Some of the calculational techniques used to compute the order ${\mathrm{\alpha }}^6$ln(${\mathrm{\alpha }}^{\mathrm{-}1}$) contribution to the energies of the 1s and 2s states of positronium reported in an earlier paper [Fell, Phys. Rev. Lett. 68, 25 (1992)] are demonstrated. Recently, this same calculation was done by an independent group [Khriplovich, Milstein, and Yelkhovsky, Phys. Lett. B 283, 237 (1992)]. Although the initial results of the two calculations did not agree, this discrepancy has since been resolved in favor of the calculation presented here. We discuss the two calculations and then compare the theoretical and experimental values of the n=2 fine structure and the triplet 2s-1s splitting.

Large-order dimensional perturbation theory, which yields high accuracy for ground-state energies, is applied here to excited states of the two-electron atom. Expansion coefficients are computed recursively using the moment method, which we formulate in terms of normal coordinates. We consider the first two excited S states of helium, corresponding, at the large-dimension limit, to one quantum in either the antisymmetric-stretch normal mode or the symmetric-stretch normal mode. Comparison with the hydrogenic limit has identified these states as 1s2s ${}_{}{}^3{}_{}{}^{}$S and 1s2s ${}_{}{}^1{}_{}{}^{}$S, respectively. We sum the 1/D expansions at D=3, using summation procedures that take into account the dimensional singularity structure of the eigenvalues, and find convergence at D=3 to the eigenvalues predicted by the hydrogenic assignments, despite apparent qualitative differences between the eigenfunctions at large D and those at D=3. In the D→∞ limit, the electrons are equidistant from the nucleus. Our results for 1s2s energies appear to imply that the shell structure is properly accounted for by terms in the expansion beyond the lowest order. This robustness of the 1/D expansion suggests that the method will be applicable to many-electron systems.

Ab initio self-consistent all-electron spin-polarized calculations were performed for the ground state and for several low-lying states of the CoO molecule using the local-spin-density approximation. The calculated energies and spectroscopic constants are generally in reasonable agreement with experimental data. Contrary to previous theoretical reports, the ground state of CoO was found to be ${}_{}{}^4{}_{}{}^{}\mathrm{\Sigma }_{}^{\mathrm{-}}{}_{}{}^{}$ with the lowest-lying excited state, ${}_{}{}^4{}_{}{}^{}\mathrm{\Delta }$, at 0.49 eV above the ground state. An insight into the structure of these states is gained through an analysis of the electronic populations of the orbitals.

Dynamic dipole polarizabilities ${\mathrm{\alpha }}_{\mathit{d}}$(ω) have been calculated within and beyond the normal-dispersion region for the isoelectronic members of argon up to ${\mathrm{Mn}}^{7+}$ using time-dependent coupled Hartree-Fock theory. Excitation energies, oscillator strengths, and quantum-defect values have been estimated for the dipole-allowed transitions 3${\mathit{p}}^6$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}^{\mathit{e}}$→3${\mathit{p}}^5$${(}^2$P)ns ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ (n=4,...,7) and 3${\mathit{p}}^6$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}^{\mathit{e}}$→3${\mathit{p}}^5$${(}^2$P)nd ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ (n=3,...,7). Analytic representations of the singly excited Rydberg orbitals have been obtained. The results compare favorably with the existing theoretical and experimental data. The oscillator strengths show an interesting trend of variation along the isoelectronic sequence.

Static electric-dipole polarizabilities for closed-shell atoms and positive ions are calculated directly from the ground-state densities of these systems. Calculations are performed using the variational principle for the energy by making an ansatz for the change in the density when the atom is put in an electric field. Since the energies are calculated from the density, the kinetic and the exchange-correlation energies have to be approximated. The exchange-correlation energy is taken within the local-density approximation. To calculate the changes in the ground-state energies accurately, we suggest the use of a kinetic-energy functional of the density which is particularly suited for such situations where the changes in the energy are of importance.

A two-dimensional, fully numerical approach to the four-component Dirac equation utilizing the finite-element method for diatomic systems is presented. The convergence properties of the calculations, which are affected by the singularities of the relativistic wave functions, are studied and improved. In the Dirac-Fock approximation for ${\mathrm{H}}_2$, an absolute accuracy of about ${10}^{\mathrm{-}10}$ a.u. for the total energy and the 1(${\mathit{j}}_{\mathit{z}}$=1/2) orbital energy is achieved with only 2116 grid points, where ${\mathit{j}}_{\mathit{z}}$ is the component of the total angular momentum along the internuclear axis. Relativistic total energies, orbital energies, and their relativistic corrections were calculated in the Dirac-Fock-Slater approximation for some small diatomic systems such as LiH, ${\mathrm{Li}}_2$, BH, and ${\mathrm{C}}_2$. The accuracies available previously have been improved by several orders of magnitude, yet without presently exceeding 2601 grid points.

The Hartree-Fock ground-state energy and electron density are first shown to be derivable from a local one-body effective potential v(r). As a nontrivial example, attention is then focused on the Be atom and isoelectronic atomic ions, the wave functions being written in terms of the density amplitude and phase. Some related general comments on the two-level one-dimensional system are included; kinetic-energy density is shown to be a local functional of electron density generated by the harmonic-oscillator potential.

Using the path-integral method, the propagator, the wave function, and the expectation values are evaluated explicitly for a time-dependent bound quadratic Hamiltonian system. We also have derived the relation between the wave function and a dynamical invariant which determines whether or not the system is bound. The expectation value of the quantum-mechanical invariant obeys the uncertainty relation with an auxiliary condition as the solution of the classical equation of the system.

We derive an expression for a lower bound of the ground-state energy of N identical fermions. In principle, this relation can describe any order of multiplicity of many-body forces and represents a generalization of a Hall inequality. Applying the Hall lower-bound inequality to the Calogero and Sutherland potentials, we show the great importance of spin states. Furthermore, using a generalized formula, we obtain a lower bound for a system with three-body forces.

We describe measurements of the lifetimes of metastable states in one- and two-electron nickel ions. The 2 ${}_{}{}^2{}_{}{}^{}$${\mathit{S}}_{1/2}$ level in one-electron nickel was found to have a lifetime of 217.1(1.8) ps, in agreement with a theoretical calculation of 215.45 ps. The lifetimes of the 2 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ and 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$ levels in two-electron nickel were found to be 156.1(1.6) and 70(3) ps, respectively, in agreement with the theoretical results of 154.3(0.5) and 70.6 ps. We also studied the phenomenon of hyperfine quenching of the He-like 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ level by comparing decay curves for the isotopes ${}_{}{}^{61}{}_{}{}^{}\mathrm{Ni}$ and ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$. The lifetime of the 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ level in ${}_{}{}^{61}{}_{}{}^{}\mathrm{Ni}_{}^{26+}{}_{}{}^{}$ was found to be 470(50) ps, in agreement with a theoretical prediction. The measurements were carried out using the beam-foil time-of-flight technique with a fast beam of highly charged nickel ions. We discuss the handling of systematic effects in the measurements, including the study of yrast cascades following the beam-foil interaction.

A mathematical study of the problem of mappings on the n-electron configurations induced by one-electron orbital transformations is carried out. The main objective is to design a procedure that uses the chemical information of valence-bond functions in the determination of a limited number of significant orthogonal configurations for a molecular-orbital treatment. The example of the ${\mathrm{He}}_2^{+}$ ion is given.

Taking into account results of earlier hyperfine-structure (hfs) measurements, the hfs of altogether 20 fine-structure (fs) levels has been analyzed by the simultaneous parametrization of the one- and two-body interactions in the atomic hfs for the model space (3d+4s${)}^{\mathit{N}+2\mathrm{}}$ (N=7). The values of the one- and two-body hfs parameters have been determined. The evaluation of the nuclear quadrupole moment of ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$ including Sternheimer corrections up to second order yielded the value of 0.41(1) b. Moreover, the values of the magnetic-dipole constants A and the electric-quadrupole constants B for all levels of the model space (3d+4s${)}^9$ have been predicted.

We have measured the rotational dependence of the absorption linewidth of transitions from the v=0 a’’ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{+}{}_{}{}^{}$ state to the v=4 levels of the 3pσ,3pπ complex of ${\mathrm{N}}_2$. We compare our results with a model that describes the electronic and rotational mixing between the Rydberg and valence states. We find that the linewidths correlate with the magnitude of the electronic admixture of the character of the b’ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{+}{}_{}{}^{}$ valence state. This suggests that predissociation of the Rydberg states is mediated by the b’ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{+}{}_{}{}^{}$ state, which in turn is predissociated by a manifold of triplet valence states.

A numerical scheme for evaluating the part of the one-photon vacuum-polarization effect not accounted for by the Uehling potential (the Wichmann-Kroll effect) is presented. The method can be used with an arbitary atomic model potential describing the bound electrons. Benchmark results for this effect are presented for hydrogenlike levels using a uniform nuclear-charge distribution. The effect of direct and exchange electron screening on the vacuum polarization are discussed in connection with the accurately measured 2${\mathit{p}}_{1/2\mathrm{-}}$2${\mathit{s}}_{1/2}$ transition in lithiumlike uranium.

A semiclassical, many-body atomic model incorporating a momentum-dependent Heisenberg core to stabilize atomic electrons is used to study antiproton capture on helium. Details of the antiproton collisions leading to eventual capture are presented, including the energy and angular-momentum states of incident antiprotons which result in capture via single- or double-electron ionization, i.e., into ${\mathrm{He}}^{2+}$p¯ or ${\mathrm{He}}^{+}$p¯, and the distribution of energy and angular-momentum states following the Auger cascade. These final states are discussed in light of recently reported anomalously long-lived antiproton states observed in liquid He [Iwasaki et al., Phys. Rev. Lett. 67, 1246 (1991)].

We discuss in some detail the self-similar potentials of Shabat [Inverse Prob. 8, 303 (1992)] and Spiridonov [Phys. Rev. Lett. 69, 298 (1992)] which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape-invariant potentials within the formalism of supersymmetric quantum mechanics. In particular, using a scaling Ansatz for the change of parameters, we obtain a large class of new, reflectionless, shape-invariant potentials of which the Shabat-Spiridonov ones are a special case. These new potentials can be viewed as q deformations of the single-soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for the energy eigenvalues, eigenfunctions, and transmission coefficients for these potentials are obtained. We show that these potentials can also be obtained numerically. Included as an intriguing case is a shape-invariant double-well potential whose supersymmetric partner potential is only a single well. Our class of exactly solvable Hamiltonians is further enlarged by examining two new directions: (i) changes of parameters which are different from the previously studied cases of translation and scaling and (ii) extending the usual concept of shape invariance in one step to a multistep situation. These extensions can be viewed as q deformations of the harmonic oscillator or multisoliton solutions corresponding to the Rosen-Morse potential.

The four logarithmic excitation eneriges I(ν) for ν=-1, 0, 1, and 2 have been calculated for helium, lithium, beryllium, and the 2s state of hydrogen. They appear in the expressions of the total cross section, the stopping power, and the straggling effect for fast charged particles, and in the expressions of the Lamb shift of atomic energy levels. The method was introduced some years ago [Rosendorff and Birman, Phys. Rev. A 31, 612 (1985)]. For hydrogen the method is rigorous. Exact one-particle wave functions given by Clementi were used. Thus, correlation and symmetrization effects were neglected. For the nonhydrogen states, the relevant differential equations were solved by using a computer. An effective charge was defined which has interesting features. It is helpful in gaining some physical insight into the results obtained for helium and the 1s and 2s states of lithium and beryllium.

A many-body theory of electron-impact excitation out of excited atomic states is presented. After the fundamental equations and formulas of the general theory are given, first- and second-order approximations are introduced. In the case of the first-order theory, detailed analytical formulas are also developed. The physical interpretation of the first- and second-order theories are presented with the aid of Feynman-type diagrams. Following a discussion of initial- and final-state effects, the many-body theory is also related to the distorted-wave approximation.

Target LMM atomic Auger electron emission has been studied by low-energy ion bombardment on light-element surfaces. Our results show that the threshold energies for Mg, Al, and Si 2p core electron excitation are the same for impact of ${\mathrm{Ar}}^{+}$, ${\mathrm{Kr}}^{+}$, and ${\mathrm{Xe}}^{+}$ projectiles but are substantially lower for ${\mathrm{Ne}}^{+}$. A sensitive dependence of the energy onset on the ion incidence angle has also been observed. The intensity behavior in the near-threshold energy range is in excellent agreement with simple kinematic calculations using a binary-collision model and by taking into account only the first target-target symmetric encounters.

An approach to electron scattering from molecules is discussed, in which an algebraic description of the rovibrational states in the molecule (vibron model) is combined with a rotating-frame approximation. The latter was first introduced for atomic-molecule scattering under the name centrifugal sudden approximation. The coupled multichannel problem reduces to single-channel central potential scattering with a fluctuating potential. The method is applied to electron scattering from a rigid molecule with large dipole moment. Comparison with exact coupled-channel calculation shows that the approach works well for all partial waves except those with very low angular momentum. The method is also compared with the algebraic eikonal approach.