We have used time-of-flight coincidence techniques to study multielectron reactions in 10-keV/u (v=0.632 a.u.) ${\mathrm{Ar}}^{\mathit{q}+}$ (5≤q≤17) on Ar collisions. Absolute cross sections for total charge-transfer (${\mathrm{\sigma }}_{\mathit{q}}$), projectile charge-change (${\mathrm{\sigma }}_{\mathit{q},}$${\mathit{q}}_{\mathrm{-}\mathit{k}}$), recoil production (${\mathrm{\sigma }}_{\mathit{q}}^{\mathit{i}}$), and phenomenological cross sections (${\mathrm{\sigma }}_{\mathit{q},}$${\mathit{q}}_{\mathrm{-}\mathit{k}}^{\mathit{i}}$) have been obtained by normalizing to cross sections reported in the literature [H. Klinger, A. Müller, and E. Salzborn, J. Phys. B 8, 230 (1975)]. The data have been used to critically test the predictions of the molecular classical overbarrier model (MCBM) [A. Niehaus, J. Phys. B 19, 2925 (1986)] and rather impressive agreements have been obtained. In particular, the predictions of target outer-shell excitation seem to have supporting evidence in this set of data. A stabilization scheme for the multiply excited projectile following charge transfer is proposed to complement the MCBM predictions and the gross features of the final reaction products are fairly accounted for. In addition, enhanced electron loss from the projectile-target system is observed in hard collisions for low-charged projectiles (q≤8) and is attributed to inner-shell excitation via molecular-orbital promotion.

We have calculated the energy and angular distributions for double ionization of He(1${\mathit{s}}^2$) and He(1s2s ${}_{}{}^3{}_{}{}^{}$S) by one photon, over a range of photon energies up to a few keV. The calculations were based on using a fairly accurate initial-state wave function, determined so as to exactly satisfy the Kato cusp conditions, and a final-state wave function which is a product of three Coulomb wave functions modified by a short-range correction term. There are at least three different mechanisms for double ionization, and each one leaves a mark on the angular distribution. When the energies of the two electrons are equal, the contribution of each mechanism to the angular asymmetry parameter can be estimated on theoretical grounds; we compare these estimates with the calculated results to give a further indication of the roles of the various mechanisms. Concerning the shapes of the energy and angular distributions, we find significant differences between double ionization of singlet and triplet helium; in particular, the probability for one high-energy photon to eject two equal-energy electrons from triplet helium nearly vanishes owing to the Pauli exclusion principle and to interference effects resulting from antisymmetrization. In two appendixes we present some details of the integration involved in the calculations.

A collision integral is derived that gives the rate of change of an electron distribution function due to ionizing collisions made by electrons with gas atoms. The treatment is valid for nonisotropic electron distribution functions. The development of the collision integral in this paper uses doubly differential cross sections (DDCS’s) for ionization since accurate analytical approximations for different target gases will be more easily available for DDCS’s than for the other cross sections that give a more complete description of the ionizing collisions. The treatment takes advantage of the inherent incompleteness in the description provided by the DDCS’s and reduces (the incompletely specified) three-body ionization problem into a set of two, fictitious, binary collision processes. These binary collisions are valid in mutually exclusive ranges of parameter space and complement each other in their contributions to the collision integral. The price for this simplification is that these binary collisions conserve neither kinetic energy nor orbital angular momentum. To handle this, the phase space of the gas atoms has been expanded by introducing fictitious scalar and vector parameters, which lend extra internal degrees of freedom to the atoms and destroy the isotropy of space. The overall approach is based on the treatment of S. Chapman and T. G. Cowling $[—The Mathematical Theory of Non-Uniform Gases (Cambridge University Press, London, 1952)].

The electron-Na system is the prototype for nonrelativistic scattering of a charged particle from a quasi-one-electron system. At scattering energies below several eV, e-Na cross sections are particularly sensitive to the exchange interaction and manifest a rich variety of near-threshold structures in various spin channels. By applying the nonperturbative coupled-channel R-matrix method in carefully converged calculations we have generated a comprehensive data base of accurate scattering quantities for studying these phenomena and for comparison to present and future experimental data. In particular, we examine elastic scattering and excitation of the 3p, 4s, 3d, and 4p excited states at energies from threshold to 8.6 eV. In addition to conventional integrated and differential cross sections, we consider partial cross sections for changes in the projection of the spin and orbital angular momentum of the Na valence electron, comparing results for all these quantities to experimental data where available.

Two-electron capture from helium by fast α particles is investigated. Working within the four-body framework of scattering theory, we perform detailed computations for differential as well as total cross sections, by means of the second-order Born distorted-wave (BDW) approximation, and find good agreement with the available experimental data. We also report the results obtained by means of the continuum distorted-wave (CDW) method in both the four-body formalism and the independent-particle model. The former fails to reproduce the measurement, whereas the latter emerges as a satisfactory method for α-He double-charge exchange. The reported study of the electronic continuum intermediate states clearly indicates that double-charge exchange is remarkably sensitive to inclusion of these long-range Coulomb effects, even at incident energies at which the Thomas double scattering is completely unimportant. This is in sharp contrast to the familiar situation at the comparable energies encountered in treating single-electron transfer in ion-atom collisions.

The method of complex-coordinate rotation is used to calculate ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}^{\mathit{e}}$, ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{o}}$, ${}_{}{}^1{}_{}{}^{}$${\mathit{F}}^{\mathit{o}}$, ${}_{}{}^3{}_{}{}^{}$${\mathit{F}}^{\mathit{e}}$, ${}_{}{}^1{}_{}{}^{}$${\mathit{G}}^{\mathit{e}}$, ${}_{}{}^3{}_{}{}^{}$${\mathit{G}}^{\mathit{o}}$, ${}_{}{}^1{}_{}{}^{}$${\mathit{H}}^{\mathit{o}}$, and ${}_{}{}^3{}_{}{}^{}$${\mathit{H}}^{\mathit{e}}$ shape resonances lying above the N=4 hydrogen threshold in ${\mathit{e}}^{\mathrm{-}}$-H scattering. Resonance energies and widths are obtained by employing up to 1611 term wave functions constructed by the products of Slater-type orbitals. The shape resonances are the top portions of the supermultiplet structures for doubly excited intrashell states of ${\mathrm{H}}^{\mathrm{-}}$ associated with the N=4 hydrogen threshold.

A high-purity germanium detector was used to determine differential cross sections for the elastic scattering of 81-keV γ rays by aluminum, nickel, tantalum, gold, and lead through angles of 60°, 90°, 120°, and 133°. The atomic Rayleigh scattering amplitudes were obtained in the independent-particle approximation by calculations of modified relativistic form factors (MF’s), a combination of MF’s and angle-independent ‘‘anomalous’’ scattering factors (ASF’s), and the relativistic second-order S matrix. Most experimental cross sections for gold and lead are slightly smaller than the calculations in the S matrix or the MF-ASF approaches, the differences being larger in the latter case. The calculated cross sections based on MF’s are enormously larger than these values. The tantalum data are in good agreement with S-matrix calculations. The data for Al show agreement with the different calculations, which differ by less than about 6%.

The Schrödinger equation for electron-hydrogen scattering is solved directly using finite-element analysis. Below the n=2 threshold, accurate phase shifts for 0≤L≤3 are obtained and compared with variational and R-matrix results. Resonance positions and widths are also calculated and are in good agreement with other theoretical values. Above the n=2 threshold, partial-wave contributions to the cross sections ${\mathrm{\sigma }}_{1\mathit{s}\mathrm{-}1\mathit{s}}$, ${\mathrm{\sigma }}_{1\mathit{s}\mathrm{-}2\mathit{s}}$, and ${\mathrm{\sigma }}_{1\mathit{s}\mathrm{-}2\mathit{p}}$ are calculated and compared with those obtained using close-coupling and R-matrix methods. Wave functions are shown for both elastic and multichannel scattering.

We have measured absolute differential excitation cross sections for the longest and second bands of molecular oxygen by electron impact. A crossed-beam method was used. The angular range covered was 12° to 156°, while the impact energy range was 15 to 50 eV. Two pronounced minima are present in the angular distributions of both cross sections, indicating in both cases substantial D-wave character. Additionally, the angular distributions show that both the longest and second bands are composite structures, arising from a combination of electric dipole allowed and electric dipole forbidden transitions. We also computed integrated cross sections from the present differential cross sections, and found a broad maximum in the former near 20-eV impact.

An experimental and theoretical study is presented of the 2p→ms,nd inner-shell excitations in the elements Ar, K, and Ca with special emphasis on the 2p→3d excitations. The present work is mainly concerned with investigations of K and Ca. An interpretation is given of the resonant Auger spectra in which it is shown that the difference in collapse of the 3d wave function in the presence of holes in the 2p shell compared to holes in the 3p shell leads to qualitative differences between the three atoms. In Ar, shake effects are very strong between the initial state with one 2p hole and the final state with two holes in the 3p shell due to the fact that the 3d orbital collapses between the two. However, in K and Ca the 3d orbital is collapsed in both states and shake effects are found to be much smaller for this excitation. In contrast, for K and Ca it is predicted that the 4d orbital will show strong shake effects. The collapse of the 3d orbital in the final state of all three atoms leads to resonant Auger spectra which are very different from those following direct ionization in the 2p shell. The details of the resonant Auger spectra depend on the degree of collapse; we discuss the differences in the observed spectra in terms of the relative strengths of the electrostatic 3p⇆3p and 3p⇆3d interactions in the three elements. The second-step Auger decays in K and Ca are studied both experimentally and theoretically.

Expressions are given for the convenient factorized form [Bar-Shalom, Klapisch, and Oreg, Phys. Rev. A 38, 1773 (1988)] for the collision strength with inclusion of the generalized Breit interaction. This is used to explore further the importance of the inclusion of the generalized Breit interaction in calculating electron-impact excitation cross sections or collision strengths, by considering the inner-shell excitation of Be-like uranium and the n=2 to n=3 transitions in neonlike xenon and uranium.

A time-independent scattering theory is introduced for time-periodic Hamiltonians. The theory is applicable in cases where at infinite time (t=±∞) the relative motion between the colliders is free, and therefore the asymptotic kinetic energy can be defined experimentally. This asymptotic condition and the time periodicity of the Hamiltonian lead to time-independent expressions for the distribution of the kinetic energy in the relative motion of the fragments for a half-collision and for a full-collision experiment. These expressions are combined with the complex-coordinate method to give an efficient numerical algorithm for the calculation of multiphoton ionization-dissociation probabilities within the framework of the finite-range-potential approximations. The theory is applied to a model Hamiltonian of an atom in a strong ac field. The obtained above-threshold-ionization spectra are in excellent agreement with theoretical results previously obtained from time-dependent calculations.

Problems of diatomic molecules and atom-atom collisions, in which two identical atoms take part, or nearest-neighbor interactions in hot plasmas require the computations of the electric potential and the electron charge distribution around such a two-centered object. The electric potential around two such identical atoms or ions fulfills special symmetry conditions. These symmetries include a cylindrical symmetry around the line connecting the centers of the two atoms and a reflection symmetry around the plane perpendicular to this line halfway between the two atoms. When the two atoms are far apart, the asymptotic behavior of the charge-state distribution and the potential are those of two separated isolated atoms each of which can be expanded into multipole components around its nucleus. We define a set of new functions ${\mathit{T}}_{\mathit{m}\mathit{k}}$(y,${\mathit{y}}_{\mathit{n}}$) Eq. (2.25), which connect the various multipole components of the electric potential to those of the electron charge distribution in such a two-identical-atom problem, and which take into account all the above symmetry conditions. The great advantage of these transformation functions is the fact that by accounting for the above symmetry conditions, the three-dimensional integration required for the computation of the local electric microfield directly from the Poisson equation is practically reduced to a one-dimensional one. It is shown that the use of these functions greatly reduces the complexity and computation times of problems in which two identical atoms are involved, particularly for high-Z atoms. Explicit exact formulas are given for the computation of the ${\mathit{T}}_{\mathit{m}\mathit{k}}$ functions. An example is given which illustrates the use of these functions in first-order perturbation theory. For this special class of problems the procedure presented here results in a closed recursive equation, in which the interatomic distance is the only free parameter.

The asymptotic theory is developed for the calculation of the charge-exchange amplitudes for large impact parameters ρ. The case of the small energy defect is considered which corresponds to the Demkov model (nonadiabatic transitions induced by the switching of the wave functions from the atomic states to the molecular-orbital regime). The effect of electron momentum transfer is included. The initial and final states with nonzero orbital momentum are considered with a special emphasis on the simplest case of s→p charge exchange. The large-ρ asymptote of the charge-exchange amplitude is calculated both for the transitions induced by radial and rotational couplings. One-center depolarization transitions (changing the projection of the angular momentum) are also incorporated in the general theory. The orientation and alignment parameters characterizing the asymmetry created in the s→p process are obtained in a simple analytical form for large ρ (or small scattering angles). They include contributions both from the one-center depolarization and from the competition of the charge exchange induced by radial and rotational coupling. The relative role of both mechanisms is analyzed and a strong dependence of the asymmetry parameters on the sign of the process energy defect is predicted. The theory is applied to the process Na(3p)+${\mathrm{H}}^{+}$→${\mathrm{Na}}^{+}$+H(n=2).

A theoretical investigation is carried out for double-electron excitation processes of ${\mathrm{H}}^{\mathrm{-}}$ induced by proton and antiproton impact at the enegy of 1.5 MeV. Excitation cross sections to the 2${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}^{\mathit{e}}$, 2s2p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$, and 2${\mathit{p}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{e}}$ states are calculated by using the plane-wave Born approximation, the distorted-wave Born approximation, and the close-coupling method. Wave functions of ${\mathrm{H}}^{\mathrm{-}}$ are generated employing the hyperspherical coordinate method. It is shown that the low-lying continuum 1skp ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ is identified as an important intermediate state in the double-electron excitation process to the 2${\mathit{p}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{e}}$ state. We have also evaluated the ejected-electron spectra from the 2s2p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ shape-resonance state. It is found that its spectral shape is close to the observed line profile of the photodetachment of ${\mathrm{H}}^{\mathrm{-}}$ since the excitation mechanism to this state is mostly dominated by the optically allowed transition at the projectile energy concerned here.

We present a phase-amplitude (PA) procedure, which emphasizes the evolution of the ${\mathrm{He}}^{\mathrm{*}\mathrm{*}}$ wave function from the origin of the hyper-radius R= √${\mathit{r}}_1^2$+${\mathit{r}}_2^2$ . This method, combined with quantum-defect theory, produces an R-dependent phase shift πτ(R) of the ionized channel, whose variation with R illustrates explicitly its coupling with the closed resonant channels. Previous calculations (e.g., of the R-matrix type) whose dynamical information remains hidden within a core region are thus complemented and extended by displaying the R dependence of phase shifts for several low doubly excited resonances of He${(}^1$${\mathit{S}}^{\mathit{e}}$). The large R limit yields the familiar scattering phase shift, in fair agreement with experimental data. The results illustrate the dominant role of short-range channel coupling in the formation of resonances.

Based on the Dirac-Slater self-consistent-field method, we have calculated the reduced normalization factors of all occupied shells for atomic ions. Applying a screened hydrogenic approximation, a nonrelativistic theoretical model is presented to explain the dependence of the reduced normalization factor on the atomic number, the degree of ionization, and the quantum number of the subshell. Both our theoretical model and numerical calculations suggest that the reduced normalization factors are almost proportional to the effective charges.

We present results of a complete treatment of electronic, vibrational, and rotational motion in numerical calculation of harmonic generation (HG) of 1064-nm laser radiation by the ${\mathrm{H}}_2^{+}$ molecular ion for intensities ${10}^{13}$≤I≤${10}^{14}$ W/${\mathrm{cm}}^2$. We show that efficient HG can be enhanced by suppression of photodissociation, a phenomenon which results from vibrational trapping in laser-field-induced potential wells. The HG spectra exhibit peaks clustered around even and odd harmonic orders. All peaks can be assigned to Raman-like transitions between dressed eigenstates of the field-molecule system. Rotational excitation is shown to compete with HG. Thus harmonic generation and photon scattering in molecules holds the promise of a potential diagnostic for molecular stabilization by intense laser fields.

Fixed-energy inverse scattering theory has been used to analyze the differential cross sections for the elastic scattering of electrons from water molecules. Both semiclassical (WKB) and fully quantal inversion methods have been used with data taken in the energy range 100–1000 eV. Constrained to be real, the local inversion potentials are found to be energy dependent, a dependence that can be interpreted as the local equivalence of true nonlocality in the actual interaction. Further improvement in fits to the data was found by allowing the interactions to be complex, reflecting the role of coupling of the elastic to nonelastic channels.

A vector quantum field theory is developed to describe the interaction of an ultracold atomic ensemble with a laser field. The ultracold atomic ensemble is composed of either bosonic atoms or fermionic atoms. The photon exchanges between different ultracold atoms result in a long-range interatom interaction. Under appropriate conditions, such a many-body interaction leads to an effective ‘‘Kerr-type’’ nonlinearity of atomic waves. In terms of the nonlinearity, we construct a general formalism of nonlinear atom optics for an ultracold atomic beam. Applying the formalism to the diffraction of an ultracold atomic beam composed of bosonic atoms by a standing-wave laser field, we find that the many-body nonlinearity induces self-phase and cross-phase modulation of diffracted atomic waves. As a result, a standing-wave laser acts as a nonlinear atomic grating which diffracts atoms in the same way as a nonlinear periodic medium diffracts photons.