${\sigma }_{d-f}$, the $l$-mixing cross sections for a microwave-induced mixture of $d$ and $f$ states. Using the previously measured values of ${\sigma }_d$, we have derived values of ${\sigma }_f$ which have the same $n$ dependence as ${\sigma }_d$. ${\sigma }_f$ is larger than ${\sigma }_d$ for Ne, but smaller for He and Ar. In addition, we have analyzed the final states after one collision with Ar using selective field ionization of the $17l$ states and have observed that after one collision all the $l$ states are equally populated indicating that there are no $\Delta l$ selection rules for the process. This confirms the earlier suggestion that $l$ mixing is caused by a short-range interaction.

The nodal expansion of equilibrium properties of a two-component classical plasma in $2+\epsilon$ dimensions ($0\le \epsilon \le 1$) is used to investigate higher-order corrections with respect to the plasma parameter of the transverse-diffusion coefficient relative to an arbitrarily strong and constant magnetic field. Only the shortrange compact nodal graphs decaying faster than Debye contribute to the third and higher nonvanishing orders. The usual fluid-limit ($k\to 0$) procedure delivering the first-order Bohm result is shown to be self-consistent for any dimension $2\le \nu \le 3$.

Calculations of cross sections for elastic $e$-${\mathrm{N}}_2$ collisions have been performed for impact energies from 0.01 to 1.0 Ry using model exchange potentials based on a free-electron-gas approximation in order to evaluate the utility of such local potentials in low-energy electron-molecule scattering. A body-frame fixed-nuclei formulation of the collision problem is used which treats the molecule as rigid and does not allow for electronic or vibrational excitation. Coupled integro-differential scattering equations which incorporate exchange rigorously are derived and the simplification of the nonlocal exchange potential to an approximate energy-dependent local potential is described. An initial study of $e$-${\mathrm{H}}_2$ collisions is reported in which results obtained with various model excahnge potentials are compared to those of exact static-exchange calculations. Cross sections for the $e$-${\mathrm{N}}_2$ system obtained using the model exchange potentials (with and without polarization) are reported and compared with measured cross sections and the results of other theoretical studies. For both systems, good agreement with more rigorous treatments of the exchange can be obtained.

The theory of the classical or semiclassical $S$ matrix is combined with the use of perturbation dynamics to derive an approximately unitary expression for the scattering matrix for a very general class of potential interactions. The $S$ matrix takes the form of a sum over products of Bessel functions whose orders are related to the changes in quantum numbers occurring in the transition, and whose arguments depend on the dynamical variables of the problem, including the unperturbed quantum numbers. In the general case, these arguments can be expressed as simple integrals over the unperturbed trajectory, and for well-behaved potentials they can be explicitly evaluated in terms of the modified Bessel functions $K_0$ and $K_1$. The connection between the semiclassical perturbation scattering theory and other approximations, such as the Born and eikonal approximations, is demonstrated. The general theory is illustrated by applications to electron- (or ion-) polar-molecule scattering, including quadrupole as well as dipole interactions and including coupling to vibrations in both harmonic and anharmonic approximations. The more complicated interactions involve lengthier products of Bessel functions in the sum-and-product representation, but these are easily and systematically evaluated, and they reduce smoothly to the appropriate simpler expressions when the coupling coefficients of the higher-order terms become small. More complicated potentials, including interactions between polyatomic molecules, can be handled by a simple systematic extension of the same principles. For electron-molecule scattering, these expressions can be used in their present form since the sums are dominated by Bessel functions of comparatively low order which can be evaluated directly; extensions to molecule-molecule scattering and ion-molecule scattering are equally valid formally, but their practical application will often require the use of asymptotic approximations to the Bessel functions.

Semiclassical perturbation scattering theory is applied to electron—polar-molecule scattering. Cross sections for elastic and rotationally inelastic transitions are obtained for $\Delta j=0, 1, 2, 3, 4$, in the case of a pure charge-dipole interaction potential. Results are presented in terms of functions of dimensionless parameters involving the moment of inertia $I$ and dipole moment $\mu$ of the target, and the mass, charge, and energy of the projectile. A range of these parameters sufficient to describe most situations of practical interest is explored. Significant oscillations are found in the cross sections for $\left|\Delta j\right|=0\mathrm{} \mathrm{and} 2$ as a function of dipole strength $\beta =\frac{m\mu e}{{\hslash }^2}$. For $\left|\Delta j\right|=1\mathrm{}$, the Born approximation is shown to be appropriate for $\beta \ll 1$, and invalid for $\beta \approx 1 or >1\mathrm{}$, Scaling rules are deduced which should aid in the correlation and extrapolation of quantal calculations on specific systems. With the guidance of the Born approximation, scaling principles are also suggested for differential scattering.

Semiclassical perturbation scattering theory is applied to electron—polar-molecule collisions, assuming a pure charge-dipole interaction potential. Cross sections for momentum transfer are given in terms of dimensionless parameters involving the moment of inertia and dipole moment of the target, and the mass, charge, and energy of the projectile. A range of these parameters is explored corresponding to collisions at energies above 0.1 eV for most molecules. For large values of the dipole moment, the momentum transfer is much smaller than the prediction of the first-order Born approximation, and involves significant contributions both from elastic scattering and from transitions with large values of $\left|\Delta j\right|$. The behavior of the cross section as a function of the rotational quantum number $j$ is found to obey a simple scaling rule.

Plane-wave Born-approximation calculations of $K$-shell ionization cross sections are made using one-electron Dirac and Dirac-Hartree-Fock wave functions to describe the $1s$ and continuum electronic orbitals. Calculations are reported for selected elements between Ca and $Z=170\mathrm{}$ and for values of the ratio of the ion velocity to the $K$-electron velocity $\frac{v_1}{v_K}\lesssim 0.2$. Simple relativistic correction factors are derived which, when multiplied by easily obtainable nonrelativistic cross sections, allow the accurate determination of relativistic $K$-shell ionization cross sections without having to perform further extensive calculations. The relativistic correction factors are compared with approximate correction factors discussed by Amundsen, Kocbach, and Hansteen.

Measurements of $K$-vacancy production cross sections are reported for 0.5- to 3.5-MeV/amu H, He, O, F, and Cl bombardments of selected elements between Y and U. Ratios of H- to He-induced cross sections corrected for binding effects are compared with proposed Coulomb-deflection correction factors. The validity of the Kocbach factor is confirmed. Ratios of experimental H- and He-induced cross sections to plane-wave Born-approximation cross sections, corrected for binding and Coulomb-deflection effects, agree with theoretical relativistic correction factors calculated in the preceding paper. A new semiempirical formula for predicting $1s\sigma$-vacancy production cross sections is derived. The overall agreement of the new formula with H-, He-, O-, F-, Cl-, Kr-, and Xe-induced cross sections is generally within experimental uncertainties (10%-20%).