The theories of Tsironis and Grigolini [Phys. Rev. Lett. 61, 7 (1988); Phys. Rev. A 38, 3749 (1988)] and of de la Rubia et al. [Phys. Rev. A 38, 3827 (1988)] are discussed. A comparision with a digital simulation is made, and interesting conclusions on the application of a ‘‘fluctuating potential’’ to bistable systems driven by strongly correlated noise are drawn.

We present a new coordinate-space model of spherically averaged exchange-hole functions in inhomogeneous systems that depends on local values of the density and its gradient and Laplacian, and also the kinetic energy density. Our model is completely nonempirical, incorporates the uniform-density electron gas and hydrogenic atom limits, and yields the proper 1/r asymptotic exchange potential in finite systems. Comparisons of model exchange energies, holes, and potentials with exact Hartree-Fock results in selected atoms are very encouraging.

The ground-state energy of helium is calculated to all orders in perturbation theory starting from a relativistic ‘‘no-pair’’ many-body Hamiltonian in which contributions of virtual electron-positron pairs are ignored. In this calculation only Coulomb interactions between the electrons are considered. Two all-order calculations are presented: one calculation is based on nuclear Coulomb-field orbitals and the second is based on Hartree-Fock orbitals. For each calculation the all-order equations of many-body perturbation theory are solved iteratively. The resulting numerical value for the ground-state energy from the Coulomb-field calculation is -2.903 856(1) a.u., while the Hartree-Fock calculation gives -2.903 855(2) a.u. Both of these values agree with that obtained by correcting the well-established nonrelativistic energy for lowest-order relativistic effects.

We present a detailed study of the classical and quantum mechanics of a strongly chaotic quartic oscillator. The topology of the motion is such that there is a channel in which one has good separation of time scales. Many quantum states are found to scar along these channels. An adiabatic breakup for the action of the periodic orbits based on adiabatic stability of orbits is used to derive an approximate, integrable Hamiltonian. Semiclassical quantization of this Hamiltonian yields accurate energies for all states scarred along the channels.

In a recent paper [Phys. Rev. A 37, 1087 (1988)] Gorceix and Indelicato study the difference between the multiconfiguration Dirac-Fock (MCDF) expectation value of the Lorentz and Coulomb gauge forms for the Breit interaction. After a slight rearrangement of their expressions, we have found that the difference can be written as a commutator with the full Hamiltonian. This commutator is nonvanishing due to projection operators onto positive energy states implicit in the MCDF approach and gives contributions O($Z^2$${\alpha }^2$). It is shown that the diagram involving the excitation of a single virtual electron-positron pair, which removes the discrepancy if the low-frequency limit is used also where it is not valid, does not do so for the proper frequency-dependent form and that a more detailed analysis is required.

The influence of a weak harmonic uniform electric field, switched on adiabatically, on a nonrelativistic hydrogenlike atom is examined. Each of the φ- and A-gauge first-order corrections to the wave function of a stationary state ‖N〉 is determined by a vector function that we denote ${\mathrm{v}}_N$ and ${\mathrm{w}}_N$, respectively. The absolute starting point of our calculations is Schwinger’s formula for the Coulomb Green’s function in momentum space. In the case of a bound state with definite angular momentum, we report a compact integral representation and also an explicit expression of the φ-gauge vector ${\mathrm{v}}_{\mathrm{nlm}}$, which are analogous to those of the corresponding A-gauge vector ${\mathrm{w}}_{\mathrm{nlm}}$ studied previously. We have derived compact analytic expressions of the linear-response vectors ${\mathrm{v}}_{n_{\xi }{n}_{\eta }m}$ and ${\mathrm{w}}_{n_{\xi }{n}_{\eta }m}$ associated to an arbitrary Stark state. These are written first as contour integrals, and then explicitly in terms of a new generalized hypergeometric function with five variables, ${}_2{}^{}{}_{}{}^{}\mathrm{\phi }_{\mathrm{H}}^{}{}_{}{}^{}$, which is a finite sum of Humbert functions ${\phi }_1$. We have calculated the static limit of the regular part of the vector ${\mathrm{v}}_{n_{\xi }{n}_{\eta }m}$. Also discussed are the Sturmian-function expansions of the linear-response vectors for angular momentum states.

By use of the linear-response-vectors method, the Kramers-Heisenberg matrix elements for arbitrary bound-bound transitions of a nonrelativistic hydrogenlike atom have been evaluated. To illustrate the discussion, Rayleigh and Raman scattering have been selected as relevant examples of second-order processes. We have derived, in a unitary manner, A- and φ-gauge compact analytic formulas, both for angular momentum and Stark states. Our results are expressed in terms of two new generalized hypergeometric functions with four variables, ${}_1{}^{}{}_{}{}^{}\mathrm{F}_{\mathrm{E}}^{}{}_{}{}^{}$ and ${}_2{}^{}{}_{}{}^{}\mathrm{F}_{\mathrm{E}}^{}{}_{}{}^{}$, which are finite sums of Gauss hypergeometric functions. Special attention is given to the two-photon transitions involving the atomic ground state. For angular momentum states, we mention the connection that we have established between our general results and earlier ones.

The damped harmonic oscillator is used to represent the damping processes in nature. Therefore it is necessary to find the Hamiltonian for the damped oscillator. The Hamiltonian is developed for the harmonic oscillator with frictional force proportional to velocity. The solution of the Schrödinger equation gives nonstationary states. The quantum friction coefficient is derived to be zero for massless particles. It is thought that velocity-dependent forces exist near the nucleus and therefore, the scattering amplitude for the deep inelastic process is derived.

The ground state of hydrogen in a magnetic field has been analyzed using the finite-element method. Accurate values for the binding energy have been obtained for fields up to ${10}^{12}$ G. Unlike other approaches, the computational effort required to obtain converged results is independent of the strength of the magnetic field. Values obtained for the lower bounds on the binding energy at very high fields are the most accurate to date.

A small electrostatic accelerator (65 kV) was built as a postaccelerator for measuring the charge-state fractions of ions backscattered from solid or gas targets. A new method is described in which the charge-state fractions of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ions backscattered from gold films are determined simultaneously. The added features in this work are the facts that the method can be efficiently used for low-energy incident ions and that spectra could be measured, compared, and analyzed by minimizing uncertainties inherent in experimental parameters. The energy dependence of the charge-state fractions of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ions are measured between 3 MeV and 150 keV. The ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ charge-state-fraction data nicely fit the Gaussian model but none of the ${\chi }^2$ models. The mean ion charge $i_m$ and the standard deviation s are also measured. Preliminary measurements of the dependence of the charge-state fractions on target thickness are also discussed.

A scheme of evaluating a generalized three-photon excitation cross section ${\sigma }_{\mathrm{}\left(3\right)\mathrm{}}$ in neutral atomic argon at 3144.67 Å is outlined. Three photons at this wavelength can excite the neutral argon atoms from the ground 3$p^6$ ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ state to the 3$p^5$4s’${[1/2]}_1^0$ state. The fourth photon will ionize the argon atoms. Assuming linear polarization of the incident laser radiation, contributions from several channels in various energy-level schemes are summed in the evaluation of the transition probability. For a laser linewidth of Δ${\lambda }_L$=1 Å, our maximum numerical value of the computed result for the three-photon excitation cross section is ${\sigma }_{\mathrm{}\left(3\right)\mathrm{}}$=1.414×${10}^{\mathrm{-}80}$ ${\mathrm{cm}}^6$ ${\mathrm{s}}^2$. .AE

Energy spectra of electrons resulting from collisions of bare ions ${\mathrm{C}}^{6+}$+${\mathrm{H}}_2$ and ${\mathrm{O}}^{8+}$+He are presented. A detailed analysis is given for those parts of the spectra that are due to two-electron capture into (3l,3l’) configurations of the He-like projectile ions and subsequent autoionization. Measured peaks are uniquely identified by comparison with existing theoretical calculations. Based on a detailed investigation, it is concluded that an influence of interference effects on the spectra cannot be identified. A quantitative fit of the spectra allows us to determine the population probabilities of the various states with (3l,3l’) configuration. We find a preferential population of states that can be characterized by a correlated electronic motion with the two electrons on opposite sides of the capturing ion and rotating in the same sense. This result is discussed in terms of a classical picture for the capturing process.

The discrete and continuous spectrum of atomic magnesium below the 3p${\mathrm{}}^2$${\mathit{P}}^{\mathrm{o}}$ ionization threshold has been investigated by a valence-shell frozen-core ${\mathit{L}}^2$ configuration-interaction calculation with a phenomenological polarization potential. The results presented include positions of bound and autoionizing levels, oscillator strengths and radiative lifetimes, the ground-state one- and two-photon ionization cross sections, and several observables of interest for long-range interaction and Zeeman-effect studies. In particular, the two-photon ionization cross section is discussed in the near-threshold region, where one experimental result is available for comparison

Doubly and singly differential cross sections for electron emission have been calculated by means of the classical trajectory Monte Carlo method for the $p^{+}$, $p^{\mathrm{-}}$, and ${\mathrm{He}}^{2+}$+He systems at impact energies of 50 and 100 keV/amu. The calculations for the $p^{+}$ and ${\mathrm{He}}^{2+}$+He systems exhibit the capture to the continuum peak and agree in both shape and magnitude with experimental data. Analysis of the classical trajectories has helped to understand the dynamical formation of this peak. The dependence of the cross sections on the projectile charge (-1, +1, and +2) is analyzed and compared with first-order scalings. It is concluded from this analysis that the combined influence of both the projectile and target Coulomb fields prevails over all the electronic spectra.

The thermally averaged depolarization cross sections, σ${¯}_D$(T), for Mu+${\mathrm{O}}_2$ electron spin exchange, have been measured by the muon spin relaxation (μSR) technique in a ${\mathrm{N}}_2$ moderator at total pressures near 1 atm over the temperature range 88–500 K. These values are related to the thermal spin-flip cross sections of interest (σ${¯}_{\mathrm{SF}}$) by a simple numerical factor. At temperatures ≳120 K, σ${¯}_D$(T) is essentially temperature independent [with σ${¯}_{\mathrm{SF}=(5.7\mathrm{}\pm 0.5)\times {10}^{\mathrm{-}16}}$ ${\mathrm{cm}}^2$], though exhibiting a slight tendency to increase with temperature. At lower temperatures, σ${¯}_{\mathrm{SF}(\mathrm{T}}$) decreases noticeably. Comparison with the only currently available theoretical calculations of Mu(H)+${\mathrm{O}}_2$ spin-flip cross sections by Aquilanti, Grossi, and Laganà [Hyperfine Interact. 8, 347 (1981)] on the potential-energy surface of Farantos et al. [Mol. Phys. 34, 947 (1977)] gives poor agreement with the data, particularly in their temperature dependence. The present results for σ${¯}_{\mathrm{SF}(\mathrm{T}}$) for Mu+${\mathrm{O}}_2$ qualitatively exhibit the same trend with temperature as found by Desaintfuscien and Audoin [Phys. Rev. A 13, 2070 (1976)] for H-H spin exchange over a comparable temperature range, but the H-H cross sections are, surprisingly, about four times larger. Comparisons with the experimental H+${\mathrm{O}}_2$ spin-exchange cross sections of Anderle et al. [Phys. Rev. A 23, 34 (1981)] and of Gordon et al. [JETP Lett. 17, 395 (1973)], indicate a significant isotope effect, with σ${¯}_{\mathrm{SF}\left(\mathrm{H}\right)\mathit{\gtrsim }1.5\mathit{\sigma }{¯}_{\mathrm{SF}}}$(Mu). While this effect can be qualitatively understood in terms of the differing numbers of partial waves involved, detailed theoretical calculations on more recent potential-energy surfaces for ${\mathrm{HO}}_2$ are called for.

Absolute K-shell x-ray production cross sections have been measured for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ ions in the energy range from 0.175 to 1.6 MeV/u incident on selected thin-foil targets from Ti (Z=22) through Ag (Z=47). A few measurements were made for incident ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ions at energies from 0.2 to 0.6 MeV/u in order to study the effects of Coulomb deflection and retardation. Newly measured values are also reported for incident protons at energies from 0.5 to 2.5 MeV on numerous target elements from Sc (Z=21) through Zn (Z=30). The x-ray production cross sections were determined from x-ray yields normalized to simultaneous measurements of particle-scattering yields at 75°. The K-shell ionization cross sections inferred from these results are compared with the predictions of the energy-loss Coulomb-deflection perturbed-stationary-state relativistic theory. There is agreement generally to within 10% although a systematic discrepancy, previously observed, is reproduced. Close agreement is obtained for protons with the reference values of Paul and Muhr [Phys. Rep. 135, 47 (1986)]. This investigation is part of an overall experimental-theoretical program whose goals are (1) to enlarge the data base of ion-induced x-ray production cross sections by establishing accurate experimental values and (2) to determine the limitations of the current theoretical descriptions of the inner-shell ionization process and their ability to calculate experimental quantities precisely.

We have investigated the contributions of excitation-autoionization and resonant-excitation-double-autoionization indirect-ionization processes to the electron-impact ionization of ${\mathrm{Fe}}^{15+}$ using a close-coupling approximation. The total ionization cross sections are obtained by adding the cross sections for these indirect processes to the direct-ionization cross sections. Eleven autoionizing levels arising from the 2$p^5$3$s^2$, 2$p^5$3s3p, 2$p^5$3$p^2$, and 2$p^5$3s3d configurations, together with the ground 2$p^6$3s state, are included in the close-coupling expansion. Large numbers of bound terms of appropriate symmetry are included in the expansion to account for the resonant-excitation-double-autoionization process. The present results are in good agreement with the recent crossed-beam measurement.

Convoy electrons emitted in collisions of 100–340-keV protons with a Si(111) surface at grazing incidence are investigated. The observed cusp shape in the electron spectra is significantly broadened in comparison to that observed in ion-atom and beam-foil interaction. We attribute this broadening to a deviation from the Coulombic final-state interaction near the surface due to the image potential.

Partial cross sections and angular-distribution asymmetry parameters were measured for subshell photoionization of xenon for photon energies between 40 and 1000 eV. These large-scale measurements show that the pronounced interchannel coupling between the valence and the 4d electrons persists beyond the 4d shape resonance in the subsequent Cooper-minimum region. Multielectron processes associated with 4d and 4p photoemission were measured directly for the first time over a broader energy range covering the near-threshold behavior up to the sudden limit. Comparing our experimental results with calculations based on the single-particle model shows that this theory, which fails to describe the intermediate energy range even qualitatively for the valence electrons, gives partial cross sections in reasonable agreement with experiment at higher photon energies, particularly beyond the 3d threshold. The same result is shown by the angular-distribution asymmetry parameter β, except for the photoionization of the ‘‘4p’’ subshell which resembles more the behavior of a 4d electron, corroborating the theoretical assumptions of core-hole fluctuations between these two subshells. In the shape resonance region the presented 4d partial cross sections are in reasonable agreement with theoretical results obtained recently by many-body perturbation theory.

We have measured the resonance-enhanced four-photon ionization of atomic hydrogen. The degenerate four-photon process occurs via a three-photon resonance between the 1s and the 2p levels, with subsequent one-photon ionization near threshold. We have studied the highly asymmetric resonance-enhanced profile, i.e., the photoion yield as a function of laser detuning from three-photon resonance between the 1s and 2p levels. In particular, we have determined the width, shift, peak, and asymmetry of the profile as a function of laser intensity. The experimental results are compared to theoretical models. These models involve both the properties of the atom in an intense near-resonant radiative field, and a detailed model for the multimode laser field, particularly the field fluctuations due to mode beating. The asymmetric resonance-enhanced photoionization profile is well reproduced by both a random-phase and a chaotic-light model.