We construct effective Hamiltonians which, despite their apparently nonrelativistic form, incorporate relativistic effects by involving parameters which depend on the relevant momentum. For some potentials the corresponding energy eigenvalues may be determined analytically. Applied to two-particle bound states, it turns out that in this way a nonrelativistic treatment may indeed be able to simulate relativistic effects. Within the framework of hadron spectroscopy, this lucky circumstance may be an explanation for the sometimes extremely good predictions of nonrelativistic potential models even in relativistic regions.

We investigate the geometrical features of one-dimensional wave propagation, whose dynamics is described by the (2+1)-dimensional Lorentz group. We find many interesting geometrical ingredients such as spinorlike behavior of wave amplitudes, gauge transformations, Bloch-type equations, and Lorentz-group Berry phases. We also propose an optical experiment to verify these effects.

Numerical computation of optimum values for nonlinear parameters in a Rayleigh-Ritz variational trial function is considerably more difficult than numerical computation of optimum values for linear parameters. Thus, an analytic understanding of the mechanisms that determine these optimum values can be quite useful. Uniform asymptotic expansions can be used to explore these mechanisms for the nonlinear parameter that sets the length scale for a basis set. These uniform asymptotic expansions usually involve two or more different kinds of terms whose relative importance changes as the nonlinear parameter changes, with two different terms being equally important at the point where the nonlinear parameter has its optimum value. Interference effects between these different terms are typical, and tend to become most pronounced near the optimum value. These different kinds of terms arise from singularities of the wave function, from the neighborhood of the classical turning point for the basis functions, and/or from saddle points. Comparisons of theory with (numerical) experiment will be given for Rayleigh-Ritz calculations on three model problems that illustrate the kinds of terms listed above.

Populations of excited atoms that all have the same z component of velocity can be produced by pumping a vapor with a narrow-band laser. This velocity-selected population is then thermalized by velocity-changing collisions. However, in a pure vapor, even at low densities where velocity-changing collisions can be ignored, the mechanisms of radiation trapping and resonance exchange collisions can still lead to substantial thermalization of excited-atom velocity distributions. In this paper, we present data demonstrating these effects. We compare our data with results from a simple model of these processes. The model is in qualitative agreement with the experimental results.

The isotope shifts of the 6 ${}_{}{}^2{}_{}{}^{}$${\mathit{S}}_{1/2}$–5 ${}_{}{}^2{}_{}{}^{}$${\mathit{D}}_{5/2}$ transition in ${\mathrm{Ba}}^{+}$ have been measured using the high-resolution laser spectroscopy of a single trapped ion. The shifts are measured among three even ${\mathrm{Ba}}^{+}$ isotopes, ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}_{}^{+}{}_{}{}^{}$, ${}_{}{}^{136}{}_{}{}^{}\mathrm{Ba}_{}^{+}{}_{}{}^{}$, and ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ba}_{}^{+}{}_{}{}^{}$. The results are ${\nu }_{138\mathrm{-}}$${\nu }_{136}$=-106.143(4) MHz and ${\nu }_{138\mathrm{-}}$${\nu }_{134}$=-38.455(15) MHz. This experiment gives a measurement of isotope shifts for a heavy atom. The results should provide a stringent test for the theoretical calculations of the isotope shifts of alkali-metal-like atoms.

We examine the effects of relativity on the high-Z (where Z denotes nuclear charge) behavior of isoelectronic sequences and the modifications required of the traditional charge expansion theory. We propose that the idea of a complex be refined to include hydrogenic angular-momentum degeneracy, so that a relativistic complex should be defined as the set of all configurations with the same occupation of angular-momentum quantum numbers j as well as the same principal quantum numbers n. This leads to asymptotic, high-Z grouping of states that might cut across the conventional LS-coupled states, grouping together levels from different configurations, as long as the n and j occupation numbers remain the same. This regrouping substantially reduces the asymptotic configuration interaction from that predicted by a nonrelativistic theory. Frequently correlation configurations that are significant in low-Z ions disappear entirely in high-Z ions.

The recently built electron-energy-loss spectrometer (EELS) (typical FWHM 60 meV) was employed to measure the EELS spectra of argon in the discrete and autoionization resonance regions at a 2.5-keV impact energy and a mean scattering angle of 0°. Relative differential optical oscillator strength spectra were established by multiplying the EELS spectra by the known Bethe-Born conversion factor of the spectrometer, and were normalized at a single point in the smooth continuum using the absolute values reported by Chan et al. [Phys. Rev. A 46, 149 (1992)]. The absolute oscillator strengths corresponding to these energy regions are reported and compared with previously published experimental and theoretical values. The values of parameters q, ${\mathrm{\rho }}^2$, ${\mathit{E}}_{\mathit{r}}$, and Γ for autoionization resonances involving states 3s3${\mathit{p}}^6$np ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1^0$ (n=4, 5, and 6) have been determined.

Kohn-Sham wave functions yielding the Hartree-Fock ground-state densities of alkaline-earth and noble-gas atoms are calculated. From the Kohn-Sham wave functions the corresponding noninteracting kinetic energies and the exchange energies are calculated according to the density-functional definition. The difference between the density-functional and the Hartree-Fock exchange energies for a given electron density is found to be surprisingly small. This justifies, at least for the systems studied here, the common practice of using Hartree-Fock exchange energies as reference values to assess the quality of today’s approximate density functionals for the exchange energy. The calculated Kohn-Sham wave functions give energies with the atomic Hamiltonian operators which are de facto identical to the corresponding values obtained from the optimized potential method. The influence of a coupling parameter turning on the electron-electron interaction on the difference between Kohn-Sham and Hartree-Fock kinetic and exchange energies is investigated. Various hybrid schemes which combine the Kohn-Sham and the Hartee-Fock methods are compared. For the atomic systems investigated here, the different exchange and correlation energies occurring in these schemes are found in most cases to deviate very little from the standard Kohn-Sham exchange and correlation energies. Finally, the formulation and validity of the Hohenberg-Kohn theorem in basis set representations are discussed.

The (${\mathit{e}}^{\mathrm{-}}$,${\mathit{e}}^{+}$)-pair annihilation in the bound ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ state of the ${\mathrm{Ps}}_2$ molecule (${\mathit{e}}^{\mathrm{-}}$${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$${\mathit{e}}^{+}$) is studied. It is shown that the expectation values of the two-, three-, and four-body Dirac δ functions 〈${\mathrm{\delta }}_{+\mathrm{-}}$〉, 〈${\mathrm{\delta }}_{++\mathrm{-}}$〉 (≡〈${\mathrm{\delta }}_{+\mathrm{-}\mathrm{-}}$〉), and 〈${\mathrm{\delta }}_{++\mathrm{-}\mathrm{-}}$〉 determine the photonless, one- and many-photon annihilation rates, i.e., the values of ${\mathrm{\Gamma }}_{0\gamma }$, ${\mathrm{\Gamma }}_{1\gamma }$, and ${\mathrm{\Gamma }}_{\mathit{n}\gamma }$, where n≥2. The appropriate analytical expressions are presented together with numerical estimates. As expected, the two-photon annihilation process dominates.

Relativistic O(${\mathrm{\alpha }}^2$) corrections to the orthopositronium decay rate are calculated on the basis of a local quasipotential equation. We take into account the necessary contributions resulting from the amplitude of three-photon decay, the normalization condition of the wave function, and the second-order perturbation theory.

The behavior of the rsonances of a hydrogen atom in parallel magnetic and electric fields is obtained with a complex scaling plus B-spline method. The resonant parameters E and ${\mathrm{\Gamma }}_0$ in an electric field alone are consistent with those obtained by other methods. In a fixed electric field F the widths Γ of both the ground and excited resonances decrease with an increase of the magnetic field B, and the relative variation (Γ-${\mathrm{\Gamma }}_0$)/${\mathrm{\Gamma }}_0$ is directly proportional to the ratio of the magnetic-field strength to the electric-field strength. The positions of the resonances, however, are pushed higher by an increasing of magnetic field. The pushing effect is insensitive to the electric-field strength and depends almost entirely on the magnetic-field strength.

In the standard interpretation of spin-density functional theory, a self-consistent Kohn-Sham calculation within the local spin density (LSD) or generalized gradient approximation (GGA) leads to a prediction of the total energy E, total electron density n(r)=${\mathit{n}}_{\mathrm{\uparrow }}$(r)+${\mathit{n}}_{\mathrm{\downarrow }}$(r), and spin magnetization density m(r)=${\mathit{n}}_{\mathrm{\uparrow }}$(r)-${\mathit{n}}_{\mathrm{\downarrow }}$(r). This interpretation encounters a serious ‘‘symmetry dilemma’’ for ${\mathrm{H}}_2$, ${\mathrm{Cr}}_2$, and many other molecules. Without changing LSD or GGA calculational methods and results, we escape this dilemma through an alternative interpretation in which the third physical prediction is not m(r) but the on-top electron pair density P(r,r), a quantity more directly related to the total energy in the absence of an external magnetic field. This alternative interpretation is also relevant to antiferromagnetic solids. We argue that the nonlocal exchange-correlation energy functional, which must be approximated, is most nearly local in the alternative spin-density functional theory presented here, less so in the standard theory, and far less so in total-density functional theory. Thus, in LSD or GGA, predictions of spin magnetization densities and moments are not so robust as predictions of total density and energy. The alternative theory helps to explain the surprising accuracy of LSD and GGA energies, and suggests that the correct solution of the Kohn-Sham equations in LSD or GGA is the fully self-consistent broken-symmetry single determinant of lowest total energy.

A large number of magnetically dressed states of the hydrogen molecular ion for parallel internuclear and magnetic field axes are investigated. The numerical calculations of the molecular states and potential-energy curves in the fixed-nuclei approximation are based on a recently established and optimized atomic orbital basis set. We study electronic states within the range 0≤‖m‖≤10 of magnetic quantum numbers and for several field strengths. In particular, we also investigate many excited states within a subspace for fixed magnetic quantum number and parity. In order to understand the influence of the magnetic field on the chemical bond of excited molecular states, we perform a detailed comparison of the electronic probability distributions and potential-energy curves in the field-free space with those in the presence of a magnetic field. As a major result we observe the existence of two different classes of strongly bound, i.e., stable, magnetically dressed states whose corresponding counterparts in the field-free space exhibit purely repulsive potential-energy curves, i.e., are unstable. Corrections which are going beyond the fixed-nuclei approach, i.e., the coupling of the center of mass to the electronic motion, as well as the mass corrections are investigated in order to ensure the physical validity of our results.

Rydberg atoms in strong fields have scaling properties that allow detailed interpretation of photoabsorption spectra in terms of classical trajectories. The classical dynamics remains invariant if a spectrum is obtained at constant scaled energy. Since each orbit which is closed at the nucleus produces a sinusoidal modulation in the absorption spectrum, its signature is a peak in the Fourier transform of a scaled-energy spectrum. This paper identifies the effect of closed orbits in the computed spectrum of the hydrogen atom in parallel electric and magnetic fields in a region where chaos is just beginning to develop.

Asymmetry parameter (β) values have been determined from the ${\mathrm{C}}^{+}$, ${\mathrm{O}}^{+}$, and ${\mathrm{CO}}^{+}$ signals in the time-of-flight (TOF) mass spectra and the ${\mathrm{CO}}^{+}$-${\mathrm{O}}^{+}$ signal in the photoion-photoion coincidence (PIPICO) spectra of ${\mathrm{CO}}_2$ excited and/or ionized with monochromatic synchrotron radiation around the C K and O K ionization edges using a rotatable time-of-flight mass spectrometer. Positive β values of 0.4 were found for the ${\mathrm{C}}^{+}$ ions at the C 1${\mathit{s}}^{\mathrm{-}1}$2${\mathrm{\pi }}_{\mathit{u}}^{\mathrm{*}}$ and O 1${\mathit{s}}^{\mathrm{-}1}$2${\mathrm{\pi }}_{\mathit{u}}^{\mathrm{*}}$ resonances, respectively, and negative values between -0.1 and -0.4 were obtained for the other TOF and PIPICO signals at the same photon energies. The difference between these values and the expected value of -1 results from bending the molecule in the excited state before or during its ionic fragmentation. An O-C-O bond angle of 124° was found for ${\mathrm{CO}}_2$ in the C 1${\mathit{s}}^{\mathrm{-}1}$2${\mathrm{\pi }}_{\mathit{u}}^{\mathrm{*}}$ state from the β value for the ${\mathrm{O}}^{+}$-${\mathrm{CO}}^{+}$ PIPICO signal. The β values were close to the isotropic value of zero at all other photon energies for the ${\mathrm{C}}^{+}$ ions. β values for the ${\mathrm{O}}^{+}$ and ${\mathrm{CO}}^{+}$ signals in the TOF spectra and the ${\mathrm{O}}^{+}$-${\mathrm{CO}}^{+}$ signals in the PIPICO spectra were found to be similar.

Slightly negative β values were found below the C K edge, rising to a maximum value of 0.9 at the ${\mathrm{\sigma }}_{\mathit{u}}^{\mathrm{*}}$ shape resonance at 312.2 eV. Strongly positive β values were found just below the O K edge and were assigned to a transition of an O 1s electron to an s-type Rydberg orbital coupled with a shape resonance in the ${\mathrm{\sigma }}_{\mathit{g}}$ ionization channel. Two maxima were observed in the β values above the O K edge and assigned to shape resonances in the ${\mathrm{\sigma }}_{\mathit{g}}$ and ${\mathrm{\sigma }}_{\mathit{u}}$ continuum channels. The lower energy resonance in the ${\mathrm{\sigma }}_{\mathit{g}}$ channel was found at 542.5 eV and the position of the higher energy shape resonance in the ${\mathrm{\sigma }}_{\mathit{u}}$ channel was found to be 560 eV. The importance of using mass-resolved ion spectra to determine the β parameters for molecules which undergo a change in geometry upon excitation of a core electron is highlighted by a comparison of these results with the symmetry-resolved ion yield spectra of ${\mathrm{CO}}_2$.

Earlier studies of line strengths for ${\mathit{ns}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$–nsn’p ${}_{}{}^{1,3}{}_{}{}^{}$${\mathit{P}}_1$ resonance and intercombination transitions for intrashell (n’=n) cases have revealed isoelectronic regularities that have been used to make accurate predictions along the sequence. Although lifetime data exist for intershell (n’>n) cases, the lack of branching ratio measurements has until now prevented similar analyses. Through new lifetime measurements, a critical evaluation of the available data, and determinations of branching fractions from a differential measurement and from calculational considerations, we have extended these methods to systematize and predict line strengths for Δn=1 resonance and intercombination transitions in the Be and Ne sequences.

To study the impact of the choices of complete model spaces (CMS’s) and of orbital basis sets on the performance of valence-universal (VU) coupled-cluster (CC) methods, extensive calculations have been performed for Be and ${\mathrm{C}}^{2+}$ by means of the atomically oriented form of these methods accounting for one(S)- and two(D)-electron radial (R) excitations (VU-CCSD/R method). In addition to the commonly used complete model space defined by the orbital set (2s,2p) we have employed the CMS’s defined by the (2s,3s) and (2s,2p,3s) sets. Despite the anticipated increase of intruder state difficulties, for the new CMS’s, no problems have been encountered when solving the nonlinear VU-CCSD/R equations. The results for the total energies and energy differences disclosed a weak dependence on the CMS chosen. We have used four Slater-type orbitals basis sets partially balanced for an accurate description of the ground and excited states. It turned out that the energies of excited states strongly depend on the basis set used, which emphasizes the importance of developing methods for constructing well balanced basis sets. It has been demonstrated that the VU-CCSD/R method can be used for the accurate localization of the position of the 2${\mathit{p}}^2$ ${}_{}{}^1{}_{}{}^{}$S resonance with respect to the ionization limit. Some attention is also paid to a singular behavior of the energy obtained with the linearized version of the VU-CCSD/R method.

The hyperfine structure of the one-electron ion ${}_{83}{}^{209}{}_{}{}^{}\mathrm{Bi}_{}^{82+}{}_{}{}^{}$ is evaluated within the framework of a dynamical model in which the electron is assumed to interact with the valence proton through the exchange of a photon.

The multiconfiguration Dirac-Fock model is employed to study the effects of relativity and electron correlation on the hyperfine interaction constants of the 3${\mathit{d}}^2$ ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$, ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$, ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$, and ${}_{}{}^3{}_{}{}^{}$${\mathit{F}}_2$ levels of ${\mathrm{Sc}}^{+}$ and the 4${\mathit{d}}^2$ ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ level of ${\mathrm{Y}}^{+}$. The wave function expansions are obtained with the active space method, where configuration state functions of a specific parity and J value are generated by excitations from the most important reference configurations to an active set of orbitals. The active set is then increased in a systematic way, allowing the convergence of the hyperfine interaction constants to be studied. It is demonstrated that expansions generated by single excitations from the reference configurations, together with the most important double excitations, account for the dominant contributions to the hyperfine interaction constants and lead to very good agremeent between theoretical and experimental values. To obtain converged values of these constants within the single excitation approach, typically a few thousand configuration state functions are needed.

Systematic multiconfiguration-Hartree-Fock procedures are applied to the study of the electron affinity of boron. For a valence correlation calculation, an electron affinity of 273.2(2) meV is obtained, which is reduced by 1.1 meV by a relativistic correction. Core polarization and core rearrangement were found to increase the electron affinity to 279.5(20) meV. The latter agrees well with the experimental value of 277(10) meV. Results are compared also with other theories.