We analyze the anapole moment or toroidal dipole moment (TDM) of an atom, resulting from the weak interaction between electrons. A simple estimate can be made if the electron density is assumed to be constant. The TDM is found to grow like ${\mathit{Z}}^{4/3}$, reaching approximately (${\mathit{eG}}_{\mathit{F}}$/ħc) for the heaviest atoms. An algorithm for calculating the TDM of an atom with a slowly varying electron density is derived using a unitary transformation which removes the weak interaction from the Hamiltonian. We have not attempted to apply this method, but it appears to be a useful method for calculating anapole moments and other effects of weak interactions in complex atoms.

Multiconfiguration Hartree-Fock (MCHF) calculations of hyperfine constants for the 2s2p ${}_{}{}^3{}_{}{}^{}$P states of beryllium and the ground states of boron and carbon are reported. The capacity of a recently developed configuration-interaction program [Froese Fischer and Tong (unpublished); Stathopoulos and Froese Fischer (unpublished)], allowing for large configuration expansions, is explored. Using a systematic active-space MCHF approach, combined with large multireference configuration-interaction calculations, it is shown that hyperfine constants can be calculated very accurately. To reliably account for spin-polarization of the 1s and 2s shells in boron and carbon, three-particle effects had to be included in a systematic way. The relativistic, finite-nuclear-size- and finite-nuclear-mass-corrected values of the hyperfine constants are compared with experimental values and with the most accurate theoretical values obtained with other methods.

Weak decay of the negative muon in hydrogenic media is generally routed through muonic molecular or atomic states. The distortions to the free-muon decay rate due to the muon’s Coulomb dressing is computed for all isotopic combinations for muonic molecular states in hydrogen and compared with the atomic case in light media. The nucleoweak channels corresponding to nuclear fusion accompanying the weak decay of the muon from a molecular environment are also investigated.

We discuss the resonant formation mechanism of muonic molecular ions in a high-density D-T system, putting emphasis on a condensed-matter effect. After generally formulating the problem, we apply the formulation to a solid phase of an admixture of ${\mathrm{D}}_2$, DT, and ${\mathrm{T}}_2$. The spectral intensity distribution of a whole system proves to be essential in understanding the above-mentioned effect. Namely the numerically calculated distribution exhibits the presence not only of a Lorentzian peak centered at a conventional, slightly shifted resonance energy but also of a broad peak lying over an energy domain that extends from the resonance energy with a scope comparable to the bandwidth of the elementary excitation spectra of the solid. The profile of the spectral distribution suggests the possibility that the condensed matter should take part in the quasiresonant reaction as an absorber of excess energy in the initial state. In fact, the formation rate at low temperatures turns out to be enhanced dramatically in the presence of subthreshold resonance levels, as compared with Vesman’s mechanism [Sov. Phys. JETP Lett. 5, 91 (1967)], i.e., molecular formation in a free space. The numerical calculation of formation rates is carried out for a target system involving ortho-, para-${\mathrm{D}}_2$, or their thermal admixture.

Singly, doubly, and triply excited states of the Li isoelectronic sequence have been represented by small expansions of self-consistent, state-specific wave functions containing important contributions from localized and asymptotic correlation components. These wave functions have been used for the prediction of wavelengths and probabilities of one-, two-, and three-electron radiative transitions along the sequence, up to ${\mathrm{Ne}}^{7+}$. For Z around 8–10, the radiative lifetimes of the triply excited states are about ${10}^{\mathrm{-}11–}$${10}^{\mathrm{-}13}$ s, a fact which might render them observable in emission.

Rigorous upper and lower bounds on the atomic spherically averaged electron density are found for all radial values in terms of the charge density at the nucleus, ρ(0), and the first few radial expectation values. Moment-theory methods and Chebyshev inequalities are used to obtain the bounds. This type of result can be employed to compare diverse information obtained by using different models, numerical approximations or experimental data. In order to study the goodness of the bounds, a computation in a Hartree-Fock framework is done. The accuracy of our simplest upper bound is similar to a previous one found by King [J. Chem. Phys. 78, 2459 (1983)] using very different methods and information. Other bounds, containing more information, clearly improve the aforementioned result. The same method allows one to obtain bounds on the derivative and primitive functions of the electron density as well as on the atomic charge.

The unitary-group approach is extended to the treatment of composite systems such as ionic states in molecules (ligands, etc.). Those are represented hierarchically in terms of SU(n)-based Weyl-Young tableaux which reflect the permutational symmetry of the ionic sites themselves labeled by SU(2) based tableaux which, in turn, reflect the internal electronic structure. Matrix elements of quantum-mechanical tensor operators, including both spin-independent and spin-dependent multipole-multipole interactions, are presented using corresponding spin-graphical representations. The hierarchy of the state definitions is shown to reveal the ‘‘fine structure’’ of the ionic interactions.

Formulas for the direct calculation of convolved photoabsorption cross sections are presented. Atomic parameters used for the calculation of infinite resolution cross sections can be used in a very accurate approximate formula for the convolved cross section. The direct calculation of convolved cross sections is usually 20–100 times faster than the calculation of numerically convolved cross sections. Numerically convolved cross sections are compared to the preconvolved cross section for a recent atomic calculation.

We develop an alternative construction of bound states based on matching the Riccati threshold and asymptotic expansions via their two-point Padé interpolation. As a form of quantization it gives highly accurate eigenvalues and eigenfunctions.

The low-lying energy levels of a hydrogen atom in a uniformly strong magnetic field B (B<${10}^{10}$ G) are calculated in a simple perturbative variational approach which combines the spirit of the variational principle and the conventional perturbation method. The total Hamiltonian is separated into four parts: a one-dimensional hydrogen-atom system; a two-dimensional harmonic-oscillator system; a z-component angular-momentum operator; and a perturbation part which contains an undetermined variable parameter but is independent of B. The first three parts can be solved exactly. The variational parameter introduced in the Hamiltonian can be determined by requiring the energy-correction expansion to converge as fast as possible. It is found that our calculated ground-state energy is in good agreement with those obtained by the previous works that used the wave-function-expansion approach for high magnetic fields up to γ=7 (i.e., ${10}^{10}$ G for atoms).

We study the classical electron motion of two-electron atoms. We present techniques to regularize singularities in the equations of motion and to calculate stability properties of periodic orbits in six-dimensional phase space. Depending on the configuration of the electron pair the classical phase space turns to be regular, purely chaotic, or of mixed structure. For the fully hyperbolic case of collinear electron motion a strong correlation between ionizing trajectories and the collision manifold of the triple collision is found. For the near-integrable collinear motion with both electrons on the same side of the atom we (numerically) derive an action-angle representation of the Hamiltonian.

A nonlocal exchange energy functional developed within the weighted spin-density approximation (WSDA) and a local Coulomb correlation energy functional are combined within the density-functional scheme for the calculation of the electronic structure of many-electron systems. Both functionals include alternative forms of the pair-correlation functions governing the size and shape of the Fermi and Coulomb holes. Self-consistent calculations have been performed for all atoms from He to Rn within the exchange-only WSDA scheme. These have been compared to the results of similar calculations using Becke’s exchange functional. Besides, the results of calculations for all atoms from He to Ar, including both exchange and correlation, are compared with those of the self-interaction-corrected method. In addition to obtaining accurate total, exchange, and correlation energies, we perform a successful calculation of the s→d interconfigurational energies (ICE’s) for transition-metal atoms. The average error of the calculated ICE values for 3d atoms is only 0.2 eV.

The original derivation by Lifshitz [Sov. Phys. 2, 73 (1956)] of ${\mathit{P}}_{\mathit{D}\mathit{D}}$, the force per unit area between two plane parallel dielectric walls, is extremely complicated; the later derivations are simpler but still difficult. The standard derivation of the interaction ${\mathit{V}}_{\mathrm{At}}$ D of an atom and a dielectric wall uses the expression for ${\mathit{P}}_{\mathit{D}\mathit{D}}$ as its starting point. The results are valid for all values of the separation l. For l∼∞, where the interactions are retarded, we obtain resonably accurate approximate expressions for ${\mathit{P}}_{\mathit{DD}}$ and for ${\mathit{V}}_{\mathit{A}\mathrm{t}\mathrm{}\mathit{D}}$—and also for ${\mathit{V}}_{\mathit{E}\mathrm{l}\mathrm{}\mathit{D}}$, the retarded interaction of an electron and a dielectric wall—by the elementary procedure of assuming simple forms with one or two open parameters, adjusted to give the known results for retarded interactions which do not include dielectric walls. These include ${\mathit{P}}_{\mathit{M}\mathit{M}}$ (the force per unit area between two parallel plate metallic walls), ${\mathit{V}}_{\mathit{At}\mathrm{}\mathit{M}}$ (the atom-metal) interaction, ${\mathit{V}}_{\mathit{At}\mathrm{}\mathit{At}}$ (the atom-atom interaction), and ${\mathit{V}}_{\mathit{El}\mathrm{}\mathit{M}}$ (the electron-metal interaction). We also consider the possibility of obtaining an improved estimate of ${\mathit{P}}_{\mathit{D}\mathit{D}}$ by using known properties of ${\mathit{V}}_{\mathit{At}\mathrm{}\mathit{D}}$. The explicit results obtained by Lifshitz for the various interactions are also very complicated. The simple approximate forms of the interactions can be particularly useful for the wall-wall interaction, since ${\mathit{P}}_{\mathit{D}\mathit{D}}$ is a double integral with a complicated integrand which depends upon two parameters, the zero-frequency dielectric constants of each of the walls.

A number of different approaches have been used to determine the interactions between a variety of pairs of polarizable systems asymptotically far apart; these are examples of retardation or Casimir interactions. The pairs include two dielectric walls, and an atom and a dielectric wall, but not an electron and a dielectric wall. (The asymptotic value of the interaction between an electron and an ideal conducting wall has been evaluated.) We here apply a method not previously used in the evaluation of retardation potentials, quantized Fresnel modes, to determine the interaction in the asymptotic domain of a polarizable system and a dielectric wall. We thereby reproduce the known result for an atom and a dielectric wall and obtain a previously unobtained result, that for an electron and a dielectric wall. The result simplifies greatly for an ideal metallic wall and for a wall made from a material such as liquid helium for which the dielectric constant is very close to unity. We also discuss the question of a connection between the electron–dielectric-wall interaction and Lifshitz’s force per unit area between two dielectric walls. The determination of the amplitudes of the Fresnel modes, by quantization, is the only nonclassical element in the calculation.

Using an expansion of the electromagnetic field in terms of quantized Fresnel modes, we calculate the retarded Casimir interaction, in the asymptotic domain, of a polarizable system and a dielectric permeable wall, that is, a wall characterized by a dielectric constant ${\mathrm{\epsilon }}_2$ and a magnetic permeability ${\mathrm{\mu }}_2$. We obtain explicit analytic results for the atom-wall and for the electron-wall interactions. When magnetic effects are ignored, the results reduce to those obtained by Lifshitz [Sov. Phys. 2, 73 (1956)] for the atom-wall interaction and by the present authors for the electron-wall interaction. The results simplify greatly for an ideal metallic wall and for a wall made of material such as liquid helium, for which the dielectric constant and the permeability are very close to unity. Other than in the determination of the amplitudes of the Fresnel modes, the calculations are entirely classical.

We present scaling relations for the total cross sections and collision strengths of bound-state excitation in positive ions. The colliding particle can be positively or negatively charged and can be a fully ionized atom, an electron, or a positron. We consider collisions in which the kinetic energy of relative motion is large and consequently the adiabaticity parameter ξ≪1. We illustrate our general method by calculating collision strengths for proton-impact excitation of fine-structure transitions in hydrogenlike ions. The limiting case of infinite nuclear charge is also included in our calculations. Using a unitarized Coulomb-Born approximation, we show that, for dipole transitions, colliding particles with large orbital angular momenta (l≳2000) make an important contribution (∼70%) to the collision strength of proton-impact excitation. For a nonrelativistic projectile energy ${\mathit{E}}_{\mathit{i}}$→∞, we use the Born approximation to obtain the scaled collision strengths. These limiting values, dependent only on the particular transition, confirm the correct high-energy behavior of our data. We also use the interactive graphics computer program omeups [Burgess and Tully, Astron. Astrophys. 254, 436 (1992)] to extrapolate our data to higher energies.

The total electron loss, target ionization, and simultaneous projectile-target ionization are measured for ${\mathrm{He}}^{+}$ projectiles on ${\mathrm{H}}_2$ and He in the energy range of 1.5–4.0 MeV. The experimental data are in good agreement with calculations based on the independent-particle model including screening, antiscreening, and target-ionization probabilities as well as second-order mechanisms for the simultaneous projectile-target ionization.

We extend previous nonrelativistic dipole-approximation theoretical studies of two-photon electron bremsstrahlung in the Coulomb field by calculations exploring the cross section that describes the emitted photons, irrespective of the direction of the scattered electron, and its dependence on the charge Z of the target, for different detection geometries. A Born-approximation equation, valid for any emitted-photon configuration, is derived. Comparisons with the most recent experimental data are presented.

The real-time path-integral formulation of resonant electron-molecule scattering presented previously [Winterstetter and Domcke, Phys. Rev. A 47, 2838 (1993)] is extended to the second order of the cumulant expansion and to the case of many vibrational modes within the harmonic-oscillator approximation. The performance of the path-integral method is demonstrated for several models of electron-molecule shape resonances including up to five vibrational degrees of freedom. The coupling of the electronic tunneling dynamics with many vibrational modes is shown to result in an additional damping of the time-dependent correlation functions. Nontrivial multimode effects in the inelastic electron-molecule scattering cross sections are demonstrated for a model example.

Absolute ionization cross sections for ${\mathrm{In}}^{+}$ and ${\mathrm{Xe}}^{+}$ by electron impact have been measured from below threshold to 200 eV using the crossed-beams technique. The cross sections for ${\mathrm{In}}^{+}$ were possibly enhanced by indirect ionization processes. The excitation of the ion from the 4${\mathit{d}}^{10}$5${\mathit{s}}^2$ ground state to the 4${\mathit{d}}^9$5${\mathit{s}}^2$5p state followed by autoionization has been postulated. The ${\mathrm{In}}^{+}$ cross sections show a peak value of 15.9×${10}^{\mathrm{-}17}$ ${\mathrm{cm}}^2$ at about 80 eV. The cross sections for ${\mathrm{Xe}}^{+}$ peak at a value of 25.6×${10}^{\mathrm{-}17}$ ${\mathrm{cm}}^2$ at about 35 eV. Experimental measurements are compared to configuration-averaged distorted-wave calculations [M. S. Pindzola et al., J. Phys. B 16, L355 (1983)], the semiempirical formula of Lotz [Z. Phys. 216, 241 (1968)], and, in the case of ${\mathrm{Xe}}^{+}$, previous experimental results [C. Achenbach et al., J. Phys. B 17, 1405 (1984)]. Also presented are ionization-rate coefficients and fitting parameters for both ions for temperatures in the range ${10}^4$ K≤T≤${10}^7$ K.