X rays resulting from $L$-subshell vacancies in Hf, Ta, and W produced by bombarding thin targets with ${\mathrm{H}}^{+}$ (0.6-2.5 MeV) and ${\mathrm{He}}^{+}$ (1.2-4.2 MeV) were detected by Si(Li) spectrometry. Ionization cross sections were obtained by using the above measurements, branching ratios from theoretical calculations, and values of the fluorescence yields and Coster-Kronig factors by interpolating from experimental data. The observed projectile-energy dependence of the $L_{\mathrm{II}}$-subshell ionization cross section is reproduced reasonably well by the plane-wave Born approximation (PWBA), but the introduction of relativistic, trajectory, and binding corrections (PWBA-BTR) are essential for the description of the $L_{\mathrm{I}}$ and $L_{\mathrm{III}}$ data. Scaling of the ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ data shows that one agrees well with the other. The behavior of the ionization cross section versus bombarding energy is correlated with some special features of the electronic bound-state wave functions.

Previous work on potential scattering in the field of a low-frequency laser and a model multichannel problem are combined to present a theory of electron-atom scattering in the field of a low-frequency laser. The atomic distortion by the laser is treated in perturbation theory, which is consistent with the other approximations of the theory. The only additional assumption necessary is that the scattering in the absence of the laser has no sharp resonances which participate in the scattering in the presence of the laser. A result is obtained which is a simple multichannel generalization of that of Kroll and Watson. It is used to calculate the average number of photons absorbed or emitted during scattering.

Integrated and differential cross sections for vibrationally elastic $e^{-}$-${\mathrm{N}}_2$ scattering from 0 to 1000 eV are calculated by means of the continuum multiple-scattering method (CMSM) with the Hara free-electron-gas and semiclassical exchange approximations. The present results represent a significant improvement over earlier CMSM calculations employing the Slater $X\alpha$ exchange approximation. The physical basis for this improvement is discussed. Resonance structures appear at 2.4, 13, and 26 eV in the ${\pi }_g$, ${\delta }_g$, and ${\sigma }_u$ channels, respectively; however, the latter two are very weak and only the ${\sigma }_u$ resonance has been observed in elastic scattering. Agreement between the present calculation and experiment is good over the entire energy range, although at fixed (equilibrium) internuclear distance, the ${\pi }_g$ resonance is too narrow and high. The agreement at the ${\pi }_g$ resonance is significantly improved by taking into account the effects of nuclear motion in the adiabatic nuclei approximation.

Light absorption and emission spectroscopy was used to study the time dependences of the ${\mathrm{He}}^m\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$, ${\mathrm{He}}_2^m\left(a{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\right)$, and ${\mathrm{Ne}}^m\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)$ number densities and spectral-line emission intensities from 19 ${\mathrm{Ne}}_{\mathrm{I}}$ states during the afterglow of helium-neon discharges. The ${\mathrm{Ne}}_{\mathrm{I}}$ states below 20.56 eV are produced, either directly or by cascading, by excitation transfer between ${\mathrm{He}}^m\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ and Ne with a reaction rate constant of 4.3×${10}^{-12\mathrm{}}$ ${\mathrm{cm}}^3$${\mathrm{s}}^{-1\mathrm{}}$, in agreement with previous studies. The $\mathrm{Ne}\left(2\mathrm{}{p}^{5}3s\right)$ states are formed directly by the dissociative-excitation-transfer mechanism ${\mathrm{He}}_2^m\left(a{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\right)+\mathrm{Ne}\to {\left({\mathrm{He}}_2\mathrm{Ne}\right)}_r^{*}\to \mathrm{Ne}\left(2\mathrm{}{p}^{5}3s\right)+2\mathrm{He}$ involving an intermediate repulsive state. No evidence was found for the production of ${\mathrm{Ne}}_{\mathrm{I}}$ energy levels above 20.56 eV by binary energy-transfer processes.

A method previously developed for one-dimensional nonrelativistic perturbation theory is extended to three-dimensional problems. This method essentially consists of performing the perturbation expansion on the logarithm of the wave function instead of on the wave function itself. It is shown that, for the first-order corrections in problems that are not reducible to one dimension, this method is equivalent to that of Sternheimer and to that of Dalgarno and Lewis. In the present approach, the higher-order corrections can be obtained in a hierarchical scheme and there exists an isomorphisim between the equation for the first-order correction and the equation for the $i\mathrm{th}$-order correction. As an illustration of the technique developed, the authors consider the hydrogen atom in an external multipole field and in two different spherically symmetric perturbation potentials, $\delta \mathrm{}(r-a)\mathrm{}$ and $e^{-\alpha r}$. The last potential is related to the problem of the screened Coulomb potential. By considering the $\delta \mathrm{}(r-a)\mathrm{}$-type potential, two interesting sum rules are obtained.

The authors describe practical methods for calculating the Stark structure of Rydberg states of the alkali metals based on diagnolization of the energy matrix. A survey of Stark structures is presented for all of the alkali metals in the vicinity of $n=15\mathrm{}$. Topics discussed include general methods for evaluating radial matrix elements, the treatment of fine structure, oscillator-strength distribution, scaling laws, the structure of a level anticrossing, and sources of error. Experimental Stark maps are compared with calculated results for lithium and cesium. Experimental studies of the oscillator-strength distribution within a Stark manifold and the structure of a level anticrossing are also presented.

The author has calculated the Sternheimer shielding factor pertaining to the atomic quadrupole moment for N, P, As, and Sb in the $n{p}^2\mathrm{}(n+1\mathrm{})s$ electronic configuration. The calculated values are 0.94, 1.25, 1.29, and 1.59, respectively. The results suggest that it is essential to incorporate the Sternheimer factor in theoretical calculation of the interactions involving the atomic quadrupole moment, e. g., the long-range ionquadrupole interaction as studied in recent merged-beam experiments.

Accurate values for the density shift and broadening of five isolated ${\mathrm{H}}_{\alpha }$ fine-structure transitions have been measured. Doppler-free polarization and double-quantum saturation spectroscopy with a cw dye laser are used in a He dc discharge with 1% ${\mathrm{H}}_2$. The negative shifts and the huge broadening values are correctly predicted by an impact-approximation theory taking into account the large cross sections for fine-structure transfer (quenching) collisions and only Van der Waals interaction between ${\mathrm{H}}^{*}$ and He. Consequences of a comparison with the positive shift of the unresolved ${\mathrm{H}}_{\alpha }$ line and of the alkali-metal $D$ lines in He buffer gas are discussed. For pressures below 0.1 Torr hfs decoupling collisions give rise to a positive shift of single ${\mathrm{H}}_{\alpha }$ fine-structure lines and to a collisional narrowing effect analogous to that observed in nuclear magnetic resonance.

The authors derive asymptotic formulas for the energies of the strongly bound states of hydrogen for large magnetic fields. Rigorous lower bounds on the binding and also upper bounds are given based on generous estimates of the errors. Comparison with variational and other previous numerical results shows their tendency to underestimate the binding.

A theory describing collisions between arbitrary atoms or ions and atomic hydrogen is developed. Results are obtained in terms of amplitudes for electron-hydrogen and proton-hydrogen collisions and the arbitrary atom or ion transition form factor. No recourse to scattering by fictitious electron-plus-proton atoms is necessary. Applications are made to the differential and total cross sections for ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{He}}^{+}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}(n=2\mathrm{})\mathrm{}$. Agreement with recent measurements is obtained. A simple approximation to the results, $\sigma \approx {\sigma }_{p\mathrm{H}}(1s\to n=2)+8\mathrm{}{\sigma }_{p\mathrm{H}}(1s\to 2s)$, is obtained and is in fair agreement with recent data.

Excitation probabilities for the $1s-2s$ transition of hydrogenlike ions by low-energy $\mathrm{}(4-100)\mathrm{}{E}_{\mathrm{th}}$ protons are calculated in the Coulomb-Born approximation and compared to the corresponding calculations in the semiclassical approximation with hyperbolic trajectories. Through the use of a Fourier-Bessel transform, an effective energy is derived for the semiclassical approximation, which brings the total cross section into agreement with the Coulomb-Born results.

The effect of elastic collisions of ${\mathrm{U}}^{+}$ with U, ${\mathrm{U}}^{+}$, and ${\mathrm{U}}^{2+}$ in a ${\mathrm{U}}^{+}$ plasma has been investigated. The required potential-energy curves were calculated by means of the electron-gas (Gordon-Kim-Rae) statistical method. An effective polarization potential was added to the ion-neutral potential curve. Collisional phase shifts were evaluated by the semiclassical JWKB method using a very efficient algorithm. Modifications necessary to take into account the long-range shielded Coulomb potential in ion-ion collisions are described. Momentum-transfer and viscosity cross sections, without charge transfer, are presented and their dependences on the long- and short-range potentials are examined.

Ab initio configuration-interaction methods are used to obtain the potential curves and coupling-matrix elements describing the charge transfer reactions ${\mathrm{N}}^{2+}\left({}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}\right)+\mathrm{H}\to {\mathrm{N}}^{+}+{\mathrm{H}}^{+}$ and ${\mathrm{N}}^{3+}\left({}_{}{}^1{}_{}{}^{}S\right)+\mathrm{H}\to {\mathrm{N}}^{2+}+{\mathrm{H}}^{+}$. The basis sets are chosen to reproduce efficiently the crossing region and the polarization effects important for coupling-matrix elements. Correlation-energy problems are discussed in the context of rearrangement collisions and procedures are developed to minimize them. The computed reaction energies for the important channels of the reaction are within 7 and 1%, respectively, of the experimental values.

Detailed measurements of the collisionally induced electron detachment of ${\mathrm{H}}^{-}$ during collisions with He at an ion energy of 0.5 MeV are reported for $\theta =0-173\mathrm{}°$. These data are compared to similar measurements using Ar as the target and to electron elastic scattering from He. These comparisons reveal that, while some characteristics of the electron energy spectra are similar for both targets, one feature shows a marked target dependence. Further experiments, in the forward direction only, using other ${\mathrm{H}}^{-}$ energies in the range 0.35-1.35 MeV, as well as ${\mathrm{D}}^{-}$ at 1.0 MeV, indicate that the results have no simple interpretation in the rest frame of the projectile.

Doubly differential cross sections of secondary electrons ejected from C${\mathrm{O}}_2$ by electron impact have been measured by means of a crossed-beam method. The incident energies used were 50, 100, 200, and 400 eV. The energy range and angular range of secondary electrons measured were from one-half of the difference between incident energy and ionization potential to 1.0 eV and from 12 to 156°, respectively. The present results agree with the results of Rapp and Englander-Golden for the total ionization cross sections and with that of Opal et al. for the singly differential cross sections. The doubly differential cross sections show larger values at extreme angles and smaller values near 90° than those of Opal et al.

Cross sections have been measured for $K$-shell vacancy production for ${\mathrm{F}}^{6+}\left(1\mathrm{}{s}^{2}2s\right)$ ions incident on He target atoms in the projectile energy range from 10 to 40 MeV. Collisions leading to ${\mathrm{F}}^{6+}\mathrm{}\left(1s2s2p\right)\mathrm{}$ states are attributed to $K$-shell excitation. The cross sections for ${\mathrm{F}}^{6+}\left(1\mathrm{}{s}^{2}2s\right)$ to ${\mathrm{F}}^{6+}\mathrm{}\left(1s2s2p\right)\mathrm{}$ excitation agree with a Born calculation for $1s$-electron excitation. Collisions leading to ${\mathrm{F}}^{7+}\mathrm{}\left(1s2p\right)\mathrm{}$ states are referred to as $K$-vacancy production to distinguish it from the $K$-shell excitation process. The energy dependence of the $K$-vacancy production cross section for the ${\mathrm{F}}^{6+}\left(1\mathrm{}{s}^{2}2s\right)$ to ${\mathrm{F}}^{7+}\mathrm{}\left(1s2p\right)\mathrm{}$ process does not agree with the calculation for single $1s$-electron ionization. The observed energy dependence is understood in terms of the sum of two two-step processes. One two-step process is $1s$-electron ionization simultaneous with $2s-2p$-electron excitation and the other is $2s$-electron ionization simultaneous with $1s-2p$-electron excitation. The latter process is dominant. The ${\mathrm{F}}^{q+}$ charge-state dependence at 15 MeV and the ${\mathrm{F}}^{8+}$ energy dependence for electron excitation, as previously reported, are also compared with theory.

The calculation of complex resonance eigenvalues for electron-atom and electron-molecule scattering by discrete-basis-set methods yields total resonance widths directly. The authors show that, as a consequence of the separable nature of the $S$ matrix near a resonance, discrete-basis-set methods may also be used to compute partial widths for resonances in a multichannel problem. The procedure is applied to a model three-channel problem to demonstrate its numerical effectiveness.

Differential cross sections for the elastic scattering of electrons from molecular hydrogen are calculated within the independent-atom model. The required differential cross sections of atomic hydrogen have been obtained by using the eikonal-Born-series method. The effect of the molecular binding is also considered. The present results compare well with recent absolute experimental measurements.

The relative photoionization cross section of ground-state Rb is measured near threshold as a function of applied electric field strength. The cross section is found to have a wavelength-dependent resonance structure that changes with the strength of the electric field. This resonance structure is observed not only for energies above the classical field ionization limit, but for the case of $\pi$ excitation, beyond the zero-field ionization limit as well. An analysis of the data is presented that connects the concepts of "strong-field mixing" and the perturbation calculations of the energies of hydrogenic Stark components.

Dirac-Fock calculations of the photoionization of the outer $\mathrm{ns}$ electrons in Na, K, Rb, and Cs have been performed. The resulting photoelectron angular distribution asymmetry parameters $\beta$ show strong variations with energy, in contrast to the nonrelativistic prediction of $\beta =2\mathrm{}$, independent of energy, for $s$ electrons. This deviation is due to the spin-orbit interaction of the continuum electron which gives rise to two final states $\epsilon p_{\frac{1}{2}}$ and $\epsilon p_{\frac{3}{2}}$, in place of the single $\epsilon p$ nonrelativistically. The transitions to the $\epsilon p_{\frac{1}{2}}$ and $\epsilon p_{\frac{3}{2}}$ have matrix elements and phase shifts which differ and interfere, thereby resulting in an energy-dependent $\beta$. The effects are particularly dramatic between the Cooper minima in the two channels, and they persist even for $Z$ as low as that for Na.