A four-component relativistic self-consistent-field scheme based on the squared Dirac operator is presented. Just as in the one-electron case, discussed previously [Chem. Phys. Lett. 78, 341 (1981)], the variation principle holds and no variational collapse appears if the expansion method is applied. Numerical results with scalar Gaussian-lobe basis sets are given for He, Li, Be, ${\mathrm{H}}_2$, and LiH.

Approximate relativistic corrections to the atomic radial wave functions of the recently reported $\Xi$ method are presented based on the approach of Cowan and Griffin. The major relativistic effects are shown to be incorporated into the wave function while retaining the nonrelativistic format. The one-electron eigenvalues, total energies, expectation values of $r^n$ for $n=-1,1, \mathrm{and} 2$ and spin-orbit parameter values are reported. The results are comparable with the fully relativistic Dirac-Hartree-Fock values.

It is proved that $N_c$, the number of negative particles that can be bound to an atom of nuclear charge $z$, satisfies $N_c<2z+1\mathrm{}$. For a molecule of $K$ atoms, $N_c<2Z+K$ where $Z$ is the total nuclear charge. As an example, for hydrogen $N_c=2\mathrm{}$, and thus ${\mathrm{H}}^{--}$ is not stable, which is a result not proved before. The bound particles can be a mixture of different species, e.g., electrons and $\pi$ mesons; statistics plays no role. The theorem is proved in the static-nucleus approximation, but if the nuclei are dynamical, a related, weaker result is obtained. The kinetic energy operator for the particles can be either $\frac{{\left[\frac{p-eA\left(x\right)\mathrm{}}{c}\right]}^2}{2m}$ (nonrelativistic with magnetic field) or ${\{{\mathrm{}[pc-eA(x\left)\right]}^2+m^2{c}^4\}}^{\frac{1}{2}}-m{c}^2$ (relativistic with magnetic field). This result is not only stronger than that obtained before, but the proof (at least in the atomic case) is simple enough to be given in an elementary quantum-mechanics course.

Projectile $K$-Auger-electron production measurements were performed for the bare, one-, and two-electron ions of C, N, O, and F incident on He, Ne, Ar, and Kr gases. The measurements were taken over an energy range of $\frac{1}{4}$ to $\frac{2}{3}$ MeV/amu using a cylindrical mirror analyzer. For the incident two-electron ions, single-electron capture to excited states of the ${\left(1s2s\right)}^{3}S$ metastable component of the incident beam was the principal mechanism giving rise to the observed $K$-Auger transitions. For the bare and one-electron ions, double electron capture to excited states was the dominant mechanism leading to $K$-Auger-electron production. In addition to Auger-spectroscopy measurements, total $K$-Auger production cross sections were determined as well as the partial cross sections for electron capture to specific $n$ levels of the projectile. The $n$ distributions were also measured for double electron capture to excited states of the bare and one-electron ions.

The atomic-orbital-expansion description has been employed in calculations of electron transfer in ${}_Z{}^{}{}_{}{}^{}X_{}^{Z+}{}_{}{}^{}+\mathrm{H}$ collisions ($Z=2,4-8\mathrm{}$) in the energy range 0.1-30 keV/amu. Total transfer cross sections have been determined as well as partial cross sections for transfer into individual $n,l$ subshells of the projectile. Results are compared to those derived with other methods and to available experimental data. Generally, qualitative agreement is found between results of the present study and those calculated with other close-coupling schemes. Quantitatively good agreement is found in cases where other studies based on large-scale computations are available, i.e., for ${\mathrm{C}}^{6+}$ +H and ${\mathrm{O}}^{8+}$ +H collisions. But even in these cases, the results from the most involved calculations appear to have converged towards each other for the dominant partial cross sections only.

Cross sections for ${\mathrm{Cs}}^{2+}$ formation in ${\mathrm{Cs}}^{+}$ + ${\mathrm{Cs}}^{+}$ collisions have been measured by a plasma-target technique for center-of-mass energies from 50 to 110 keV. The measured cross sections for the sum of ionization and charge exchange are in moderate agreement with the results of Peart et al., and disagree with the results of Dunn et al. and of Neill et al. at the lower energies. The experimental technique and possible sources of error are discussed in light of the discrepancy between the results of the three groups.

A purely theoretical semiclassical method without any ambiguity is presented for the calculation of differential cross sections for atomic collision processes involving both radial and rotational (Coriolis) nonadiabatic couplings. The method is based on the recently proposed dynamical-state representation, which enables us to deal with radial and rotational couplings in a unified way. This theory is applied to the asymmetric charge transfer and excitation in the ${\mathrm{Li}}^{+}$ + Na and Li+${\mathrm{Na}}^{+}$ collisions. The calculated differential cross sections are in good agreement with experimental results.

A triple-center atomic-state method is proposed for treating ionization in low-energy ion-atom collisions. This method intrinsically accounts for the Wannier mechanism, in which the electron will not have been removed in a slow collision unless it is asymptotically at the point of unstable equilibrium between the nuclei (the chosen third center). When applied to $p-\mathrm{H}$ collisions, the method shows that most of the ionized electrons stay near the third center and that direct Coulomb ionization and charge transfer to the continuum—accounted for by normal double-center methods—are less important: The triple-center method dramatically raises the cross section above that obtained using a double-center pseudostate basis, bringing it closer to the single early experimental curve at energies below 15 keV.

We present a comparative study of several empirical and nonempirical models for the absorption potential, which is the imaginary part of an optical-model potential, for electron scattering by rare gases. We show that the elastic differential cross section is most sensitive to the absorption potential for high-impact energy and large scattering angles. We compare differential cross sections calculated by several models for the absorption potential and by several arbitrary modifications of these model potentials. We are able to associate the effect of the absorption potential on the elastic differential cross section with its form at small electron-atom distances $r$, and we are able to deduce various qualitative features that the absorption potential must possess at small and large $r$ in order to predict both accurate differential cross sections and accurate absorption cross sections. Based on these observations, the Pauli blocking conditions of the quasifree scattering model for the absorption potential are modified empirically, thus producing a more accurate model that may be applied to other systems; e.g., electron-molecule scattering, with no adjustable parameters.

The theory of spin exchange between optically pumped alkali-metal atoms and noble-gas nuclei is presented. Spin exchange with heavy noble gases is dominated by interactions in long-lived van der Waals molecules. The main spin interactions are assumed to be the spin-rotation interactions $\gamma \overrightarrow{\mathrm{N}}·\overrightarrow{\mathrm{S}}$ between the rotational angular momentum $\overrightarrow{\mathrm{N}}$ of the alkali-metal—noble-gas pair and the electron spin $\overrightarrow{\mathrm{S}}$ of the alkali-metal atom, and the contact hyperfine interaction $\alpha \overrightarrow{\mathrm{K}}·\overrightarrow{\mathrm{S}}$ between the nuclear spin $\overrightarrow{\mathrm{K}}$ of the noble-gas atom and the electron spin $\overrightarrow{\mathrm{S}}$. Arbitrary values for $K$ and for the nuclear spin $I$ of the alkali-metal atom are assumed. Precise formal expressions for spin transfer coefficients are given along with convenient approximations based on a perturbation expansion in powers of ${\left(\frac{\alpha }{\gamma N}\right)}^2$, a quantity which has been shown to be small by experiment.

Measurements of $K$ x-ray (or Auger) satellite intensities produced by ion impact have yielded $K^u{L}^v$ multiple-vacancy distributions which in most cases are nearly binomial. This implies that, statistically, the holes are nearly independent, which is surprising in view of the known influence of correlations on other collision processes. We give a detailed derivation of general expressions for ion-induced multiple-vacancy distributions in the independent-Fermi-particle collision model, based on the Hartree-Fock description of the target, which contains Pauli correlations. Our coupled-channels calculations employing these expressions have shown that the electron exchange terms tend to mutually cancel because of "random" phases, but need not cancel when a single channel, such as a resonant electron capture, is dominant.

Measurements of the dissociation of $\mathrm{D}_3^{}{}_{}{}^{+}$ ions at 300-600 keV under single- and multiple-collision conditions in Ar- and ${\mathrm{H}}_2$-gas targets have been performed. A complete separation of all dissociation channels was achieved, including the neutral channels, which were resolved using a fine-mesh technique. Data analysis in the multiple-collision regime confirms the validity of the rate equations governing the charge exchange processes. In the single-collision region the analysis yields constant relations between channel probabilities. Data rearrangement shows probability factorization and suggests that collisional dissociation is a two-stage process, a fast electron exchange followed by rearrangement and branching to the exit channels.

A model-potential method has been used to evaluate the elastic $e^{\pm }-\mathrm{H}\mathrm{e}$ scattering at the low-incident energies. The potential contains one parameter to include the effect of short-range correlation. The results for the elastic $e^{\pm }-\mathrm{H}\mathrm{e}$ scattering have been obtained using the same parameter. Two model exchange potentials, one for $s$ wave and the other for higher partial waves, have been employed. The present results are in good agreement with the measured values and refined theoretical predictions.

A method suggested by Das is modified and applied to the elastic scattering of electrons and positrons by the hydrogen atom in the intermediate-energy range varying from 50 eV to 1 keV. It is shown that the modification has removed, to a great extent, some of the deficiencies of the method suggested by Das.

The x-ray spectrum emitted by high-velocity heliumlike iron ions has been studied with a crystal spectrometer. The absolute energies of the $n=2\mathrm{}\to n=1\mathrm{}$ lines have been measured with a precision of 40 ppm. A very good agreement has been found between our experimental values and a very accurate multiconfiguration Dirac-Fock calculation. The precision of the measurement and the calculation of the energies are such that for the first time the magnetic correlation energy (spin-spin) as well as the screening of quantum-electrodynamic effects can now be appreciated. The contamination of the considered lines by the so-called dielectronic recombination satellites has been studied in great detail by varying the nature and the thickness of the targets.

We report the first measurement of the absolute cross section for photoionization of the $7S$ state of cesium. The measurement employed a new technique in which the density of the excited-state atoms was determined by the amount of fluorescence. The cross section for photoionization by 540-nm light is 1.14(10)×${10}^{-19\mathrm{}}$ ${\mathrm{cm}}^2$. We also propose a second new technique for the absolute measurement of photoionization cross sections which is based on modulated fluorescence.

The $7s{n}^{\prime }d$ autoionizing states of barium have been studied by two-photon excitation from the $6snd$ Rydberg states. An analysis of our low-intensity, electron-energy-resolved data reveals no systematic energy shifts in the spectra of the $7s{n}^{\prime }d$ states as a function of the initial value of the principal quantum number $n$. This result indicates there is no apparent shielding of the $7s$ core electron by the outer $\mathrm{nd}$ Rydberg electron, in contrast with a previous measurement.

A theory of two- and three-photon autoionization is presented for intermediate resonant and non-resonant cases, stressing the laser-intensity effect on the configuration mixing of the final state. Sample calculations are performed for the $5p6s{}_{}{}^1{}_{}{}^{}P$ autoionizing state. The involvement of the $5s5d$ intermediate state includes the effects of ac Stark shifts on the ionization rate, the line shape, and the photoelectron angular distributions.

Parameters describing the low-energy photoionization of the outer shells of the rare gases Ne, Ar, Kr, and Xe have been calculated using a relativistic generalization of the time-dependent local-density approximation. The resulting photoionization cross sections, angular-distribution asymmetry parameters, and spin polarization parameters are presented here. The results are found to be in good agreement with those from the relativistic random-phase approximation (RRPA), even though the present theory is simpler, formally and computationally, than the latter. These results, and those of the RRPA, are generally in good agreement with experiment, illustrating the utility of the present approach to photoionization, especially for heavy atoms in which both relativistic and correlation effects are important.

Linewidths of four visible Xe II lines are measured in a conventional shock tube. The Stark effect is the dominant broadening mechanism. Electron densities vary widely over the range (1-15) × ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$, but temperatures remain in the narrow range 7800-8400 K. Great care has been taken to minimize possible systematic errors in the electron-density and optical-depth measurements.