Two different perturbation series, the weak- and strong-field expansions, for approximating any resonances of the Stark effect in the hydrogen atom, are given. Together they cover the entire regime of field values up to the points when the resonances disappear.

Systematic relativistic (Dirac-Hartree-Slater) calculations of atomic $K$-shell Auger transition probabilities are reported for 25 elements with $18\le Z\le 96$. $K$-level Auger widths are found to be enhanced by relativistic effects, while total $K$-level widths are reduced. Relativistic theoretical $K$-shell fluorescence yields are in excellent agreement with experiment. Theoretical relative intensities of $K-LX$ Auger transitions in heavy elements, calculated in $j-j$ coupling, agree well with measurements; for low $Z$, configuration interaction and intermediate coupling must apparently be included.

Theoretical $K-LL$ Auger spectra have been calculated relativistically in intermediate coupling with configuration interaction. Results for 25 elements with $18\le Z\le 96$ are listed and compared with experimental data. Relativistic effects are seen to be important above $Z\simeq 35$. Intermediate coupling with configuration interaction is necessary to describe the spectra for $Z\lesssim 60$; $j-j$ coupling results are adequate above $Z\simeq 60$, except for the $\frac{K-L_2{L}_2\left({}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)}{K-L_1{L}_1\left({}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)}$ intensity ratio, which is very sensitive to correlation. The relative satellite intensity $\frac{K-L_1{L}_2\left({}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}\right)}{\left({}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)}$ is found to be exceedingly sensitive to the effects of relativity; experimental data, though scant and uncertain, appear to disagree with this theoretical ratio. Otherwise, the present relativistic $K-LL$ spectra in intermediate coupling with configuration interaction agree well with experiment over the entire range of atomic numbers from $Z=18\mathrm{} \mathrm{to} 96$.

The first relativistic calculations of radiationless transition probabilities for the filling of vacancies in atomic $M$ shells are reported. For eight elements with atomic numbers $70\le Z\le 100$, radiationless $M_4$- and $M_5$-subshell transition rates, $M$-subshell fluorescence and Coster-Kronig yields, and $L{\alpha }_{1,2}$ and $L{\beta }_1$ x-ray linewidths were computed with Dirac-Hartree-Slater wave functions using the Møller two-electron operator. The inclusion of relativity is found to affect strong Auger transitions by 10-20%, and weak transitions by as much as a factor of 2, mostly because of the difference between relativistic and nonrelativistic wave functions. The new theoretical results agree substantially better with experimental data than the results of older, nonrelativistic calculations.

Pair production cross sections near threshold have been calculated numerically in partial waves for a screened central potential, permitting a comparison of theory with recent experiments. Exchange effects are found to remain small. The level of agreement with experiment is variable and does not suggest any systematic trends. A more approximate theory of screening, energy-shift screening theory (EST), identifying screened cross sections with Coulomb cross sections of shifted spectrum energy $V_0$, is in agreement with the full calculation if the proper choice is made for the energy shift $V_0$; however, the procedure becomes more delicate as threshold is approached. A previous attempt to apply EST to threshold experiments made an incorrect choice for $V_0$.

The author has obtained Hugoniot data for uranium at a pressure of 6.7 TPa using a planar shock generated by an underground nuclear explosion. Measurements were made relative to a molybdenum standard in an impedance-matching experiment using 200-mm-diam by 20-mm-thick samples of each material. Twenty-seven electrical contact pins were used to measure shock velocities of 27.0 and 22.8 km/s (±1%) in the molybdenum and uranium, respectively; these velocities correspond to pressures and densities of 4.97 TPa and 30.8 g ${\mathrm{cm}}^{-3\mathrm{}}$ (Mo) and 6.69 TPa and 59.0 g ${\mathrm{cm}}^{-3\mathrm{}}$ (U). The measurement differs from a theoretical calculation by more than 2.5 times the experimental uncertainty and represents the highest pressure at which Hugoniot data have been obtained.

A procedure is outlined for using complex scaling to compute matrix elements of the resolvent of the Born-Oppenheimer Hamiltonian for a molecule with respect to square integrable functions. The method is superficially identical to that used previously for computing atomic photoionization cross sections—even though the molecular Born-Oppenheimer Hamiltonian is ill behaved under the scaling transformation appropriate to the atomic problem. The author gives a heuristic derivation of the method, relating it to Simon's theory of exterior complex scaling, which treats the molecular Born-Oppenheimer problem correctly. Numerical results are presented for ${\mathrm{H}}_2^{+}$ photoionization cross sections for which exact results are available for comparison.

The authors have calculated the electric dipole interaction energy of the ${}_{}{}^{205}{}_{}{}^{}\mathrm{TI}$ nucleus in TIF assuming a nonzero electric dipole moment $d_p$ on the proton. The result is used in the accompanying experimental paper to obtain a new value of $(-1.4\mathrm{}\pm 6)\times {10}^{-21\mathrm{}}e$ cm for $d_p$.

The authors describe a molecular-beam-resonance experiment to search for $P$- and $T$-violating interactions in the thallium fluoride molecule. Specifically the interactions looked for are of the form ${\mathcal{H}}_{\mathrm{PT}}=d{\hat{\sigma }}_{\mathrm{Tl}}·{\hat{\lambda }}_{\mathrm{TlF}}$, where $d$ is a coupling constant, ${\hat{\sigma }}_{\mathrm{Tl}}$ is a unit vector parallel to the spin angular momentum of the thallium nucleus, and ${\hat{\lambda }}_{\mathrm{TlF}}$ is a unit vector along the internuclear axis. The null result of the experiment is $\frac{d}{h}=11\mathrm{}\pm 42$ mHz. This result implies new upper limits on the electric dipole moment of the proton and on a possible weak, $P$- and $T$-violating, neutral-current tensor interaction.

Iterative techniques are developed and examined for the solution of the single-center, fixed-nuclei electron-molecule scattering equations. They are found to have wide application to scattering by both large and small homo- and heteronuclear diatomic molecules. It is found that enforcement of orthogonality of the bound and continuum orbitals is required for efficient convergence with iteration. Results are presented for the molecules ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, LiH, and CO.

Feshbach resonances of electrons incident on He and ${\mathrm{Li}}^{+}$ are calculated below the $3{}_{}{}^3{}_{}{}^{}S$ target threshold by means of the inelastic quasi-projection-operator technique of Temkin and Bhatia. A configuration-interaction-type wave function is employed with up to 46 configurations. The calculations reveal, with reasonable accuracy, all presently observed Feshbach resonances. The method does not reveal shape resonances, but, for isoelectronic systems with greater nuclear charge, it is argued that shape resonances should become less important. This is already apparent in the case of Li, for which the authors calculate the known resonances and also predict higher resonances for which there are as yet no experimental data.

An electrostatic analyzer positioned at various angles has been used to measure absolute values of cross sections for electron production in collisions of neutral hydrogen atoms with helium as a function of the angle and energy of the ejected electrons. These cross sections are compared with corresponding ones for proton and electron impact to infer the mechanisms of electron production. A prominent peak in the energy distribution due to electron loss from the projectile occurs at an electron velocity equal to that of the projectile. At very low electron energies the similarity of the energy distribution to that due to electron impact suggests that the large cross section there is due to ionization of the target by the electron carried by the projectile. As with proton impact, the cross sections at low projectile velocities fall off approximately exponentially with the energy of the ejected electron, in agreement with the predictions of the electron promotion model.

The equilibrium charge-state distributions of 1- and 2-MeV krypton ions in carbon foils are found to be nearly Gaussian, with mean charges $\overline{q}=3.1\mathrm{}\pm 1.0 \mathrm{and} 5.6\pm 0.35$ and full widths at half maximum (FWHM) $d=1.6\mathrm{}\pm 0.8 \mathrm{and} 1.8\pm 0.2$, respectively. The authors show a simple logarithmic behavior of $\overline{q}$ and $d$ for krypton as a function of incident beam energy. FWHM multiple-scattering angles in the laboratory frame for 1- and 2-MeV krypton ions in carbon foils (thickness 6.5±1.0 μg/${\mathrm{cm}}^2$) of ${\theta }_{\mathrm{FWHM}}=0.052\mathrm{}\pm 0.014 \mathrm{and} 0.032\pm 0.010$ radians, respectively, were observed. These values for ${\theta }_{\mathrm{FWHM}}$ agree satisfactorily with the theoretical work of Meyer and are consistent with the observations of Bernhard et al.

The excitation of the ${}_{}{}^3{}_{}{}^{}S$ state of atomic oxygen with subsequent emission of 1304-Å resonance radiation was observed in inelastic collisions between $\mathrm{O}\left({}_{}{}^5{}_{}{}^{}S\right)$ metastables and ${\mathrm{O}}_2$ and ${\mathrm{N}}_2$ molecules according to the process $\mathrm{O}\left({}_{}{}^5{}_{}{}^{}S\right)+X\to \mathrm{O}\left({}_{}{}^3{}_{}{}^{}S\right)+X\to \mathrm{O}\left({}_{}{}^3{}_{}{}^{}P\right)+X+h\nu \left(1304\mathrm{} \AA \right)$, where $X$ is ${\mathrm{O}}_2$ or ${\mathrm{N}}_2$. The cross section for this endothermic process was measured for metastable kinetic energies from threshold at 0.5 eV to about 10 eV (laboratory frame). For ${\mathrm{O}}_2$ as the target molecule, the cross section rose steeply from threshold to a plateau value of about (3±1.5)×${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ near 3 eV, from where it decreased slightly towards the maximum metastable kinetic energies available in the present experiment. For ${\mathrm{N}}_2$ as the target, the corresponding cross section was at least a factor of 30 smaller. The $\mathrm{O}\left({}_{}{}^5{}_{}{}^{}S\right)$ metastables were produced by electron impact dissociation of ${\mathrm{O}}_2$ in a pulsed source and subsequently velocity selected with a time-of-flight method. The metastable beam was monitored by spontaneous decay of metastables in the target cell resulting in 1356-Å radiation. The excited $\mathrm{O}\left({}_{}{}^3{}_{}{}^{}S\right)$ atoms produced in collisions with the target gas were monitored via 1304-Å resonance radiation.

A generalization of the conventional low-density corona-model theory is presented for determining the population densities of autoionizing levels in multiply charged ions and the intensities of satellite lines, produced by radiative transitions from these levels, which are associated with the resonance lines in the x-ray emission spectra of high-temperature plasmas. In addition to the usual processes of radiationless electron capture, inner-shell electron collisional excitation, autoionization, and radiative decay, account is taken of collisional transitions between the autoionizing levels. Results of calculations are presented to illustrate the effects of angular-momentum-changing electron collisions on the intensities of the satellites to the $1s2p{}_{}{}^1{}_{}{}^{}P\to 1s^2{}_{}{}^1{}_{}{}^{}S$ resonance line of the heliumlike ions AlXII and SiXII which are produced by the transitions $1s2pnl\to 1s^2\mathrm{nl}$ with $n=2\mathrm{}$ in the corresponding lithiumlike ions. Distorted-wave calculations have been carried out in an $\mathrm{LS}$ coupling scheme with configuration mixing for the autoionization, radiative decay, and electron collision rates. The generalized emission rate coefficients describing dielectronic recombination and inner-shell electron collisional excitation are tabulated as functions of electron density as well as temperature. The intensity of the satellite line emitted in the $1s2p^2{}_{}{}^2{}_{}{}^{}D\to 1s^{2}2p{}_{}{}^2{}_{}{}^{}P$ transition, which is the strongest at low densities, is found to be practically unaffected by electron collisional transitions between the autoionizing levels and remains a function mainly of temperature up to a density as high as ${10}^{24}$ ${\mathrm{cm}}^{-3\mathrm{}}$. However, for electron densities exceeding only ${10}^{22}$ ${\mathrm{cm}}^{-3\mathrm{}}$, the inclusion of these collisional processes causes a significant increase in the intensity of the $1s2p^2{}_{}{}^2{}_{}{}^{}P\to 1s^{2}2p{}_{}{}^2{}_{}{}^{}P$ satellite line, which is relatively weak at lower densities, and produces an enhancement of the total intensity of the radiation emitted in all of the $n=2\mathrm{}$ satellite transitions. The strong electron density dependence of the ratio of these two satellite-line intensities may be useful in the spectroscopic determination of the densities in compressed plasmas.

The author describes a calculation using the Glauber approximation (GA) to the scattering amplitudes and differential cross sections for the processes $e^{-}+{\mathrm{H}}_2\left(\mathrm{gs}\right)\to e^{-}+{{\mathrm{H}}_2}^{*}$, where (gs) means ground electronic and vibrational state, and * denotes low-lying vibrorotational excitation. A Gaussian electronic basis function is introduced, the use of which facilitates analytic reduction of integrals over target-electron coordinates, thus simplifying the computer arithmetic. In this work, neither model potentials nor adjustable parameters are employed. Results obtained are discussed in the light of GA calculations performed previously by other workers for $e^{-}$-atom systems.

Recently a modified Glauber theory was proposed by one of the authors (S.R.). In this theory a finite value of the mean excitation energy of the atom in its intermediate states is retained in each order (except the first) of the Glauber series, in a consistent way. In the present paper this theory is examined by analyzing the elastic electron-hydrogen scattering at 50, 100, and 200 eV. The excitation energy is determined by the total cross section, and turns out to be essentially independent of the energy of the incident particle. The exchange effect has been taken into account by making use of the Glauber exchange formulas of Forster and Williamson. The agreement of the theoretical results with the experimental data is very good. The proof of the unitarity of the modified Glauber amplitude is also given.

The cross sections—differential and integral—for electron capture by positrons from atomic lithium forming positronium in highly excited $\mathrm{ns}$ states are calculated by the use of the first Born approximation at several incident energies. In addition to the effect of the valence electron, the effect of the core term is taken into account explicitly. A straightforward technique is suggested for the evaluation of the transition amplitudes, the attractive part of which is given in a closed form, while the repulsive part involves a single-dimensional integral that is evaluated numerically. The asymptotic nature of the Ps formation as $n\to \infty$ is also discussed. It is seen that the asymptotic Ps-formation cross section obeys an inverse $n^3$ law irrespective of the energy. The angular distribution shows a zero depending on the projectile energies but almost independent of the principal quantum number $n$. The reported results for Ps formation for $2\le n\le \infty$ are quite new.

The equivalence of the two-body interactions between the final particles of the ion-atom ionization process is considered in the $T$-matrix formalism. This defines a final wave function which is product of Coulomb waves and describes simultaneously the capture to the continuum and the direct ionization. The relation of that approach with the wave equation for the three-particle system and the asymptotic behavior are discussed. The doubly differential cross section for the ionization of hydrogen atoms by proton impact is calculated, in first order, and compared with experimental values.

The high degree of orientation of atomic angular momentum states obtained by the interaction of fast ions with a solid surface at grazing incidence allows the application of the zero-field quantum-beat technique for high-resolution studies in atomic spectroscopy. With this new technique the authors have measured the hyperfine splitting of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ii $2p3p{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ and deduce for the hyperfine constants values of $A=102.9\mathrm{}\pm 1.0$ MHz and $B=-4.58\mathrm{}\pm 0.05$ MHz, and for the quadrupole moment $Q\left({}_{}{}^{14}{}_{}{}^{}\mathrm{N}\right)=19.3\mathrm{}\pm 0.8$ mb.