The total energies of atoms and with atomic number Z from 1 to 92 and singly charged cations with Z from 2 to 92 have been calculated to an accuracy of 1 μhartree within four variants of the Kohn-Sham local-density approximation (LDA). The approximations considered are the local-density approximation, the local-spin-density approximation, the relativistic local-density approximation, and the scalar-relativistic local-density approximation. The total energies for the LDA are found to be in 0.1% agreement with a large atomic number expansion from many-body theory for Z⩾40. A comparison to experiment is made for the ionization energies and spin-orbit splittings; also the total energies and eigenvalues of the various theories are compared among themselves.

The family of four-particle systems (${\mathrm{M}}^{+}$${\mathrm{m}}^{+}$${\mathrm{M}}^{\mathrm{-}}$${\mathrm{m}}^{\mathrm{-}}$) has been studied by means of Monte Carlo techniques. Nonadiabatic explicitly correlated wave functions for different values of the mass ratio M/m have been obtained using a variational Monte Carlo optimization method. These wave functions have been used in diffusion Monte Carlo simulations of (${\mathrm{M}}^{+}$${\mathrm{m}}^{+}$${\mathrm{M}}^{\mathrm{-}}$${\mathrm{m}}^{\mathrm{-}}$) to compute exact ground-state energies. Our results enlarge the stability range of the mass ratio for these and for similar less symmetric systems and address the problem of the stability of the hydrogen-antihydrogen system. For the special case of the dipositronium molecule (M=m) we report the ground-state energy, consistent with previous accurate calculations, and average values of various observables.

Two-dimensional (2D) multiple-quantum coherence is reported for the hyperfine ground state of rubidium and cesium atoms by applying multiple radio-frequency pulses to the optically polarized atoms. Calculations of 1D and 2D multiple quantum coherences were performed with a general theory for an arbitrary high spin system by using irreducible tensor operators. The experimental results compare very well with the calculations.

Diffusion of muonic deuterium μd and muonic hydrogen μp atoms produced following the stopping of negative muons in ${\mathrm{D}}_2$ or ${\mathrm{H}}_2$ at 300 K was studied at pressures of 47–750 mbar (${\mathrm{H}}_2$) and 94–1520 mbar (${\mathrm{D}}_2$) in two distinct target geometries. Time intervals were recorded between entry of negative muons into the gas and arrival of each resulting μd or μp atom at one of 50 foils immersed in the gas, and spaced regularly along the muon beam axis. The results of such measurements were fitted to time distributions generated by Monte Carlo methods, using theoretical scattering predictions and empirically chosen forms for the initial energy distributions of the muonic atoms in the 1S state. Results indicate muonic atom energy distributions which (a) are different for μd and μp and (b) vary with pressure. The best-fit energy distributions have mean energies ranging from 1.5 eV for μd at 94 mbar to ⩾9 eV for μp at 750 mbar. The data are also sensitive to scattering cross sections for μd and μp, and are consistent with current theoretical calculations for the μd+${\mathrm{D}}_2$ cross sections. In the case of μp+${\mathrm{H}}_2$ scattering, the experimental data suggest discrepancies with the theoretical predictions.

The accessible information obtained in combined and sequential quantum measurements is calculated for a binary pure quantum state signal. It is shown that the accessible information obtained in the combined measurement is equal to that obtained in the sequential measurement. The result indicates that the conjecture by Peres and Wootters [Phys. Rev. Lett. 66, 1119 (1991)] is not valid, at least for a binary quantum state signal. Furthermore, the result is compared with that obtained by Brody and Meister [Phys. Rev. Lett. 76, 1 (1996)].

Precise measurements are reported on the linear polarization spectrum associated with two-photon, two-color spectroscopy of the 3 ${\mathrm{s}}^2$ ${\mathrm{S}}_{1\mathrm{/}2}$ →5 ${\mathrm{s}}^2$ ${\mathrm{S}}_{1\mathrm{/}2}$ transition in atomic Na. Measurements are made in an approximately 40-${\mathrm{cm}}^{\mathrm{-}1}$ range in the vicinity of the 3 ${\mathrm{p}}^2$ ${\mathrm{P}}_{\mathrm{j}}$ (j=1/2,3/2) levels, which serve as the principal intermediate levels for the two-photon transitions. Because of interference between the transition amplitudes through each fine-structure multiplet component, the polarization varies from nearly 100% to -100% within this spectral range. Modeling the data to include the effects of more energetic p levels and allowing for a j-dependent ratio of transition amplitudes R results in an excellent fit to the data. Estimation of the contribution of higher p levels allows extraction of a value and sign for R=+1.0012(12). This result is combined with recent measurements of the lifetime of the resonance transitions in Na to obtain a value for the ratio of excited-state transition-matrix elements for the 3 ${\mathrm{p}}^2$ ${\mathrm{P}}_{\mathrm{j}}$ →5 ${\mathrm{s}}^2$ ${\mathrm{S}}_{1\mathrm{/}2}$ transition (j=3/2 compared to j=1/2) of 1.0013(15).

Symmetry breaking of electronic structure configurations for N-electron atoms in weak magnetic and electric fields at the large-dimension limit is described in terms of standard phase transitions. This symmetry breaking, which leads to ionization, is completely analogous to phase transitions and critical phenomena in statistical mechanics. This analogy is shown by allowing the nuclear charge to play a role analogous to temperature in statistical mechanics. For the exact solution of N-electron atoms at the large-dimension limit, the symmetry breaking is shown to be a first-order phase transition. For the special case of two-electron atoms, the first-order transition shows a triple point where three phases with different symmetry coexist. Treatment of the Hartree-Fock solution reveals a different kind of symmetry breaking where second-order phase transitions exist for N=2. We show that Hartree-Fock two-electron atoms in a weak external electric field exhibit a critical point with mean field critical exponents (Β=, α=$0_{\mathrm{dis}}$, δ=3, and γ=1).

Photoionization cross sections, branching ratios, and photoelectron angular-distribution asymmetry parameters have been calculated for all Ar (Z=18) subshells using the relativistic random-phase approximation, the relativistic random-phase approximation modified to include relaxation effects, and the relativistic random-phase approximation modified to include relaxation effects and Auger decay. Comparisons are made between the various theoretical results and experimental data. The importance of relaxation and Auger decay is seen to increase for deep inner subshells, particularly 1s and 2s.

The Harris-Nesbet algebraic method was used to carry out a large coupled-state calculation of ${\mathrm{e}}^{+}$ -H scattering at energies below the first excitation threshold of hydrogen. The six-state (1s,2s,2p H–1s,2s,2p Ps) coupling scheme was extended to include an adequate number of short-ranged functions of both hydrogenic and positroniumic types and the H 3p-bar pseudostate. Phase shifts and cross sections of partial waves from L=0 to 6 were obtained for ${\mathrm{e}}^{+}$ -H (1s) scattering as well as for Ps(1s)-p scattering. Our results are to be compared with those obtained by other research groups with some large-scale calculations employing, however, different numerical methods of approach. Our results agree excellently with the values calculated with a variational method by Bhatia et al. and by Humberston and co-workers and with the 21-state close-coupling approximation by Mitroy and co-workers.

The convergence problem for scattering states is studied in detail within the framework of the algebraic model, a representation of the Schrödinger equation in an ${\mathrm{L}}^2$ basis. The dynamical equations of this model are reformulated featuring new ``dynamical coefficients,'' which explicitly reveal the potential effects. A general analysis of the dynamical coefficients leads to an optimal basis yielding well converging, precise, and stable results. A set of strategies for solving the equations for nonoptimal bases is formulated based on the asymptotic behavior of the dynamical coefficients. These strategies are shown to provide a dramatically improved convergence of the solutions.

A general program to show quantum-classical correspondence for bound conservative integrable and chaotic systems is described. The method is applied to integrable systems and the nature of the approach to the classical limit, the cancellation of essential singularities, is demonstrated. The application to chaotic systems requires an understanding of classical Liouville eigenfunctions and a Liouville spectral decomposition, developed herein. General approaches to the construction of these Liouville eigenfunctions and classical spectral projectors in quantum and classical mechanics are discussed and are employed to construct Liouville eigenfunctions for classically chaotic systems. Correspondence for systems whose classical analogs are chaotic is discussed, based on this decomposition, in the following paper [Phys. Rev. A 54, 43 (1996)].

Molecular treatments of atomic collisions have traditionally been restricted to low nuclear velocities because of their failure to reproduce the fall of the capture cross sections at higher velocities. The limitation has recently been seen to be due to their description of ionizing processes. This feature is shown here to be a general one for multicharged ion-atom collisions. Its origin and characteristics are described and illustrated for the prototypical ${\mathrm{Li}}^{3+}$ +H(1s) reaction. Ionization appears as a result of the inertia of the electron cloud to adiabatically follow the nuclear motion. This gives rise to nonadiabatic transitions, which represent an ionizing flux whenever the nuclear velocity is high enough that the energy of the traveling molecular orbitals involved is positive in both moving atomic reference frames. Two strongly connected mechanisms appear, corresponding to the relative translational and rotational nuclear motions. Because of the finiteness of the basis, these mechanisms terminate with unphysical trapping effects. While interesting per se, knowledge of these features is also useful with respect to improving molecular treatments of atomic collisions with the addition of pseudostates.

K- to L-shell vacancy transfer probabilities were measured for ten elements in the atomic range 73⩽Z⩽92. Those measuring L x-ray yields from targets excited by 59.5 and 122 keV incident photons, i.e., below and above the K edge of elements, were detected with a high-resolution Si(Li) detector. For comparison with experimental results, theoretical calculations were made by using available data on radiative and radiationless transitions. The radiative transitions of these elements were observed from the relativistic Hartree-Slater model which was proposed by Scofield [At. Data Nucl. Data Tables 14, 121 (1974)]. The radiationless transitions were observed from the Dirac-Hartree-Slater model which was proposed by Chen, Craseman, and Mark [At. Data Nucl. Data Tables 24, 13 (1979)]. The measured results were found to be in good agreement with theoretically calculated values. The experimental and theoretical values were fitted versus atomic number Z.

Detailed level-by-level calculations of the excitation-autoionization (EA) cross sections and rate coefficients were performed using the relativistic distorted-wave method along the Zn isoelectronic sequence for all the elements with 34⩽Z⩽92. While in a previous work only the 3d-4l inner-shell collisional excitations were taken into account, the present calculations also include excitations to higher configurations: ${3\mathrm{d}}^9$${4\mathrm{s}}^2$nl (n=4 to 7) and ${3\mathrm{p}}^5$${3\mathrm{d}}^{10}$${4\mathrm{s}}^2$nl (n=4,5). An extrapolation method is used to evaluate the total contribution for the higher principal quantum numbers. Configuration mixing and secondary autoionization processes following radiative decay from autoionizing levels are also included. The results show that the total EA rate is dominant compared to the direct ionization rate, up to a factor 12 at Z=47. The additional inner-shell excitations for Z<59 produce an increase in the EA effect varying from 25% to almost a factor of 2, with respect to the previously predicted EA effect through 3d-4l only. The excitations to the higher configurations are the most significant for heavy elements with Z⩾61, since they open EA channels, resulting in an EA rate which varies along the sequence from 4 to 1 times the direct-ionization rate.

Measurements of the doubly excited states of helium below the ${\mathrm{He}}^{+}$(N=3) threshold populated by electron impact are presented for a range of scattering angles and residual energies. The deduced values of the energies and widths for 11 of the optically forbidden states are compared with theoretical values, which shows the agreement to be good for the energies but poorer for the widths. The data verify propensity rules in Lin's [Adv. At. Mol. Phys. 22, 77 (1986)] K, T, A classification scheme for the cross sections. By comparing the ${2\mathrm{s}}^2$${\mathrm{}}^1$${\mathrm{S}}^{\mathrm{e}}$ and ${3\mathrm{s}}^2$${\mathrm{}}^1$${\mathrm{S}}^{\mathrm{e}}$ states at the scattering angle of 20° and the residual energy of 40 eV, we obtain a dependence of ${\mathrm{n}}^{\mathrm{-}10.1\pm 0.8}$ for the cross section at these conditions.

Convergent close-coupling (CCC) and Coulomb-Born with exchange and normalization (CBE) methods are used to study electron-impact excitation of hydrogenlike ions. The nl→${\mathrm{n}}^{|\mathrm{I}\mathrm{H}}$${\mathrm{l}}^{|\mathrm{I}\mathrm{H}}$ cross sections demonstrate (i) good agreement between the CCC and CBE results, (ii) a scaling over ion nuclear charge z, (iii) a domination of the dipole (${\mathrm{l}}^{|\mathrm{I}\mathrm{H}}$=l±1) contributions in total n→${\mathrm{n}}^{|\mathrm{I}\mathrm{H}}$ cross sections, and (iv) significant effect of electron exchange in the energy range x<3 (here x is the ratio of the incident electron kinetic energy ɛ to the transition energy ${\mathrm{E}}_{\mathrm{n},{\mathrm{n}}^{|\mathrm{I}\mathrm{H}}}$). For ions with z>5 the n→${\mathrm{n}}^{|\mathrm{I}\mathrm{H}}$ cross sections obtained in the CCC and CBE approximations agree with each other to better than 10% for any x. An accuracy of the cross sections scaling over ${\mathrm{z}}^4$ depends on z: for z=6–18 the scaling is accurate to better than 10% (quantitative analysis is done for ${\mathrm{n}}^{|\mathrm{I}\mathrm{H}}$<7), for ions with z<6 the cross sections deviate from the ${\mathrm{z}}^4$ scaling more significantly (at x about unity). The n→${\mathrm{n}}^{|\mathrm{I}\mathrm{H}}$ cross sections are presented by a formula which fits our CCC and CBE results with an accuracy to better than 10% (for transitions with n<${\mathrm{n}}^{|\mathrm{I}\mathrm{H}}$<7 in ions with z>5). The new Gaunt factor G(x) suggested for the widely used Van Regemorter formula [Astrophys. J. 136, 906 (1962)] makes this formula accurate to better than 50% in the x>3 range and to better than 20% in the x>100 range. It is shown that the semiempirical formula by Vainshtein, Sobelman, and Yukov [Electron-Impact Excitation Cross Sections of Atoms and Ions (Nauka, Moscow, 1973)] provides an accuracy to better than 50% for any incident electron energy. For x<2 this formula is accurate to better than 30%. These accuracy assessments are based on a comparison with our CCC and CBE results.

We present a quantitative model to describe the formation of hydrogen atoms (1s and 2p states) following the dissociation of fast (30–120 keV/u) hydrogen cluster ions ${\mathrm{H}}_{\mathrm{n}}^{+}$ (n=2 and n= 3 – 21, odd) induced by a thin carbon foil. The model includes Coulomb explosion, multiple scattering, energy loss, and a simplified description of charge-exchange processes inside the solid. This description takes into account the dynamic screening of the moving protons by the target electrons and the relative position of the protons during the charge-exchange process. The results of the calculations performed with a Monte Carlo computer code reproduce remarkably well the experimental data.

We describe a variational method for calculating photoionization cross sections from a matrix element of the resolvent operator. Scattering boundary conditions are enforced by expanding the resolvent in a basis of square-integrable (${\mathrm{L}}^2$ ) and outgoing wave continuum basis functions. By employing several continuum basis functions, with overlaps defined by a suitable analytic continuation, we can, in a single calculation, express the cross section over a continuous range of energies without explicitly resolving the variational equations at each desired energy. The method is illustrated by calculation of the photoionization cross section of atomic Be in the autoionizing region between the ${1\mathrm{s}}^2$ 2s and ${1\mathrm{s}}^2$ 2p states of ${\mathrm{Be}}^{+}$ .

We develop a stationary-state scattering theory of dissociative photodetachment in a transition-state region for a system in which two or more potential surfaces are mutually coupled through the nonadiabatic interaction in dissociative channels. Since the present phenomenon involves electron detachment and molecular dissociation dynamics, it is a doubly half collision in a three-body problem. We perform an asymptotic analysis for the dissociative wave functions, which formally gives a closed form of the transition amplitude in which the pulse shape and polarization of a pumping laser, the kinetic energy distribution of a detached electron, and the product distribution are all correlated. The present formal theory thus provides a unified basis for the analyses in the experimental and numerical studies. We revisit the mathematical role of the so-called in-going state for general dissociation dynamics and, in particular, argue that the traditional interpretation of the ingoing wave function due to Breit and Bethe is not necessarily valid.

We have measured total (${\mathrm{Q}}_{\mathrm{T}}$ ) and positronium formation (${\mathrm{Q}}_{\mathrm{Ps}}$ ) cross sections for 1–302-eV positrons (${\mathrm{e}}^{+}$ 's) and ${\mathrm{Q}}_{\mathrm{T}}$ 's for electrons (${\mathrm{e}}^{\mathrm{-}}$ 's) scattered by hydrogen atoms and molecules. A beam transmission technique is used to measure ${\mathrm{Q}}_{\mathrm{T}}$ 's where the projectile beam passes through a low-temperature scattering cell containing a mixture of hydrogen atoms and molecules generated in an adjacent radio-frequency discharge region. ${\mathrm{Q}}_{\mathrm{Ps}}$ 's are measured using the same scattering cell by detecting coincidences of 511-keV annihilation γ rays produced by the decay of para-Ps and by the interaction of ortho-Ps with the walls of the scattering cell in which the Ps is formed. The present ${\mathrm{e}}^{+}$ -H ${\mathrm{Q}}_{\mathrm{T}}$ 's and ${\mathrm{Q}}_{\mathrm{Ps}}$ 's agree very well with theoretical calculations. Comparisons of the present ${\mathrm{e}}^{+}$ and ${\mathrm{e}}^{\mathrm{-}}$ -H ${\mathrm{Q}}_{\mathrm{T}}$ 's show a merging to within 20% for energies above 12 eV.