Measurements of oscillator strengths for the principal series of calcium 4${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$→4snp ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ (11≤n≤25) are reported. The data were acquired using the magneto-optical spectroscopic technique, utilizing the linearly polarized light emitted by the 2.5-GeV electron accelerator, a 7-T superconducting magnet, and a 3-m-high dispersion spectrograph with photographic detection. A quantum-defect plot of the density of the oscillator strengths of discrete transitions yields the photoionization cross section at threshold as 2.04±0.20 Mb, in agreement with earlier measurements.

Systematic multiconfiguration Hartree-Fock results are presented for the transition probabilities and excited-state lifetimes in the term system of the boron atom. Particularly, the interaction between the 1${\mathit{s}}^2$2s2${\mathit{p}}^2$ configuration and the 1${\mathit{s}}^2$2${\mathit{s}}^2$ns ${}_{}{}^2{}_{}{}^{}$S and 1${\mathit{s}}^2$2${\mathit{s}}^2$nd ${}_{}{}^2{}_{}{}^{}$D Rydberg series is considered. Term energies and transition-matrix elements are calculated to convergence using increasing active sets of s, p, d, f, and g orbitals.

The energy levels and eigenfunctions for electrons that are confined to moving on the surface of a sphere but are otherwise free are utilized to calculate the corresponding canonical density matrix. This matrix is then expanded in an asymptotic series for a large sphere radius R. The leading term naturally corresponds to free electrons moving on a plane and the first correction term to this, O(${\mathit{R}}^{\mathrm{-}2}$), is exhibited explicitly. This matrix is then utilized to construct both the Dirac density matrix and the Green function in the same approximation. This Green function, in relation, say, to K-doped ${\mathrm{C}}_{60}$, where added electrons are localized near the surface of a sphere, serves to emphasize first the quasi-two-dimensional character of the motion, and then to exhibit the corrections for a finite ball radius.

Useful energy-density relationships, connected with the embedding of singly charged postive or negative atomic ions in polar solvents, are developed. The insertion of the atomic charged system into the polarizable host is modeled through successive isoelectronic processes at the nucleus, involving a varying nuclear charge. In this way, the controversial procedure of selecting appropriate ionic radii, involved in the calculation of solvation energies through the Born formula, is avoided and replaced by integration in [0,∞]. The approximate expressions, derived from a variational procedure proposed by Levy [J. Chem. Phys. 68, 5298 (1978); 70, 1573 (1979)], are reformulated within the nuclear-transition-state model. The classical reaction field expression for the insertion energy is recovered. The quality of the approximations made are discussed within the frame of the Kohn-Sham formulation of density-functional theory.

Contributions to magnetic susceptibility and magnetic shielding of the nuclei, arising from electronic magnetic-quadrupole moments interacting with a magnetic field with a spatially uniform gradient, have been determined for a methane molecule, by a large-basis-set calculations within the random-phase approximation. The Hartree-Fock limit of accuracy has been achieved and the quality of the calculations has been confirmed via tests based on sum rules for the origin dependence of the response properties.

An observation of a forbidden transition in Mg xi at 8.50 Å is reported. A Mg wire X pinch generated a ≲1-keV, ∼${10}^{23}$-${\mathrm{cm}}^{\mathrm{-}3}$ Mg plasma in which the intensity of an allowed transition was reduced by a factor of about 100 by self-absorption, permitting the forbidden transition to be observed.

The atomic quadrupole moments of the ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ states of the carbon and neon cations are calculated using a finite-element multiconfiguration Hartree-Fock method. The Hartree-Fock value for ${\mathit{Q}}_{\mathit{z}\mathit{z}}$(${\mathrm{C}}^{+}$) is 0.5373 a.u., the correlation contribution from 2s and 2p is -0.0316 a.u., and the contribution from 1s is -0.0029 a.u. resulting in a final ${\mathit{Q}}_{\mathit{z}\mathit{z}}$(${\mathrm{C}}^{+}$) of 0.5028(5) a.u. For ${\mathit{Q}}_{\mathit{z}\mathit{z}}$(${\mathrm{Ne}}^{+}$) the Hartree-Fock value is -0.1964 a.u., the correlation contribution from 2s and 2p is -0.0068 a.u., and the final ${\mathit{Q}}_{\mathit{z}\mathit{z}}$(${\mathrm{Ne}}^{+}$) becomes -0.2032(5) a.u. For ${\mathrm{Ne}}^{+}$ the contribution from 1s is neglected. The estimated uncertainty is given within parentheses.

We present a computational scheme to propagate wave packets describing S states of two-electron systems. Body-fixed polar coordinates (${\mathit{r}}_{1,}$${\mathit{r}}_2$,θ) are used to represent the time-dependent wave functions on a grid in three dimensions. We handle the Coulomb singularities by transformation of the wave function and a modified finite-difference formula to evaluate the kinetic energy. We use a finite-difference split-operator scheme for the time propagation and, as a first application, we compute the low-energy spectrum of helium and ${\mathrm{H}}^{\mathrm{-}}$.

The mean lifetimes τ of the Ca ii 4p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$ and 4p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ levels, and the ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$ ii 4p’ ${}_{}{}^1{}_{}{}^{}$${\mathit{F}}_3$ level, have been measured by a variant of the collinear laser–ion-beam lifetime technique applied previously to the Ar ii 4p’ ${}_{}{}^2{}_{}{}^{}$${\mathit{F}}_{7/2}^{\mathit{o}}$ level [Jian Jin and D. A. Church, Phys. Rev. A 47, 132 (1993)]. The present results are τ(Ca ii, 4p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$)=7.098(0.020) ns, τ(Ca ii, 4p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$)=6.924(0.019) ns, and τ(Cl ii, 4p’ ${}_{}{}^1{}_{}{}^{}$${\mathit{F}}_3$) =11.17(0.06) ns. The experimental lifetimes of these, plus the Ar ii 4p’ ${}_{}{}^2{}_{}{}^{}$${\mathit{F}}_{7/2}$ level, are compared with available recent many-electron calculations. Typically 1%–3% differences between measurement and ab initio theory are found, while certain semiempirical calculations are in better agreement with experiment. Data for other precise lifetime measurements on alkali-metal systems are compared with recent ab initio and semiempirical calculations to provide perspective on the Ca II results. The hyperfine structure of the ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$ II 3d’ ${}_{}{}^1{}_{}{}^{}$${\mathit{G}}_4$–4p’ ${}_{}{}^1{}_{}{}^{}$${\mathit{F}}_3$ transition was also measured and analyzed in the course of the measurements, with the resulting hyperfine-structure constants: A${(}^1$${\mathit{F}}_3$)=301.9(0.5) MHz, B${(}^1$${\mathit{F}}_3$)=-6.7(0.8) MHz, A${(}^1$${\mathit{G}}_4$)=205.1(0.5) MHz, and B${(}^1$${\mathit{G}}_4$)=-3.9(2.4) MHz.

The energies and mean lifetimes of the different vibrational states of the ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ electronic ground state of ${\mathrm{NeAr}}^{2+}$ have been calculated using the phase-shift technique. An efficient searching method for these narrow resonances was developed. The calculated lifetime of the v=12 vibrational state is in reasonable agreement with the experimental value of 275±25 nsec, reported recently by Ben-Itzhak, Gertner, and Rosner [Phys. Rev. A 47, 289 (1993)], while the lifetimes of other states are more than three orders of magnitude off, thus determining the long-lived vibrational state detected unambiguously. From the difference between the calculated and measured mean lifetime, we have estimated that the potential curve of this 26-electron system is accurate to a few meV. We have also performed ab initio calculations of the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ electronic ground state of ${\mathrm{NeAr}}^{+}$ and calculated the Franck-Condon factors for the final vibrational-state distribution of the ${\mathrm{NeAr}}^{2+}$ molecular ion produced in the ${\mathrm{NeAr}}^{+}$ charge-stripping collisions in order to estimate that high vibrational states are indeed produced in the experiment. We have also examined the validity of the WKB method for calculating the lifetimes of highly excited vibrational states.

In this series, the recently developed explicit formalism of orthogonally spin-adapted Hibert space (or state universal), multireference (MR) coupled-cluster (CC) theory, exploiting the model space spanned by two closed-shell-type reference configurations, is applied to a simple minimum-basis-set four-electron model system consisting of two interacting hydrogen molecules in various geometrical arrangements. In this paper, we examine the nonplanar geometries of this system, generally referred to as the T4 models, and their special cases designated as P4 and V4 models. They correspond to different cross sections of the ${\mathrm{H}}_4$ potential-energy hypersurface, involving the dissociation or simultaneous stretching of two H—H bonds. They involve various quasidegeneracy types, including the orbital and configurational degeneracies, the twofold degeneracy of the ground electronic state and interesting cases of broken-symmetry solutions. We employ the CC with singles and doubles (SD) approximation, so that the cluster operators are approximated by their one- and two-body components. Comparing the resulting CC energies with exact values, which are easily obtained for these models by using the full configuration-interaction method, and performing a cluster analysis of the exact solutions, we assess the performance of various MRCC Hilbert-space approaches at both linear and nonlinear levels of approximation, while a continuous transition is being made between the degenerate and nondegenerate or strongly correlated regimes. We elucidate the sources and the type of singular behavior in both linear and nonlinear versions of MRCC theory, examine the role played by various intruder states, and discuss the potential usefulness of broken-symmetry MRCCSD solutions.

The static dipole polarizabilities of ${\mathrm{B}}^{\mathrm{-}}$, ${\mathrm{C}}^{\mathrm{-}}$, and ${\mathrm{O}}^{\mathrm{-}}$ are studied using the many-body perturbation theory (MBPT) and coupled-cluster methods. The results indicate very large values for the anisotropies and large contributions of the electron correlation, especially of the higher-order single- and triple-excitation effects. At the highest level presently studied [QCISD(T)] the average polarizabilities are 430.5 a.u. (${\mathrm{B}}^{\mathrm{-}}$), 82.8 a.u. (${\mathrm{C}}^{\mathrm{-}}$), and 40.2 a.u. (${\mathrm{O}}^{\mathrm{-}}$) with 40% to 50% coming from electron correlation effects. For ${\mathrm{F}}^{\mathrm{-}}$ the QCISD(T) value is 17.5 a.u., 3.4 a.u. below the fourth-order MBPT(4) result. The anisotropies are 339.3 a.u. (${\mathrm{B}}^{\mathrm{-}}$) and 24.0 a.u. (${\mathrm{O}}^{\mathrm{-}}$) with about 50% coming from electron correlation effects. An analysis of the correlation contribution to the average and anisotropic polarizabilities of the first-row stable atomic anions is made.

An all-order procedure is used to determine the energies of the n=1 and n=2 states of heliumlike ions with nuclear charges in the range Z=3–100. The Coulomb energies and wave functions are obtained from a no-pair Hamiltonian by an iterative scheme that sums all orders of many-body perturbation theory. The Breit energy is determined by taking the expectation value of the instantaneous Breit Hamiltonian between the Coulomb wave functions. Corrections for the frequency dependence of the Breit interaction and for two Breit interactions are included. Quantum-electrodynamic and mass-polarization corrections are taken from Drake’s unified method [Can. J. Phys. 66, 586 (1988)]. The resulting energies are complete through order (Zα${)}^3$ a.u. and include new terms of order (Zα${)}^4$ a.u. Comparisons are made with experiment and with recent configuration-interaction calculations.

The statistical analysis of energy levels, a powerful tool in the study of quantum systems, is applicable to discrete spectra. Here we propose an approach to carry level statistics over to continuous energy spectra, paradoxical as this may sound at first. The approach proceeds in three steps, first a discretization of the spectrum by cutoffs, then a statistical analysis of the resulting discrete spectra, and finally a determination of the limit distributions as the cutoffs are removed. In this way the notions of Wigner and Poisson distributions for nearest-neighbor spacing (NNS), usually associated with quantum chaos and regularity, can be carried over to systems with a purely continuous energy spectrum. The approach is demonstrated for the hydrogen atom in perpendicular electric and magnetic fields. This system has a purely continuous energy spectrum from -∞ to ∞. Depending on the field parameters, we find for the NNS a Poisson or a Wigner distribution, or a transitional behavior. We also outline how to determine physically relevant resonances in our approach by a stabilization method.

We have calculated the radiative lifetimes, and the scalar and tensor dipole polarizabilities of excited levels of helium. Our theory includes fine structure and the mixing of singlet and triplet sublevels, and gives results that are in excellent agreement with experiment. We are able to show why fine structure and mixing have negligible effects on the radiative lifetimes, but may contribute up to 20% of the polarizabilities. The trends of these properties with the quantum numbers n and L are explicated, and formulas are given which are accurate to a few percent for arbitrary n and L≥2.

The lifetime of the 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$ state in He-like niobium (${\mathrm{Nb}}^{39+}$) has been precisely determined with a beam-foil time-of-flight technique. The isotope ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$ (I=9/2) was chosen in order to minimize cascade effects through hyperfine quenching of the primary feeding state. Further precision was obtained by removing blends with a Doppler-tuned transmission filter. Other cascade contributions were analyzed and found to be negligible. The result is 45.45(16)×${10}^{\mathrm{-}12}$ sec and respresents increased sensitivity to corrections of O(Zα${)}^2$ in the Zα-series expansion for the lifetime by a factor of 5.

We present a theoretical model for studying the shape of the rotational lines of molecular ions perturbed by collisions with neutral species. This model shows that the interaction between the ionic monopole and the multipole moments of the perturber has no role in the collisional relaxation of the lines. The effect of the ionic monopole is restricted to that of inducing a polarization of the neutral perturbers that can cause relaxation by interaction with the other permanent moments of the absorbing ion. We also present, for ${\mathrm{HCO}}^{+}$ perturbed by argon, an experimental study of the pressure broadening and shift of the rotational lines J=1←0, 2←1, and 4←3. The agreement between theory and experiment is satisfactory.

Direct muon transfer to helium from excited muonic hydrogen with principal quantum number n=2, 3, 4, and 5 is considered in a quasiclassical approximation. Reaction rates turn out to be ∼${10}^{11}$–${10}^{12}$ ${\mathrm{s}}^{\mathrm{-}1}$ and should be taken into account when considering the cascade of excited muonic hydrogen in hydrogen-helium mixtures.

We present a simple proof of the stability of the hydrogen molecule (${\mathit{M}}^{+}$${\mathit{M}}^{+}$${\mathit{m}}^{\mathrm{-}}$${\mathit{m}}^{\mathrm{-}}$). It does not rely on the proton-to-electron mass ratio M/m being very large, and actually holds for arbitrary values of M/m. Some asymmetric molecules of the type (${\mathit{m}}_1^{+}$${\mathit{m}}_2^{+}$${\mathit{m}}_3^{\mathrm{-}}$${\mathit{m}}_4^{\mathrm{-}}$) are also stable. Possible applications to molecules containing antiparticles and to exotic hadrons in the quark model are briefly outlined.

Various properties of the ${\mathrm{Ps}}^{\mathrm{-}}$ ion in its bound ground ${(}^1$S) state are calculated from a very accurate explicitly correlated wave function. From the expectation value for the triple delta function 〈${\mathrm{\delta }}_{321}$〉=‖ψ(0,0,0)${\mathrm{\Vert }}^2$ we estimate the one-photon annihilation rate ${\mathrm{\Gamma }}_{\gamma }$ in the ${\mathrm{Ps}}^{\mathrm{-}}$ ion and show that ${\mathrm{\Gamma }}_{\gamma }$≪${\mathrm{\Gamma }}_{3\gamma }$≪${\mathrm{\Gamma }}_{2\gamma }$. The statistical angular correlation coefficients are analyzed for the series of two-electron ions (${\mathit{e}}^{\mathrm{-}}$${\mathit{e}}^{\mathrm{-}}$${\mathit{Z}}^{+}$) which includes ${\mathrm{T}}^{\mathrm{-}}$, ${\mathrm{D}}^{\mathrm{-}}$, ${\mathrm{H}}^{\mathrm{-}}$, ${\mathrm{Mu}}^{\mathrm{-}}$, and ${\mathrm{Ps}}^{\mathrm{-}}$.