We study doubly excited ridge states using hyperspherical coordinates. Viewing the two electrons as a pair, as we did for ${}_{}{}^1{}_{}{}^{}$S states in a previous paper [Phys. Rev. A 46, 6933 (1992)], here we extend to the L=1 states. By diagonalizing the potential energy within manifolds of fixed grand angular momentum, we get simple, even analytical, expressions for the effective charge. Upper bounds for the energies of the L=1 states are derived through the Runge-Kutta numerical procedure.

Autoionizing multiply excited states offer unusual challenges to the theory of electronic structure and spectra because of the presence of strong electron correlations, of their occasional weak binding, of their proximity to more than one threshold, and of their degeneracy with many continua. Here we discuss a theory that addresses these difficulties in conjunction with the computation of their wave functions and intrinsic properties. Emphasis is given on the justification of the possible presence of self-consistently obtained open-channel-like (OCL) correlating configurations in the square-integrable representation of such states and on their effect on the energy E and the width Γ. Application of the theory has allowed the prediction of two hitherto unknown ${\mathrm{He}}^{\mathrm{-}}$ triply excited resonances, the 2s2${\mathit{p}}^2$ ${}_{}{}^2{}_{}{}^{}$P (E=59.71 eV, above the He ground state, Γ=79 meV) and the 2${\mathit{p}}^3$ ${}_{}{}^2{}_{}{}^{}$${\mathit{D}}^{\mathit{o}}$ (E=59.46 eV, Γ=282 meV) (1 a.u.=27.2116 eV). These resonances are above the singly excited states of He and are embedded in its doubly excited spectrum. The relatively broad 2${\mathit{p}}^3$ ${}_{}{}^2{}_{}{}^{}$${\mathit{D}}^{\mathit{o}}$ state interacts strongly with the He 2s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ εd continuum. The effect of this interaction has been studied in terms of the coupling with fixed core scattering states as well as with a self-consistently computed OCL bound configuration.

The position of the ${\mathrm{He}}^{\mathrm{-}}$ 2${\mathit{p}}^3$ ${}_{}{}^2{}_{}{}^{}$${\mathit{D}}^{\mathit{o}}$ resonance is below that of the He 2${\mathit{p}}^2$ ${}_{}{}^1{}_{}{}^{}$D autoionizing state at 59.91 eV and of the He 2${\mathit{p}}^2$ ${}_{}{}^3{}_{}{}^{}$P bound state at 59.68 eV. The partial decay widths to the three important open channels are γ(2s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$)=252 meV, γ(1s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$)=21 meV, γ(1s2p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$)=9 meV. The final core states are also represented by correlated (multiconfigurational Hartree-Fock) functions. The 2s2${\mathit{p}}^2$ ${}_{}{}^2{}_{}{}^{}$P state couples to four neighboring He thresholds, the 2s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$, 2${\mathit{p}}^2$ ${}_{}{}^3{}_{}{}^{}$P, ${}_{}{}^1{}_{}{}^{}$D, and 2s2p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$. It is above the He 2s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ threshold at 58.31 eV, with respect to which it is a valence shape resonance, and below the He 2${\mathit{p}}^2$ ${}_{}{}^1{}_{}{}^{}$D and 2s2p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ autoionizing states. In the limit of an exact energy calculation, we suggest that its position would also come below that of the 2${\mathit{p}}^2$ ${}_{}{}^3{}_{}{}^{}$P state, which it overlaps. Its partial widths are γ(2s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$)=60 meV, γ(1s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$)=9 meV, γ(1s2p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$)=10 meV. The present results, considered together with published ones on other n=2 intrashell states, show that the recently measured [R. N. Gosselin and P. Marmet, Phys. Rev. A 41, 1335 (1990)] closely lying structures at 58.415 and 58.48 eV cannot correspond to the ${\mathrm{He}}^{\mathrm{-}}$ 2${\mathit{p}}^3$ ${}_{}{}^4{}_{}{}^{}$${\mathit{S}}^{\mathit{o}}$ and ${}_{}{}^2{}_{}{}^{}$${\mathit{D}}^{\mathit{o}}$ states, as these authors proposed.

We have studied two different systems producing resonances, a highly excited multielectron Coulombic negative ion (the ${\mathrm{He}}^{\mathrm{-}}$ 2s2${\mathit{p}}^2$ ${}_{}{}^4{}_{}{}^{}$P state) and a hydrogen atom in a magnetic field, via the complex-coordinate rotation (CCR) and the state-specific complex-eigenvalue Schrödinger equation (CESE) approaches. For the ${\mathrm{He}}^{\mathrm{-}}$ 2s2${\mathit{p}}^2$ ${}_{}{}^4{}_{}{}^{}$P resonance, a series of large CCR calculations, up to 353 basis functions with explicit ${\mathit{r}}_{\mathit{i}\mathit{j}}$ dependence, were carried out to serve as benchmarks. For the magnetic-field problem, the CCR results were taken from the literature. Comparison shows that the state-specific CESE theory allows the physics of the problem to be incorporated systematically while keeping the overall size of the computation tractable regardless of the number of electrons.

The spectrum of four-times-ionized krypton, Kr v, has been observed in the vuv region using a θ-pinch as a light source. The 4s4${\mathit{p}}^{3\mathrm{-}}$4${\mathit{p}}^4$ transition array has been observed in this ion. This transition has not previously been observed in the Ge i isoelectronic sequence. Thirteen lines were classified that belong to this transition array. All levels of the 4${\mathit{p}}^4$ configuration were determined. The identifications are supported by relativistic Hartree-Fock calculations.

Doubly excited ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ autoionizing states in He below the N=2 and N=3 thresholds of ${\mathrm{He}}^{+}$ ions are calculated by use of a method of complex-coordinate rotation. Hylleraas-type wave functions are used to calculate resonance parameters for intrashell states (the two electrons occupy the same shell) and other low-lying states, and products of Slater orbitals are used for high-lying intershell states (the two electrons occupy different shells). A total of 16 resonances below the N=2 ${\mathrm{He}}^{+}$ thresholds are reported in this work. This includes seven members in the 2${\mathit{snp}}_{+}$ (2≤n≤8) series, five members in the 2${\mathit{snp}}_{\mathrm{-}}$ (3≤n≤7) series, and four members in the 2pnd (3≤n≤6) series. A total of 19 resonances below the N=3 ${\mathrm{He}}^{+}$ threshold are also reported here. Using the (KTNn) notation, the present work includes five members in the (203n) series with (3≤n≤7), five members in the (003n) series (3≤n≤7), four members in the (113n) series (4≤n≤7), three members in the (-113n) series (4≤n≤6), and two members in the (-203n) series (4≤n≤5). Comparisons are made with other theoretical calculations.

The excitation energies of the 3d4p ${}_{}{}^3{}_{}{}^{}$${\mathit{F}}^{\mathit{o}}$, 4s4f ${}_{}{}^3{}_{}{}^{}$${\mathit{F}}^{\mathit{o}}$, 3d4p ${}_{}{}^1{}_{}{}^{}$${\mathit{F}}^{\mathit{o}}$, and 4s4f ${}_{}{}^1{}_{}{}^{}$${\mathit{F}}^{\mathit{o}}$ states relative to the ground state 4${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$S and the ground-state ionization potential of neutral calcium (Ca i) are calculated using a finite-element multiconfiguration Hartree-Fock method, through the use of a systematic sequence of active spaces of increasing size. It is confirmed, through large-scale ab initio calculations, that a wrong position of the 3d4p perturber in the ${}_{}{}^1{}_{}{}^{}$${\mathit{F}}^{\mathit{o}}$ series, found in valence multiconfiguration Hartree-Fock calculations, is due to the missing core-valence correlation. Some interference effects between core-valence and core-core correlation effects are also analyzed.

A generalized deformed oscillator giving the same spectrum as the Morse potential is constructed through the use of quantum-algebraic techniques. The model of n coupled anharmonic oscillators of Iachello and Oss [Phys. Rev. Lett. 66, 2976 (1991)], suitable for the description of vibrational spectra of polyatomic molecules, is subsequently written in terms of such generalized deformed oscillators. In addition to clarifying the relation of the model of Iachello and Oss to other models using coupled oscillators for the description of vibrational molecular spectra, the present formalism allows for the construction of a large class of exactly soluble models with no extra computational effort. As an example, the way of including a coupling of the Darling-Dennison type is shown.

We report investigations of one- and two-electron processes in the collisions of 0.9-keV/u to 60-keV/u (${\mathit{v}}_{\mathit{p}}$=0.19–1.55 a.u.) ${\mathrm{Ar}}^{16+}$ ions with He targets. The cross sections for these processes were measured by observing the final charges of the Ar ions and the recoiling target ions in coincidence. The average Q values for the capture channels were determined by measuring the longitudinal momenta of the recoiling target ions. Single capture (SC) is the dominant process and is relatively independent of the projectile energy. The two-electron transfer-ionization (TI) process is the next largest and slowly increases with projectile energy. The Q values for both SC and TI decrease with increasing projectile energy. Our data thereby suggest that electrons are captured into less tightly bound states as the collision velocity is increased. Both double capture and single ionization are much smaller and fairly independent of the projectile energy. The energy independence of SI is somewhat surprising as our energy range spans the region of the target electron velocity where ionization would be expected to increase. Our analysis suggests that the ionization process is being suppressed by SC and TI processes.

We have studied the real-time dynamics of dissipative tunneling between two coupled diabatic surfaces. The interplay of tunneling, vibrational relaxation, dephasing, and resonances leads to various regimes of population dynamics, from coherent oscillations between the surfaces to exponential decay described by a rate constant. To describe these phenomena, we exploited recent efficient discretized-path-integral techniques; the two-surface system is treated exactly using a numerically constructed propagator, while the effects of the dissipative environment are incorporated through an influence functional. This procedure results in a low-dimensional integral, which is evaluated by quadrature. Use of a discrete-variable representation (DVR) allows us to replace continuous paths by paths that sample a small set of coordinate points; in particular, the conventional two-level-system approximation is shown to correspond to the limit of two DVR points. The specific features pertinent to nonadiabatic tunneling are discussed.

The results of an experimental spectroscopic study of the 3pnp ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}^{\mathit{e}}$ (n=3–6) and 3p4f ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{e}}$ autoionizing states of Mg populated via two-photon absorption are presented and compared with those of different recent theoretical calculations. The study includes excitation spectra and electron angular distributions resulting from the autoionization decay. Photoelectron angular distributions following resonantly enhanced multiphoton ionization via the 3s3p ${}_{}{}^1{}_{}{}^{}$P, 3s4s ${}_{}{}^1{}_{}{}^{}$S, and 3s3d ${}_{}{}^1{}_{}{}^{}$D intermediate states are also reported and discussed. A strong observed single-photon excitation of the 3s3d ${}_{}{}^1{}_{}{}^{}$D state via an electric quadrupole transition is also presented.

The radiation emitted from ions excited by a directed electron beam can be strongly linearly polarized. According to Itikawa, Srivastava, and Sakimoto [Phys. Rev. A. 44, 7195 (1991)] the degree of polarization should be independent of atomic number in an isoelectronic sequence when expressed as a function of incident-electron energy in threshold units. We used a distorted-wave computer code to calculate cross sections for electron-impact excitation to specific magnetic sublevels of H- and He-like ions with Z=13, 18, 22, 42, 56, 79, and 92. We found that the polarization of the resulting radiation is indeed independent of atomic number in the nonrelativistic limit. But when relativistic effects are properly taken into account, the polarization is markedly Z dependent. We show how the differences between the relativistic and nonrelativistic results vary with the incident-electron energy, as well as with increasing atomic number.

Electron capture in collisions of ${\mathrm{O}}^{5+}$ ions with H atoms is investigated theoretically by using a semiclassical molecular-orbital method in the energy range from 6 eV/amu to 10 keV/amu. Electron translation effects are properly included (to the first order of relative velocity). The primary contributors to electron capture are ${\mathrm{O}}^{4+}$(2s4l) states. However, two-electron transfer-excitation processes are also important in the entire energy range studied. The contribution from these processes amounts to 50% of the total at 1 keV/amu; it remains at 27% even at studied energy as low as 6 eV/amu. The ${\mathrm{O}}^{4+}$(2p3p ${}_{}{}^3{}_{}{}^{}$S) and ${\mathrm{O}}^{4+}$(2p3d ${}_{}{}^3{}_{}{}^{}$P) states for the triplet and the ${\mathrm{O}}^{4+}$(2p3p ${}_{}{}^1{}_{}{}^{}$S) state for the singlet contribute dominantly to the transfer-excitation process at low collision energies. Results of an analysis based on polarization parameters for electron capture are reported.

Electron capture in close, energetic collisions between protons and Ar atoms is studied. As the proton energy is varied across the 1859.7-keV ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$(p,p${)}^{40}$Ar elastic nuclear resonance at a fixed deflection angle of 60°, a dip of about 27% in the atomic-electron-capture probability is found, demonstrating the influence of the nuclear process on the atomic-charge exchange. The effect is very large considering that the similar dip found in the probability for scattering the proton without capture is only about 37%. A systematic comparison with previously reported capture probabilities for other elastic reactions has been made.

Electron capture in ${\mathrm{H}}^{+}$+${\mathrm{N}}_2$ collisions is studied at small scattering angles and energies in the range from 0.5 to 3.0 keV. The important collision processes are identified using time-of-flight techniques for energy analysis. Our results show that the quasiresonant ${\mathrm{H}}^{+}$+${\mathrm{N}}_2$→H(1s)+${\mathrm{N}}_2^{+}$(X) channel dominates the electron capture only at the smallest angles. As an example, at 1.0 keV, capture to this channel occurs with a probability less than 0.5 for scattering angles beyond 0.7°. The reduced cross section for excitation of the quasiresonant channel shows a maximum which moves to larger reduced scattering angles with increasing projectile energy. A second important process, populating H(1s)+${\mathrm{N}}_2^{+}$(C) is found. Although the excitation of this channel involves a multielectron rearrangement it is found to dominate over the ‘‘one-electron’’ ${\mathrm{H}}^{\mathrm{*}}$(n=2)+${\mathrm{N}}_2^{+}$(X) channel which lies close in energy. We also find that the electron capture, even at small scattering angles, can generate highly excited ${\mathrm{N}}_2^{+}$ states.

The radiative-recombination rate coefficients for electrons impinging on ${\mathrm{Li}}^{+}$, along with the associated excited-state photoionization cross sections for Li, are calculated in the low-energy region. In addition to the totals, the contribution of the recombination of individual excited states to the total is discussed.

Theoretical results for ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{4+}{}_{}{}^{}$-H(2s) and ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}_{}^{5+}{}_{}{}^{}$-H(2s) partial and total charge-exchange cross sections at low relative velocities (0.027–0.32 a.u.) are given, using the Landau-Zener method. The necessary molecular parameters for this method are obtained from the exact one-electron diatomic molecule (OEDM) molecular energies. The partial cross sections which are mainly populated are those corresponding to the principal quantum number of separated atoms n=5 for ${\mathrm{Be}}^{3+}$ and n=6 for ${\mathrm{B}}^{4+}$. The total cross sections show a rather strong increase with increasing collision energies and a quite large maximum. They lie between the cross sections corresponding to the neighbor reactions for the incident nuclei with Z=3 (Li), Z=6 (C), and Z=7 (N). The atomic collisions with beryllium are very important in plasma tokamaks.

We have studied the angular distributions of double-electron capture in ${\mathrm{C}}^{4+}$+He collisions in the 400–800-eV collision energy range. At all measured energies an interference pattern has been observed which is attributed to Stueckelberg oscillations. A comparison with calculated differential cross sections using a two-state diabatic potential matrix of Danared and Bárány [J. Phys. B 19, 3109 (1986)] shows a reasonable agreement at 800 eV, while at lower energies the calculations show a shift of the peak positions towards larger angles. An alternative model by Barat et al. [J. Phys. B 23, 2811 (1990)], developed for collisions in the keV range, was also employed and was found to agree less well with our data, succinctly illustrating the increasing sensitivity to the ‘‘exact’’ potential shape with decreasing collision energy.

Differential cross sections d${\mathrm{\sigma }}^{\mathit{q}+}$(E,cphi)/dΩ for multiple ionization of Ne and Ar by protons have been measured for final charge states q=1–6, impact energies E=0.4–3 MeV, and scattering angles cphi=0.28–6.5 mrad. Within these ranges of energies and scattering angles, the angular dependence of the differential cross section for single ionization at constant energy follows a power law, d${\mathrm{\sigma }}^{+}$/dΩ∝${\mathit{cphi}}^{\mathrm{-}\mathit{k}}$. The power k is found to be near 3.8 for Ne and 3.65 for Ar. A monotonic increase of all the multiple-ionization cross sections d${\mathrm{\sigma }}^{\mathit{q}+}$/dΩ, q≥2 relative to the single-ionization cross section d${\mathrm{\sigma }}^{+}$/dΩ, is observed for increasing scattering angle. This behavior is most likely due to the combined effect of two multiple-ionization mechanisms. At the most distant collisions, the multiple ionization is dominated by the direct removal of valence electrons by the projectile. At the closest collisions, inner-shell ionization, followed by vacancy cascades, adds to the production of high-charge states. For Ne, this interpretation is supported by qualitative agreement with a model calculation based on the assumption that the multiple ionization of each shell follows binomial statistics. Quantitative agreement between experiment and theory requires a more thorough analysis of the many-body problem.

We study the classical collisions of electrons with one-electron atoms or ions in a model where both electrons are restricted to spherical states. At negative total energy, we calculate the probability for bound motion of both electrons occurring—as opposed to undelayed direct or exchange scattering. At positive total energy, we calculate the probability for (e,2e) reactions. There is a finite threshold for the onset of (e,2e) reactions. Its value depends on the nuclear charge and can be deduced from a simple transcendental equation. The general behavior of the probability for (e,2e) reactions as a function of energy is quite similar to the results of quantum-mechanical calculations and to experimental data.

Total cross sections are reported for electron transfer and ionization from the K shell of neon atoms by proton impact at proton energies from 250 to 1500 keV using a coupled-Sturmian-pseudostate approach. This approach was recently generalized by Winter [Phys. Rev. A 47, 264 (1993)] to quasi-one-electron systems using an analytic Hartree-Fock potential and applied to proton-carbon collisions. After a binding-energy correction is made to the single-particle energy phase, the calculated p-Ne cross sections for both ionization and electron transfer agree with the experimental values of Ro/dbro et al. [Phys. Rev. A 19, 1936 (1979)] within the range of basis sensitivity.