The reliability of density-functional theory in predicting nuclear quadrupole resonance (NQR) frequencies and nuclear quadrupole coupling constants was tested for a series of straight-chain chloroalkenes (vinyl chloride, 2-chloropropane, cis- and trans-1-chloropropene, cis-dichloroethylene, and tetrachloroethylene). The calculations were performed using the linear combination of Gaussian-type orbitals local-spin-density method and the generalized gradient approximation. The calculated NQR frequencies are in good agreement with experimental data. Less satisfactory agreement is found in the prediction of quadrupole coupling constants. The results show that the calculated NQR frequencies and nuclear quadrupole coupling constants can be used to study the electron distribution in molecular systems. © 1996 The American Physical Society.

We use a recently established and optimized atomic orbital basis set to perform extensive numerical calculations on the hydrogen molecular ion in a strong magnetic field. Many excited electronic states with gerade and ungerade parity as well as their potential-energy curves are investigated for the perpendicular configuration, i.e., for orthogonal internuclear and magnetic-field axes. The main issues of our investigation are the local as well as global topological properties of the potential-energy surfaces of the six energetically lowest electronic states of the ${\mathrm{H}}_2^{+}$ ion in a strong magnetic field B=1.0 a.u. Our results show the existence of a variety of different possibilities for the topological behavior of the potential-energy surfaces: for the lowest electronic states the global equilibrium configuration is either the parallel or the perpendicular configuration, which are both distinguished by their higher symmetry. As a major result we observe, for the $3_{\mathit{u}}$ electronic state, the effect of a global symmetry lowering: the global equilibrium configuration of the $3_{\mathit{u}}$ potential-energy surface is at Θ=27°, i.e., a configuration that strongly deviates from the distinct parallel or orthogonal configurations. Examinations of the electronic probability density distributions with varying angle Θ reveal the origin of the topological behavior of the different surfaces. © 1996 The American Physical Society.

A theory is presented of radiation trapping effects in time-resolved, stepwise-excited, electron-photon coincidence signals. The theory is based on a detailed analysis of laser-induced optical pumping effects in the stepwise excitation process combined with a multipole treatment of the radiation trapping processes. New data from a stepwise excitation experiment on the inelastic excitation of the 6${\mathrm{}}^1$${\mathit{P}}_1$ state in ${\mathit{e}}^{\mathrm{-}}$-Hg collisions and previously reported data are compared with the predictions of the theory. Good agreement is found between experiment and theory, including confirmation that under some experimental conditions, the ${\mathit{P}}_{10}$ Stokes parameter of the coincidentally detected stepwise excited fluorescence increases in magnitude with increasing target gas density. © 1996 The American Physical Society.

O(${\mathrm{\alpha }}^7$${\mathit{mc}}^2$) QED corrections to the fine structure of helium are presented. They are expressed in the form of expectation values of nonrelativistic operators. Self-energy corrections of second order are derived rigorously. Others are obtained phenomenologically. © 1996 The American Physical Society.

We discuss the prospects for parity-nonconservation experiments with highly charged heavy ions. Energy levels and parity mixing for heavy ions with 2–5 electrons are calculated. We investigate two-photon transitions and the possibility of observing interference effects between weak-matrix elements and Stark matrix elements for periodic electric field configurations. © 1996 The American Physical Society.

Multiconfiguration Dirac-Fock and relativistic coupled cluster results are reported for electron affinities, ionization potentials, and excitation energies of Tl and element 113 and their cations. Large basis sets are used, with l up to 6, the Dirac-Fock or Dirac-Fock-Breit orbitals found, and the external 35 electrons of each atom are correlated by the coupled-cluster method with single and double excitations. Very good agreement with experiment is obtained for the Tl transition energies. As in the case of elements 111 [Eliav et al., Phys. Rev. Lett. 73, 3203 (1994)] and 112 [Eliav, Kaldor, and Ishikawa, Phys. Rev. A 52, 2765 (1995)], strong relativistic stabilization of the 7s orbital is observed for E113, leading to dramatic reduction (relative to Tl) in the energies of excitation from ${\mathit{d}}^{10}$ to ${\mathit{d}}^9$ levels. Thus the ${\mathit{d}}^{10}$s→${\mathit{d}}^9$${\mathit{s}}^2$ energy of ${\mathrm{E}113\mathrm{}}^{2+}$ is 0.1 eV, compared to 8 eV for ${\mathrm{Tl}}^{2+}$. It is predicted that divalent or trivalent compounds of E113 with an open 6${\mathit{d}}^9$ shell could possibly exist. The calculated electron affinities of Tl and E113 are 0.40±0.05 and 0.6–0.7 eV, respectively. © 1996 The American Physical Society.

The hyperspherical coordinates approach to three-electron atomic systems is further refined by taking into account the symmetry of the electrons analytically. Spins are treated explicitly for both doublet and quartet cases to reduce the three-electron Schrödinger equation to a set of coupled two-dimensional partial differential equations in a compact, symmetric form ready for numerical calculations. It is shown that the resulting equations can be accurately solved using B splines. By adopting the adiabatic approximation, the hyperspherical potential curves for singly, doubly, and triply excited states for the ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ symmetry of Li are obtained. © 1996 The American Physical Society.

The unrestricted Hartree-Fock and unrestricted Kohn-Sham calculations generally result in spin-contaminated solutions. Moreover, the energies from these calculations cannot be directly compared with the results of corresponding restricted calculations since the latter yield higher energies due to restrictions imposed on the form of the wave function. We present here a simple method of correcting the mixed spin energies resulting from unrestricted Hartree-Fock or density-functional theory calculations and removing the foreign spin components. The method allows for elimination of higher-multiplet components from the given mixed spin state solution by performing unrestricted calculations at the same fixed geometry for the higher multiplets and the state under consideration. The performance of the method is illustrated with several examples of density-functional calculations of radical species. The current method is also variational in nature and can be further extended in a self-consistent field fashion. © 1996 The American Physical Society.

X-ray spectra of 2l-nl′ transitions with 3≤n≤12 in the row-5 transition metals zirconium (Z=40), niobium (Z=41), molybdenum (Z=42), and palladium (Z=46) from charge states around neonlike have been observed from Alcator C-Mod plasmas. Accurate wavelengths (±0.2 mÅ) have been determined by comparison with neighboring argon, chlorine, and sulfur lines with well-known wavelengths. Line identifications have been made by comparison to ab initio atomic structure calculations, using a fully relativistic, parametric potential code. For neonlike ions, calculated wavelengths and oscillator strengths are presented for 2p-nd transitions with n between 3 and 12. The magnitude of the configuration interaction between the (2${\mathit{p}}^5$${)}_{1/2}$6${\mathit{d}}_{3/2}$ J=1 level and the (2${\mathit{p}}^5$${)}_{3/2}$7${\mathit{d}}_{5/2}$ J=1 levels has been measured as a function of energy-level spacing for successive-atomic-number neonlike ions, and the agreement with theory is good. Transitions in the 2${\mathit{p}}_{1/2}$-${\mathit{nd}}_{3/2}$ series in neonlike ${\mathrm{Mo}}^{32+}$ with n≥13 are not observed; the upper levels lie above the first ionization potential of the neonlike ion and have a large branching ratio towards autoionization. Measured and calculated wavelengths and oscillator strengths of selected transitions in the aluminum-, magnesium-, sodium-, fluorine-, and oxygenlike isosequences are also presented. © 1996 The American Physical Society.

Consider H${\mathrm{^}}_{\lambda }$=T^+λV${\mathrm{^}}_{\mathit{ee}}$+${\sum }_{\mathit{i}=1\mathrm{}}^{\mathit{N}}$${\mathit{v}}_{\lambda }$(r${\to }_{\mathit{i}}$), where, in atomic units, T^=${\sum }_{\mathit{i}=1\mathrm{}}^{{\mathit{N}}^{\mathrm{-}}}$1/2${\mathrm{\nabla }}_{\mathit{i}}^2$ and V${\mathrm{^}}_{\mathit{ee}}$=${\sum }_{\mathit{i}}$${\sum }_{\mathit{j}\mathrm{\gtrsim }\mathit{i}}$‖r${\to }_{\mathit{i}}$-r${\to }_{\mathit{j}}$${\mathrm{\Vert }}^{\mathrm{-}1}$ and the local-multiplicative potential ${\mathit{v}}_{\lambda }$ is constructed to keep n, the Hartree-Fock density of H${\mathrm{^}}_{\lambda }$, independent of the coupling constant λ. Moreover, n is simultaneously the exact physical ground-state density of interest and ${\mathit{v}}_{\lambda =0\mathrm{}}$ is its Kohn-Sham potential. For the purpose of extracting the exact Kohn-Sham exchange potential ${\mathit{v}}_{\mathit{x}}$([n];r→), it is shown that ${\mathit{v}}_{\mathit{x}}$([n];r→)=-∂${\mathit{v}}_{\lambda }$([n];r→)/∂λ${\mathrm{\Vert }}_{\lambda =0\mathrm{}}$-∫[ n(r→′)/‖r→-r${\to }^{\prime }$‖]${\mathit{d}}^3$${\mathit{r}}^{\prime }$. The correlation potential for n(r→) is then obtained by subtracting the above ${\mathit{v}}_{\mathit{x}}$ from the exact exchange-correlation potential for n(r→). Furthermore, it is shown that the potential ${\mathit{w}}_{\lambda }$(r→), which keeps the exact ground-state density of T^+λV${\mathrm{^}}_{\mathit{ee}}$+${\sum }_{\mathit{i}=1\mathrm{}}^{\mathit{N}}$${\mathit{w}}_{\lambda }$(r${\to }_{\mathit{i}}$) independent of the value of λ, determines the functional derivative of ${\mathit{T}}_{\mathit{c}}$[n] with respect to the density, i.e., the kinetic contribution to the correlation potential ${\mathit{v}}_{\mathit{c}}$, δ${\mathit{T}}_{\mathit{c}}$[ρ]/δρ(r→)${\mathrm{\Vert }}_{\mathrm{\rho }=\mathit{n}}$=${\mathit{v}}_{\mathrm{xc}}$([n];r→)+∫n(r→′)${\mathit{d}}^3$${\mathit{r}}^{\prime }$/‖r→-r${\to }^{\prime }$‖-∂${\mathit{w}}_{\lambda }$([n];r→)/∂λ${\mathrm{\Vert }}_{\lambda =1\mathrm{}}$. © 1996 The American Physical Society.

A relativistic many-body perturbation theory, which accounts for relativistic and electron-correlation effects for general open-shell multiplet states of atoms and molecules, is developed and implemented with analytic basis sets of Gaussian spinors. The theory retains the essential aspects of Mo/ller-Plesset perturbation theory by employing the relativistic single-Fock-operator method of Koc and Ishikawa [Phys. Rev. A 49, 794 (1994)] for general open-shell systems. Open-shell Dirac-Fock and relativistic many-body perturbation calculations are reported for the ground and low-lying excited states of Li, ${\mathrm{B}}^{2+}$, ${\mathrm{Ne}}^{7+}$, and ${\mathrm{Ca}}^{11+}$. © 1996 The American Physical Society.

The linear polarization of the 1s2p${\mathrm{}}^1$${\mathit{P}}_1$→1${\mathit{s}}^2$${\mathrm{}}^1$${\mathit{S}}_0$ resonance line, the 1s2p${\mathrm{}}^3$${\mathit{P}}_{1,2}$→1${\mathit{s}}^2$${\mathrm{}}^1$${\mathit{S}}_0$ intercombination lines, and the 1s2s${\mathrm{}}^3$${\mathit{S}}_1$→1${\mathit{s}}^2$${\mathrm{}}^1$${\mathit{S}}_0$ forbidden line was measured in heliumlike Fe XXV excited near threshold by a monoenergetic electron beam. The measurement was carried out with a high-resolution x-ray spectrometer employing a set of two analyzing crystals that acted as polarizers by selectively reflecting the individual polarization components. A value of +0.${56}_{\mathrm{-}0.08}^{+0.17\mathrm{}}$ was determined for the polarization of the ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ line, -0.${53}_{\mathrm{-}0.02}^{+0.05\mathrm{}}$ for the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$ line, -0.${22}_{\mathrm{-}0.02}^{+0.05\mathrm{}}$ for the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ line, and -0.${076}_{\mathrm{-}0.007}^{+0.007\mathrm{}}$ for the ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$ line. The measurements were compared with results from a relativistic distorted-wave calculation, which was carried out for a number of mid-Z heliumlike ions (${\mathrm{Mg}}^{10+}$–${\mathrm{Kr}}^{34+}$), and good agreement was found. By contrast, disagreement was noted with predictions based on Coulomb-Born calculations, allowing us to distinguish between theoretical approaches. © 1996 The American Physical Society.

The ground-state hyperfine splitting of trapped ${}_{}{}^{113}{}_{}{}^{}\mathrm{Cd}_{}^{+}{}_{}{}^{}$ ions has been measured to be 15 199 862 858(2) Hz. The transition was detected by a laser microwave double-resonance method in the presence of He buffer gas. The result was corrected for the second-order magnetic-field dependence. This paper also discusses the possibility of using ${\mathrm{Cd}}^{+}$ ions as a microwave-frequency standard. © 1996 The American Physical Society.

A two-electron spin-independent operator is defined to represent the spatial correlation of the electrons in a general atom or ion. The spherical-tensor expansion of this operator provides a systematic method for evaluating the two-electron correlation function implied by a Hartree-Fock N-electron wave function including arbitrary configuration mixing. The method is illustrated by examples involving electron coalescence in helium and carbon, and core polarization in sodium. This technique for computing the electron correlation function provides a useful tool of wide applicability in comparing different theoretical approaches to the structure of complex atoms. © 1996 The American Physical Society.

Using excitation from five dye lasers, the ${\mathrm{Yb}}^{+}$ Rydberg series of ${\mathit{np}}_{1/2}$ and ${\mathit{np}}_{3/2}$ have been achieved. Abnormal branching ratios of ${\mathit{np}}_{1/2}$:${\mathit{np}}_{3/2}$ excited from ${\mathrm{Yb}}^{+}$ 7${\mathit{s}}_{1/2}$ are found. In the relativistic central-field independent-particle approximation, oscillator-strength distributions of ${\mathrm{Yb}}^{+}$, ${\mathrm{Ba}}^{+}$, and ${\mathrm{Sr}}^{+}$ are calculated, respectively. The calculated results are in good agreement with our experiment on ${\mathrm{Yb}}^{+}$ and previous experiments on ${\mathrm{Ba}}^{+}$ and ${\mathrm{Sr}}^{+}$ where abnormal branching ratios were also found. We have found that the abnormal branching ratios are due to the appearance of Cooper minima or shape resonances. The results can be used to estimate the oscillator strength of unsymmetric double Rydberg states. © 1996 The American Physical Society.

We present high-resolution crystal-spectrometer measurements that cover the wavelength range 3.0–3.2 Å containing the electric-dipole-allowed 2${\mathit{s}}_{1/2}$-2${\mathit{p}}_{3/2}$ transitions in highly charged uranium ions. Strong features from 2${\mathit{s}}_{1/2}$-2${\mathit{p}}_{3/2}$ transitions in lithiumlike, berylliumlike, and boronlike uranium were observed. In addition, a weak feature with intensity just above the level of background fluctuations was observed at the predicted location of the 1s2s${\mathrm{}}^3$${\mathit{S}}_1$–1s2p${\mathrm{}}^3$${\mathit{P}}_2$ transition in heliumlike ${\mathrm{U}}^{90+}$. The feature was observed in spectra where the intensity of the 2${\mathit{s}}_{1/2}$-2${\mathit{p}}_{3/2}$ transition in lithiumlike uranium, and thus the ionization balance, was optimized; it appeared absent in spectra where the average ionization balance was lower. The measured energy of the feature is 4510.05±0.24 eV, which agrees closely with the values predicted for the 1s2s${\mathrm{}}^3$${\mathit{S}}_1$–1s2p${\mathrm{}}^3$${\mathit{P}}_2$ transition by recent theories. Detailed spectral modeling calculations indicate the possibility that a weak transition in berylliumlike ${\mathrm{U}}^{88+}$ is situated within 4 eV of the location of the heliumlike ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$${\mathrm{-}}^3$${\mathit{P}}_2$ transition. This transition connects the level 1s${\mathrm{}}^2$2${\mathit{p}}_{1/2}$2${\mathit{p}}_{3/2}$${\mathrm{}}^3$${\mathit{p}}_1$ with the 1s${\mathrm{}}^2$2${\mathit{s}}_{1/2}$2${\mathit{p}}_{1/2}$${\mathrm{}}^3$${\mathit{P}}_0$ metastable ground level in berylliumlike uranium. The accuracy with which the energy of the berylliumlike transition can be predicted is insufficient to rule out a blend with the heliumlike ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$${\mathrm{-}}^3$${\mathit{P}}_2$ transition. © 1996 The American Physical Society.

The effect of an intense magnetic field on transition arrays is investigated. Explicit formulas for the first moments of the array are given in the weak- and strong-field limits. The result related to the strong-field case is particularly simple: the transition array splits into three components located at the relative positions -${\mathrm{\mu }}_{\mathit{BH}}$,0,${\mathrm{\mu }}_{\mathit{BH}}$, each component having the same variance as the array without magnetic field. The changes in the opacity of aluminum and neon at low density are then computed for a range of magnetic fields relevant to Z-pinch experiments © 1996 The American Physical Society.

We report recent progress toward a nonperturbative formulation of many-body quantum dynamics that treats all constituent particles on an equal footing. This formulation is capable of detailing the evolution of a system toward the diverse fragments into which it can break up. We illustrate the general concept with the simple example of the simultaneous excitation of both electrons in a helium atom. © 1996 The American Physical Society.

Results from large-scale multiconfiguration Hartree-Fock (MCHF) and configuration-interaction (CI) calculations of the transition probability and hyperfine structures in the sodium 3s${\mathrm{}}^2$S-3p${\mathrm{}}^2$P resonance transition are presented. In the calculations the orbital sets of the initial and final state wave functions were not restricted to be the same, but were optimized independently. The evaluation of the transition matrix elements was done using a technique where the two orbital sets are transformed so as to become biorthonormal, in which case standard Racah algebra can be used. Three-particle effects were taken into account in the CI calculations and were found to be important for the hyperfine structures, but less important for the transition probability. The calculated transition probability is in perfect agreement with the most recent experimental values, thus resolving the long-standing disagreement between theory and experiment. Also the 3s${\mathrm{}}^2$${\mathit{S}}_{1/2}$ and 3p${\mathrm{}}^2$${\mathit{P}}_{1/2,3/2}$ hyperfine interaction constants are in very good agreement with available experimental values. © 1996 The American Physical Society.

Valence shell relativistic configuration interaction calculations for the 7p attachment to the Pa I ground state yield one bound state, viz., ${\mathrm{Pa}}^{\mathrm{-}}$ 5${\mathit{f}}^2$6d7${\mathit{s}}^2$7p J=6, with electron affinity of 0.222 eV. We found no other J’s for this configuration to be bound, nor are any of the ${\mathrm{Pa}}^{\mathrm{-}}$ 5${\mathit{f}}^2$6${\mathit{d}}^2$7${\mathit{s}}^2$ levels expected to be bound. The hyperfine structure constants for the ${}_{}{}^{231}{}_{}{}^{}\mathrm{Pa}_{}^{\mathrm{-}}{}_{}{}^{}$ bound state are A=741.3 MHz and B=1309 MHz. Although the core-valence correlation effects are absent the agreement between the theory (4736 ${\mathrm{cm}}^{\mathrm{-}1}$) and experiment (4121 ${\mathrm{cm}}^{\mathrm{-}1}$) for the position of the first excited state of Pa is good (15%). We review our previous studies for the np attachment in rare earths to systematically analyze the binding of ${\mathit{np}}_{1/2}$ and ${\mathit{np}}_{3/2}$ electrons, in these species. © 1996 The American Physical Society.