The integral equation originally derived by Sharp and Horton for the optimized effective potential (OEP) is exactly transformed into an equivalent form from which it is manifestly clear that the OEP, ${\mathit{V}}_{\mathit{x}\mathrm{\sigma }}^0$(r), is an implicit functional of only {${\mathit{n}}_{\mathit{i}\mathrm{\sigma }}$}, the orbital densities of the occupied states {${\mathrm{\psi }}_{\mathit{i}\mathrm{\sigma }}$}, and the corresponding single-particle exchange potentials {${\mathit{v}}_{\mathit{i}\mathrm{\sigma }}$}. Furthermore, the transformed OEP has exactly the same form as one recently developed by the authors [Phys. Rev. A 45, 101 (1992)] from a more heuristic approach, the only difference being that in the present work a term proportional to the gradient of ${\mathit{n}}_{\mathit{i}\mathrm{\sigma }}$ is added to each ${\mathit{v}}_{\mathit{i}\mathrm{\sigma }}$ whose average value when taken over the iσ state is zero. This result leads to the natural development of an iterative approximation for ${\mathit{V}}_{\mathit{x}\mathrm{\sigma }}^0$, with the zeroth approximation being given by our previous result. The application of this technique to the calculation of the total energy and highest-energy single-particle eigenvalue for selected atoms is presented. In addition, we note that our results are applicable to the calculation of the OEP for any assumed exchange-correlation functional ${\mathit{E}}_{\mathrm{xc}}$[{${\mathrm{\psi }}_{\mathit{i}\mathrm{\sigma }}$}], where ${\mathit{v}}_{\mathit{i}\mathrm{\sigma }}$ is taken as the appropriate functional derivative of ${\mathit{E}}_{\mathrm{xc}}$. In the case that ${\mathit{E}}_{\mathrm{xc}}$ is a functional of {${\mathit{n}}_{\mathit{i}\mathrm{\sigma }}$} only, as in the case of the local-density approximation with self-interaction correction, the resulting ${\mathit{V}}_{\mathrm{xc}\mathrm{\sigma }}^0$ is a functional of the {${\mathit{n}}_{\mathit{i}\mathrm{\sigma }}$} only.

A formulation of the spin-coupled model (a generalized valence-bond model) for calculating wave functions based on the use of nonorthogonal orbitals is presented, permitting ground, valence excited, multiply excited, and core-valence excited states to be obtained using a first-order iterative scheme. A primary goal is to provide a simple single-configurational model combining visuality (e.g., readily yielding the one-particle density function) with accuracy, while allowing the variational minimum of the single-configuration function for a given basis set to be obtained automatically for almost any kind of state. The theory and its application to the ground-state properties of He, Li, and Be are presented here using even-tempered and Clementi-Roetti basis sets. Uniform scaling of the basis exponents leads to closely parallel energy profiles for both spin-coupled and full configuration-interaction (FCI) calculations. The difference in energies as a function of scale factor is considerably smaller than the corresponding difference between restricted Hartree-Fock and FCI calculations. Each energy profile displays a global minimum and one or more local minima, and, for the associated values of the scale factor, the calculated atomic properties show little variation in magnitude.

The variation-perturbation approach with a time-dependent electric field is used in order to obtain the third-order energy and to find the first hyperpolarizability with the first-order perturbed function. The function used is the same as the one described in a previous paper [M. Rérat, M. Merawa, and C. Pouchan, Phys. Rev. A 45, 6263 (1992)] relative to dynamic-polarizability calculation from a time-dependent gauge-invariant method. Static-hyperpolarizability components are given for FH and LiH and discussed in comparison with previous calculations. Dynamic components are calculated for the electro-optic Pockels effect up to the first resonances.

Many-body perturbation-theory formulas are derived for one-particle–one-hole excited states of closed-shell atoms. Both analytic results and Goldstone diagrams complete through third order are presented, and a sample calculation of a transition energy in neonlike xenon is carried out.

A single-channel quantum-defect theory for the doubly excited states of helium is formulated in hyperspherical coordinates. For doubly excited states associated with each excited ${\mathrm{He}}^{+}$(N) threshold, the outer electron experiences asymptotically a combined Coulomb and dipole potential, -1/R+α/${\mathit{R}}^2$. The two independent solutions in the asymptotic region for energies below and above the threshold are explicitly given for both the attractive and the repulsive dipole potentials. Quantum defects for ${}_{}{}^1{}_{}{}^{}$P° doubly excited states of five channels in the N=3 manifold and of the dominant channels below the N=2, 3, and 4 thresholds of ${\mathrm{He}}^{+}$ are calculated in a single-channel hyperspherical potential, and the results are compared with quantum defects extracted from other theoretical calculations and recent experimental results. Procedures for obtaining diabatic curves from the adiabatic potentials are also discussed.

A semiclassical expression is derived for the potential seen by an nl-shell electron in a nonhydrogenic ion. Corresponding energies ${\mathit{E}}_{\mathit{n}\mathit{l}}$ are compared with experimental values and with results of self-consistent-field calculations.

A semiclassical formula for dipole matrix elements of single-electron nl→n’l’ transitions with arbitrary quantum numbers in nonhydrogenic ions is derived. Only the energies and angular momenta of the initial and final states are needed as input along with the charge of the ion. The definition of the intermediate state is a key element in the derivation. Results are compared with experimental values and self-consistent-field calculations for Na-like ions. The formula is shown to coincide with the exact quantum-mechanical result for hydrogen in the limit n’≫n≫1, l≪n.

The effect of the inelastic electron-electron interaction (two-center scattering) in the probability of electron loss (antiscreening effect) is studied using the time-dependent semiclassical approximation. The antiscreening probability is determined and expressed in terms of the usual semiclassical amplitudes. A case study is performed, showing that a classical view of the antiscreening effect can be used to describe the main features of this projectile ionization mode.

A technique for evaluating cross sections for two-electron excitation in collisions of atoms with fast particles of charge ${\mathit{Z}}_{\mathit{p}}$ is presented. The atomic wave function is approximated by a sum of pair products of one-electron wave functions, with the coefficients chosen by diagonalizing the fully correlated two-electron Hamiltonian. Thus spatial correlation is included in both the asymptotic and scattering regions by using these configuration-interaction (CI) wave functions for initial, intermediate, and final states. Use of CI wave function also allows the first-order contributions to be expressed in closed, analytical form. Both the energy-conserving and energy-nonconserving parts of the second-order amplitude are evaluated. The former (a correlated generalization of the independent-electron approximation) is analytical and the latter is a one-dimensional integral. In helium it is found that the double-excitation cross sections are sensitive to the sign of the projectile charge, but that the energy region where this sensitivity is of the same order as for double ionization is 0.1 to 0.5 MeV/amu, whereas the latter has peak charge sensitivity at 1.5 MeV/amu. Comparison is made with some experimental results.

Differential cross sections of the second-order Born approximation are calculated exactly for particle transfer to 1s, 2s, and 2p states of exotic atoms. The processes can be classified into three types. In the collision of p+(p${\mathrm{\mu }}^{\mathrm{-}}$), the Thomas process [Proc. R. Soc. London 114, 561 (1927)] takes place only via a single path as in the proton-hydrogen case, while, in the collision of ${\mathrm{\mu }}^{+}$+(p${\mathrm{\mu }}^{\mathrm{-}}$), it can proceed via two paths that interfere destructively or constructively depending on the parity of the final state as in the positronium formation from a hydrogen atom. In the third type, in which all the three particles have an equal mass as in positron-positronium collisions, the critical angle occurs at 180° only and the two second-order terms which are forbidden in classical mechanics are contributing significantly to the backscattering.

The distorted atomic-orbital method, proposed by Kobayashi, Ishihara, and Toshima [Muon Catalyzed Fusion 2, 191 (1988)], is applied to low-energy ion-atomic collisions. This method is free from the difficulty of spurious couplings. The basic idea of the method is discussed in detail. An iterative method for the numerical calculation is developed and, as an example, a quantum-mechanical calculation of ${\mathrm{He}}^{2+}$+H collisions for incident energy ${\mathit{E}}_{\mathit{i}}$≤200 eV is carried out. The calculated cross section connects naturally to those obtained from a corresponding semiclassical calculation for ${\mathit{E}}_{\mathit{i}}$≥200 eV [T. G. Winter and G. J. Hatton, Phys. Rev. A 21, 793 (1980)].

Double ionization of helium is investigated for 60-, 120-, and 420-MeV/u (v/c=0.34–0.72)${\mathrm{U}}^{90+}$-ion impact. The measured double-to-single ionization ratios indicate that, even for these very high velocities, double ionization of the He target results predominantly from independent interactions of the projectile with both target electrons. It is concluded that the asymptotic high-velocity regime for one-step double ionization (i.e., ‘‘shakeoff’’) has not yet been reached even for ${\mathrm{U}}^{90+}$ projectiles at 420 MeV/u, and, in fact, cannot be reached for projectiles with q≳7, thereby verifying that the ionic charge is fully as important as the velocity in determining the importance of a given ionization mechanism.

He ii–excited inner-valence photoelectron spectra of the nitrogen molecule have been recorded between 23 and 35 eV using a spectrometer resolution of better than 20 meV. In this range several photoelectron bands associated with transitions to cationic states are observed. Extensive vibrational structure has been observed in three bands, two in the (23–27)-eV range, and the third in the (31–32)-eV range. For the well-known ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ state, a substantial potential barrier towards dissociation has been found. The second vibrational progression in the (23–27)-eV range has very small vibrational spacings, on the order of 86 meV, and is associated with the second state of ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathit{g}}^{}{}_{}{}^{}$ symmetry. Transitions to the first state of this symmetry, D ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathrm{g}}^{}{}_{}{}^{}$, are found to give rise to a continuous band above the dissociation threshold. The third vibrational progression is tentatively assigned to the 3 ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{+}{}_{}{}^{}$ state. The assignments are supported by complete-active-space self-consistent-field and multireference configuration-interaction calculations on the D ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathrm{g}}^{}{}_{}{}^{}$, 2 ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathit{g}}^{}{}_{}{}^{}$, F ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$, and 3 ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{+}{}_{}{}^{}$ states, and potential curves have been computed in good agreement with the observations.

The collision dynamics in the ${\mathrm{H}}^{+}$+H system is considered at low relative velocities within the concept of hidden adiabatic energy crossings in the complex plane of internuclear distance. Detailed information is provided on the topology of all series of hidden crossings in this system which are involved in the transitions between the states with principal quantum numbers n≤4 and in the promotion of these states into the continuum. This information is used to perform cross-section calculations for the 1s→nl (n=2–4), n=2→n=3,4, and n=3→n=4 excitation transitions and for ionization from the n=1, 2, and 3 levels in the adiabatic energy region.

The photoionization branching ratio for double ionization has been measured from threshold to 800 eV for Ne and from threshold to 560 eV for He. Both sets of data have an initial rise from threshold, in general agreement with other published results, but the Ne data reach a plateau value above threshold in contrast to some of the other measurements and to the He data. The Ne data reach a value of approximately 13%, while the He data approach a value of approximately 4% before decreasing. A plateau in the He data was not reached in our measurements but may exist at higher energies. The photoionization cross section for double ionization has been extracted from the branching-ratio data.

We have measured the intensities and polarizations of fine-structure lines in the N=9-8 manifolds of Ne viii and Ar viii spectra produced in collisions of ${\mathrm{Ne}}^{8+}$ and ${\mathrm{Ar}}^{8+}$ (v=0.05–0.15 a.u.) with atomic sodium, and determined alignment and partial cross sections for electron capture as functions of projectile velocity. At low velocity the partial cross section for capture into the S levels is significantly higher than for capture into higher L levels, and at higher velocities the higher-L partial cross sections increase for Ar viii and dominate for Ne viii. The low-L-level cross sections are in fair agreement with multichannel-Landau-Zener calculations, while the high-L-level cross sections are in qualitative disagreement. For the neon projectiles, the polarization of the Bohr line is approximately 0.3 and independent of velocity; for argon projectiles, the polarization is approximately 0.15 and increases with increasing velocity. A qualitative theoretical interpretation is offered.

Theoretical and experimental studies show the strong influence of the three-photon nearly resonant 2p state on four- and five-photon ionization of atomic hydrogen near the threshold for four-photon ionization. Changes in five-photon ionization occur when the four-photon ionization channel opens. The angular distributions of photoelectrons from five-photon ionization of H are studied at five wavelengths which cover the range from four-photon resonance with high-lying Rydberg states (n≥10) to direct four-photon ionization into the continuum. The role of resonances in this ionization process is discussed. A fair agreement is found in comparing experimental and theoretical results.

Near-threshold single-photon photodetachment processes are considered for simple model systems representing negative ions exposed to monochromatic radiation. The model systems considered feature an initial discrete state, the photoelectron continuum, and in some cases an excited or autodetaching discrete state. Population trapping through the formation of a bound dressed state and the photoelectron spectra are examined. Two photoelectron spectra are defined : a primary spectrum which results from decay while the laser interaction is on and a secondary spectrum which results from the destabilization of the bound dressed state if the interaction is turned off again. Careful attention is given to the passage of the poles of the Green’s operator through the low-energy boundary of a continuum, and it is concluded that such poles move nonmonotonically through the boundary of an s-wave continuum, but monotonically through the boundary of a p-wave or higher-l-wave continuum. Two example systems, one featuring a single discrete state and an s-wave continuum and one featuring two discrete states and a p-wave continuum, are considered in detail.

We complement previous work that showed that the molecular approach, modified with plane-wave translation factors, is able to reproduce the fall of charge-exchange cross sections in ${\mathrm{He}}^{2+}$+H collisions, by presenting the molecular data, and studying the corresponding mechanism. We test the accuracy of simplifications of the method that have been employed in the literature, and that lead to very simple calculations. We show that the common-translation-factor method is also successful at high nuclear velocities, provided that sufficiently excited states are included in the basis; moreover, it yields a simple picture of the mechanism and a description of ionization processes at high velocities.

Multielectron transfer probabilities in 90-keV ${\mathrm{Ne}}^{9+}$-Ne collisions have been measured with respect to the projectile scattering angle θ in a range between θ=12 and 75 mrad. The projectile final charge state was determined in coincidence with the target-ion final charge state using a time-of-flight technique. For θ>45 mrad, projectile and target undergo a complete equilibration of their atomic shells (including the K shell) leading to the excitation of both collision partners and the autoionization of three electrons on average. A comparison of the measured final charge-state distributions of projectile and target with those obtained in a former experiment with the system 90-keV ${\mathrm{Ne}}^{7+}$-Ne [H. Schmidt-Böcking et al., Phys. Rev. A 37, 4640 (1989)] leads to the conclusion that L- and K-shell charge transfer can be treated as independent processes. Interference structure in the K-K vacancy-transfer probabilities has been observed in the final charge-state probabilities of the ‘‘heavy-ion’’–atom system.