The lithium atom is studied by treating all three electrons on an equal footing using hyperspherical coordinates. The use of asymptotic base states improves the convergence of the potential curve calculation dramatically at large $R$. A potential curve plot suggests that a few localized pathways dominate the formation and decay of the lowest triply-excited state, $2s^{2}2p$. A quantitative study of the lowest state of this symmetry, $1s^{2}2p$, shows that the adiabatic approximation in hyperspherical coordinates gives an improvement over independent-electron methods, owing primarily to its inclusion of radial correlation effects at small distances $R$.

The separated oscillatory field technique was used with a 120-keV ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$ beam to make a zeromagnetic-field measurement of the $n=4\mathrm{}$ Lamb-shift interval in ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$. Excited ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$ ions were created by collisions in a cell filled with ${\mathrm{N}}_2$ gas. The $4{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ state population was monitored by observing its decay to the $2{}_{}{}^2{}_{}{}^{}P$ state with a large solid-angle NO photoionization detector. The $n=4\mathrm{}$ to 2 light (121.5 nm) decreased when the microwave field induced transitions from the $4{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ to the $4{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state. The value obtained for the Lamb shift was 1769.16mp 0.84 MHz. This result agrees satisfactorily with previous measurements and with the theoretical value for this interval. The experimental uncertainty is dominated by systematic effects attributed to the presence of overlapping cascade signals.

Large-scale optimization of nonlinear parameters and tighter error-bound estimates yield an accurate value, $E_{\mathrm{nr}}=-2.178\mathrm{}0776\left(12\right)\mathrm{}$ a.u. (${}_{}{}^4{}_{}{}^{}\mathrm{He}$) for the nonrelativistic energy of ${\mathrm{He}}^{-}$ $1s2s2p{}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}$, in agreement with a previous result of -2.1780740(100). Using Chung's recent calculation of relativistic and mass-polarization effects, an electron affinity $A=77.51\mathrm{}\pm 0.04$ meV is obtained. The calculation and significance of error bars in electronic structure calculations is discussed.

The theory of Kohn and Sham treats a system of interacting electrons by establishing a correspondence between this system and a noninteracting system. In this paper we develop a new formulation of this theory, which differs from the original by its rigor and by the more correct treatment of the kinetic energy term. This new formulation has the additional advantage that it bypasses the $v$ representability requisite of the original Hohenberg-Kohn-Sham theory.

We derive an explicit analytic expression for the time development of a generalized class of quantum distribution functions, which include as special cases the Wigner, the normal, and the antinormal distributions. We find that the simplest result is obtained in the case of the Wigner distribution.

In nondegenerate systems, the tetraexcited clusters are well approximated by products of disconnected pair clusters and the connected quadruply excited component is negligible. In contrast, when the reference state becomes quasidegenerate with the lowest biexcited configuration(s), the connected quadruply excited clusters become very important. To extend the applicability of the coupled-pair many-electron theory to such situations, we approximate the connected tetraexcited contribution in the form suggested by the unrestricted Hartree-Fock-type wave function, or one of its projected versions, such as the alternant molecular-orbital method. We show that the incorporation of the connected quadruply excited clusters into the coupled-pair equations effectively cancels certain nonlinear terms, originating from disconnected quadruple excitations, so that the resulting equations are very similar (up to a numerical factor) to the approximate coupled-pair theory, in which only those nonlinear terms which factorize with respect to the hole-electron pairs are considered. This fact shows in turn why various approximate coupled-pair approaches can often provide better results than the full coupled-pair many-electron theory.

Limiting formulas are deduced for the state of a quantum system which is subjected to a rapid sequence of many measurements of the same two-valued observable. In the case of a semibounded Hamiltonian, the dynamics usually gets reduced to the subspace spanned by the eigenstates of the observable. In particular, the values of the observable "freeze." Exceptions to freezing occur for states which cannot be approximated by eigenstates of finite energy.

It is shown that if the electromagnetic zero-point field (ZPF) of quantum electrodynamics (QED) is taken in the realistic sense, at least within the nonrelativistic approximation of QED, free unconfined electromagnetically interacting particles increase their translational kinetic energies when exclusively submitted to the action of the ZPF. This prediction is assessed and compared with other well-known difficulties associated with a realistic version of the ZPF concept. A parallel with an analogous acceleration phenomenon predicted in stochastic electrodynamics (SED) is given and possible astrophysical applications are suggested. It is shown that neither QED, with ZPF, nor SED lead to the Schrödinger equation (SE) of ordinary quantum mechanics, despite interesting arguments to the contrary, due precisely to this acceleration prediction.

Perturbation theory is shown to be one of the most powerful tools in calculating rotational eigenenergies of molecules in electric and magnetic fields, provided that the rigid-rotator approximation holds. The energy shifts for the Stark effect in symmetric-top molecules and for the hydrogen molecular ion in a magnetic field are accurately calculated in the whole range of field intensities.

Target $K$-vacancy and $L$-x-ray production cross sections in collisions with relativistic (82—670-MeV/amu) heavy ions ranging from Ne to U are measured and compared with atomic theories of inner-shell ionization based on the plane-wave Born approximation. Because the counting methods used are unique in atomic physics, careful studies of experimental uncertainties are made. Corrections to the measured cross sections due to x-ray pileup and secondary interactions in the solid targets are also discussed.

Interactions of charged particles in the presence of a chaotic laser field are considered for the case where the quadratic $A^2$ term in the Volkov solution must be retained. This is necessary whenever the kinematics are relativistic or the masses of the particles involved change during the interaction, such as in a decay, even though the kinematics might be nonrelativistic. Spin terms of the Volkov solution are also considered. The problem reduces to the solution of a stationary Gaussian stochastic process. This allows for an explicit evaluation if the two-time correlation function of the laser field is exponential with an arbitrary correlation time, i.e., for an Ornstein-Uhlenbeck process. The evaluation is performed by two alternative methods, one relying on path integrals and the other one on functional methods. Various limiting cases are discussed, notably that of an infinite correlation time. In the latter case, a cross section in a chaotic field is obtained from that in a coherent field by integrating the latter over the intensity with an exponential weight function. This prescription was already known to hold in the nonrelativistic case. As an application, we discuss high-intensity Compton scattering. A specialization of the present results yields an ensemble average, which is needed in the evaluation of a recent $g-2\mathrm{}$ experiment for the anomalous magnetic moment of the electron.

Absolute $e^{-}$-${\mathrm{H}}_2$ total electronically elastic differential scattering cross sections have been determined from relative scattered-electron angular distribution measurements in the energy range from 1 to 19 eV by comparison to absolute $e^{-}$-He elastic differential scattering cross sections measured in the same apparatus. Integrated total cross sections have been determined as well. Absolute differences as large as 50% between the present results and some previous results have been found, although the agreement as to shape is quite good in many cases. The present results are generally in excellent agreement with recent full rovibrational laboratory-frame close-coupling calculations.

Electron capture in ${\mathrm{H}}^{+}$+${\mathrm{H}}_2$ collisions is studied at energies of 1.0, 2.0, and 3.0 keV in the reduced angular range $\tau \le 3.0$ keV deg. Time-of-flight techniques are used for state identification, and the probability of electron capture to $\mathrm{H}\mathrm{}\left(1s\right)+{\mathrm{H}}_2^{ +}\left({}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\right)$ in an exchange collision is determined. This is shown to be the dominant exchange channel at small scattering angles. The "summed" exchange channels have a reduced cross section that is found to peak in the forward direction and shows no structure, while the cross section for capture to final ground-state channels shows some small structure at 3.0 keV for $\tau \ge 1.5$ keV deg. The reduced cross section, at 1.0 keV, for capture to excited states of H (with the ${\mathrm{H}}_2^{+}$ in its ground state) is found to have a maximum at $\tau =1\mathrm{}$ keV deg. The results are in agreement with a previously proposed model for ion-molecule charge exchange.

Based on the $R$-matrix approach of Schneider et al. [J. Phys. B 12 L 365 (1979)] to reactive electron-molecule scattering, a new propagative $R$-matrix method (PRMM) is presented which is more appropriate for polyatomic systems. The new method should be useful in other calculations where complicated integrals need to be propagated. We also introduce an effective $R$-matrix model (ERMM) in which the usual resonance parameters (potential and width) can be used as input in model $R$-matrix calculations. The PRMM and ERMM have been applied to the electron-${\mathrm{N}}_2$ system and the electron-${\mathrm{F}}_2$ system. The results agree very well with previous calculations for both vibrationally inelastic scattering and dissociative attachment when identical potentials and parameters are used.

This paper presents an alternative form of the method of continued fractions proposed by the authors recently. The present form is based on a subtraction of a separable operator from an appropriate Green function and shows faster convergence than the original method. The method is again applied to the elastic scattering of the electron from the hydrogen atom. The relation to certain variational principles with functionals of a fractional form is discussed.

Radiative processes in light-ion collisions are all-inclusively formulated and discussed. Production cross sections of the radiations are calculated in terms of the second Born approximation. The cross sections of atomic bremsstrahlung production and radiative ionization have been estimated and compared with experimental results of continuum x rays from an A1 target bombarded with few-MeV protons. It is found that atomic bremsstrahlung is the most predominant component in the region of x-ray energy $\hslash \omega \ge T_m$, where $T_m$ is the maximum energy transferred from a projectile to a free electron at rest, and the disagreement between the theory and experiment, which had previously been seen in this energy region, was clearly resolved.

Relative beam-foil populations of $\mathrm{np}$ terms ($n=2-4\mathrm{}$) in deuterium have been measured as a function of the the projectile energy in the energy range $10<E<\mathrm{}500\mathrm{}$ keV/amu. For $E\gtrsim 200$ keV/amu, the excitation functions of the $\mathrm{np}$ terms studied decrease as $E^{-3\mathrm{}}$ and follow closely the equilibrium neutral fraction (${\phi }_0$) variation of deuterons (or protons) emerging from a carbon foil. This result is discussed in the frame of the kinetic model proposed recently by Kreussler and Sizmann for calculating ${\phi }_0$ and some information concerning the ratio of atomic cross sections for the production and destruction of $\mathrm{np}$ states will be tentatively deduced. At energies $E<\mathrm{}200\mathrm{}$ keV/amu, the behavior of the excitation functions of $\mathrm{np}$ terms ($n=2-4\mathrm{}$) is compatible with a decrease of the ratio of the $\mathrm{np}$ population to the ground-state population with respect to that ratio at higher energies. The relation $N_{2p}\mathrm{}\left(v\right)={\mathrm{Cv}}^{\frac{1}{2}}{\phi }_0\mathrm{}\left(v\right)\mathrm{}$ ($C$ being a normalization constant) fits very well the $2p$ population results in the energy range 10—200 keV/amu.

The ground-state—ground-state mechanical and radiative electron-capture processes are studied at very high, but not relativistic, projectile velocities. Three-body calculations were carried out with use of the continuum distorted-wave theoretical method for both processes. Total cross sections and final-atom angular distributions were computed, and the importance of each mechanism examined. For total cross sections, the numerical results reaffirm that the radiative process is the predominant mechanism at very high projectile energies. For a given incident charge, the range of projectile energies in which the nonrelativistic radiative mechanism is the most important decreases as the target charge increases. It is found that the radiative mechanism produces a very sharp final-atom angular distribution in the forward direction. When both processes, the radiative and mechanical, give the same total cross section, the calculations show that the radiative differential cross section in the forward direction is almost 2 orders of magnitude larger than the mechanical one.

We have observed beryllium $K$-shell Auger electrons from clean Be surfaces bombarded by 2.5—10-keV Ne, Ar, and Kr ions at 45° incidence. The electron spectra show a broad structure similar, although not identical, to that observed under electron impact, which was assigned to the $\mathrm{KVV}$ transition from excited Be decaying in the bulk of the solid. A small sharp line is identified to result from the decay in vacuum of neutral $\mathrm{Be}\left(1s{2s}^{2}2p\right)$ sputtered from the solid. The Auger yields can be scaled when plotted against the maximum energy transfer in a projectile-Be collision, indicating that excitations occur mainly from symmetric collisions between target atoms. This is supported by Monte Carlo simulations of the atomic collision cascade in the solid. We have applied these simulations to evaluate the relative role of symmetric and asymmetric collisions in early measurements of Be $K$ x-ray yields, at higher energies. By comparing experimental and simulated results, we obtained information about the variations of the fluorescence yields and outer-shell occupation numbers with projectile energy.

Following an idea of Rankin and Thorson, a method is proposed to determine translation factors in the molecular model of atomic collisions, and for low and intermediate nuclear velocities. The method is based on the minimization of a measure of all (electrostatic and dynamical) couplings between the states included in, and those left out from, the molecular expansion. The properties of this measure are discussed. In particular, its evaluation involves the calculation of a few new matrix elements, and this can be performed analytically when Gaussian-type orbitals are used to construct the wave functions. The method also provides a comparison between all approaches that employ translation factors, and a test of the conditions that are usually enforced on these factors.