The radiative and Auger rates of doubly excited states of positive ions where the principal quantum numbers of both electrons are large (≥6) are studied using a restricted-configuration-interaction method. The partial radiative and Auger rates to final states are calculated for doubly excited states of ${\mathrm{Ar}}^{16+}$. It is shown that the propensity rule for both the radiative and Auger decay is Δv=${\mathit{v}}_{\mathit{f}}$-${\mathit{v}}_{\mathit{i}}$=0, where v is the bending vibrational quantum number of the doubly excited state. Systematics of the radiative and Auger rates along different sequences of doubly excited states are also investigated.

The self-consistent-field treatment of the frequency-independent Breit interaction is reviewed with applications to many-electron atoms. The implementation of the matrix Dirac-Fock-Breit self-consistent-field procedure is presented for Gaussian-type basis sets that show no near-linear dependency problem. The matrix Dirac-Fock-Breit procedure has the advantage over the finite-difference approach that it does not complicate the self-consistent-field procedure in basis-set expansion calculations. Basis sets of even- and well-tempered Gaussian functions were used to expand the large and small components of Dirac four-spinors. Expressions are derived for evaluating the matrix elements of the Dirac-Fock-Breit equations. Calculations done on rare-gas atoms He, Ne, Ar, Kr, and Xe and alkaline-earth metals Be, Mg, Ca, and Sr are presented.

We have measured the lifetime of the a’’ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{+}{}_{}{}^{}$(v=0) level of ${\mathrm{N}}_2$ by monitoring through laser-induced vacuum ultraviolet fluorescence its population as a function of time after pulsed-electron excitation. The lifetime was measured for several rotational levels and found to be independent of the rotational level. The average lifetime is 3.49(10) μs. This lifetime suggests that predissociation, not radiation, is the main decay mode for this metastable level.

The results of variational calculations using large Hylleraas basis sets are reported for some low-lying excited ${}_{}{}^2{}_{}{}^{}$S states of the Li i isoelectronic series for 3≤Z≤10. The 3 ${}_{}{}^2{}_{}{}^{}$S, 4 ${}_{}{}^2{}_{}{}^{}$S, and 5 ${}_{}{}^2{}_{}{}^{}$S states are studied for Li i and Be ii, and the 3 ${}_{}{}^2{}_{}{}^{}$S and 4 ${}_{}{}^2{}_{}{}^{}$S states are investigated for the other ions. The nonrelativistic energies obtained are the lowest-upper-bound estimates so far reported. In some cases the literature estimates of these energies are found to be in error, as they lie above the results of the present calculations. Hyperfine coupling constants, specific-mass shifts, transition isotope shifts, electron density at the nucleus, and the individual energy components are reported. The rates of convergence of the various expectation values are discussed.

Linearly averaged position moments (LAPM’s) are introduced for the Hartree-Fock orbitals. When all the LAPM’s are well defined, the Hartree-Fock equation is shown to be equivalent to a set of relations between the LAPM’s involving the potential-energy operator. The true Hartree-Fock orbitals must satisfy all the relations, and hence the LAPM equations can be used as a sensitive criterion to assess the accuracy of approximate Hartree-Fock orbitals. Such an application is presented for He, Be, and Ne atoms.

An approach for many-body perturbation calculations of open-shell systems starting from multiconfiguration Dirac-Fock wave functions is developed. A procedure is described to construct an effective multiconfiguration potential for an optimized orthogonal complete set in the relativistic framework. Using a finite basis set, an infinite subset of many-body perturbation expansion terms, i.e., single- and pair-excitation amplitudes, is evaluated by using the coupled-cluster approach in the multireference model space spanned by configuration state functions. As an example, the calculation is performed for the correlation energy of ground-state beryllium. The convergence is compared with other methods.

Planck’s constant h is a fundamental physical parameter that establishes the scale of quantum phenomena. Bound-state energy eigenvalues for several well-known systems (e.g., harmonic oscillators, Morse oscillators, and square-well potentials) are formally analytic functions of h in the neighborhood of h=0, and any ‘‘physical’’ state can be reached in principle by analytic continuation. This paper explores the possibility of developing power series in h for atomic and molecular energies, with analytic continuation to access physical states. For this purpose it is necessary to modify Coulomb interactions at short range to keep the potential bounded below. As a result the h expansions appear naturally as Rayleigh-Schrödinger perturbation series in anharmonicity about collective harmonic-oscillator states. Physical eigenvalues emerge in the strong-coupling limit, and Padé approximants seem to be analytical tools well suited for entering this regime. Some basic implementation details are presented for application to the modified hydrogen atom, the two-electron isoelectronic atomic sequence, and many-electron atoms.

A high-precision measurement of the 2s ${}_{}{}^2{}_{}{}^{}$${\mathit{S}}_{1/2}$–2p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$ Lamb shift in ${\mathrm{He}}^{+}$ by the quenching-anisotropy method is reported. The theory and experimental method are described in detail. The measured value of 14042.52±0.16 MHz (±11 parts per million) rivals the accuracy of Lamb-shift measurements in hydrogen by microwave resonance. By subtracting the known low-order terms in the Lamb shift, we interpret the results as a measurement of the order α(Zα${)}^6$${\mathit{mc}}^2$ and higher contributions to the electron self-energy ${\mathit{G}}_{\mathrm{SE}}$(Zα). The various contributions to the Lamb shift are discussed, and a revised value for ${\mathit{G}}_{\mathrm{SE}}$(Zα) at low Z is extracted from high-Z calculations. The theoretical value for the Lamb shift is 14042.51±0.2 MHz, in excellent agreement with experiment. The results provide the most sensitive available determination of ${\mathit{G}}_{\mathrm{SE}}$(Zα) for low Z. Measurements and calculations for hydrogen and other members of the isoelectronic sequence are discussed.

An external electric field can induce M1 and E2 amplitudes in the D lines of alkali-metal atoms, which interfere with the normal E1 amplitudes of these lines, causing the absorption to depend linearly upon the external field and upon the initial spin polarization of the atoms. We discuss this effect and calculate its size for the D lines of rubidium.

Hartree-Fock (HF) and local-density approximation (LDA) calculations of holes in symmetric molecular ions lead to conflicting results on the sign of the energy associated with reducing the symmetry. According to the HF theory, this energy can only be negative because it corresponds to a less restricted wave function. According to the LDA, it can only be positive because it is mostly electrostatic force that concentrates the hole charge in the vicinity of a single atom. In the present paper, we discuss these diverging views and present some LDA results for molecular ions with broken symmetry.

We compare the theoretical and experimental energies for the ground state of the beryllium atom and investigate possible sources for the small discrepancy of about 60 μhartrees found by Bunge [Phys. Rev. A 14, 1965 (1976); 17, 486(E) (1978)]. Indications that the correlation energy may be underestimated in Bunge’s work have been confirmed by a recent, very extensive multiconfigurational Hartree-Fock (MCHF) calculation. We emphasize that the critical part of the comparison between theory and experiment is the sum of the first and second ionization energies—the third and fourth are known more accurately from theory—and present the theoretical results accordingly. Before a comparison with experimental results can be performed, corrections must be added to account for mass polarization, for the effect of relativity including the Breit interaction and for radiative effects. The previously unknown mass-polarization contribution to the first ionization energy has recently been determined experimentally. Relativity is most important for the 1s electrons and this effect was included in Bunge’s work, whereas the relativistic effect on the correlation involving the 2s electrons was neglected. Here, these contributions have been calculated to leading order. A crude estimate of the contribution to the Lamb shift from the 2s electrons is also given. When the revised relativistic corrections are combined with recent results from a very extensive MCHF calculation, the discrepancy in the beryllium ground-state energy is reduced to (10±50)μ hartrees.

A 170-point configuration-interaction involving all single and double excitations ab initio potential-energy surface for the ${\mathrm{LiH}}_2^{+}$ molecule was calculated using (11s3p1d)/[6s3p1d] and (8s3p1d)/[6s3p1d] contracted Gaussian basis sets for lithium and hydrogen, respectively. Various analytical functions were tested as representations of the discrete surface. A Padé-approximant function with a Dunham expansion variable was found to give the most reliable representation with a ${\mathrm{\chi }}^2$ of 1.3×${10}^{\mathrm{-}7}$. It is this surface that is recommended for rovibrational calculations.

Accurate analytical charge and spin-electron densities for the lithium atom are obtained by using a systematic and reliable method recently developed and applied to closed-shell atoms. The convergence of the densities is analyzed in terms of well-defined improvements in the corresponding configuration-interaction wave functions, and mathematical criteria are used to test the stability of the densities and their derivatives. Fully converged results for one-electron properties and, in particular, for the Fermi-contact interaction are reported.

The algorithm of Silverstone and Moats [Phys. Rev. A 16, 1731 (1977)] for the expansion of a function about a displaced center is used to derive analytical expressions for some bicentric integrals appearing in molecular and solid-state calculations. The 〈a‖b〉 (overlap), 〈a‖${\mathit{V}}_{\mathrm{eff}}$(b)‖a’〉 (effective-potential), and 〈a‖P(b)‖a’〉 (projection-operator) bicentric integrals over complex Slater-type orbitals (STO’s) are explicitly considered. Simple and compact formulas for the spherically averaged integrals are obtained by straightforward summation over the angular-momentum subspecies of center A. fortran routines adapted to a vector computer have been implemented to compute the atom-lattice bicentric integrals of the abinitio perturbed ion method, a Hartree-Fock-Roothaan scheme recently developed by us for the study of ionic and van der Waals crystals. This algorithm is 4–40 times faster than one based on elliptic coordinates and the Mulliken orientation of the A-B diatomic molecule. Furthermore, its efficiency increases progressively with the principal and angular quantum numbers of the complex STO, showing the potentiality of this method in the study of closed-shell systems containing heavy atoms or ions.

General formulas for matrix elements of the pth-order spin-adapted reduced Hamiltonian (p-SRH) are derived based on the theory of generalized reduced density operators. The method is illustrated by a diagrammatic technique developed in detail for p=4. The p-SRH is a matrix representing a p-particle operator in a finite-dimensional p-particle Hilbert space. It is related to the N-particle (N≥p) Hamiltonian defined in an N-particle spin-adapted, finite-dimensional Hilbert space. The p-SRH’s, apart from their importance in theory of atomic and molecular structure, may find applications in statistical theories of spectra and in nuclear shell theory.

We present a generalization of the extended Thomas-Fermi theory for a system of relativistic particles and antiparticles to finite temperatures. On the basis of the Kirzhnits method, we derive the gradient expansion of the free energy and entropy density functionals to second order.

All-order methods recently developed for high-accuracy calculation of energies and matrix elements in Li are extended and applied to cesium. We employ a relativistic, linearized, coupled-cluster formalism, incorporating single, double, and an important subset of triple excitations. A coupled-cluster formulation of the matrix element of a one-body operator, incorporating the random-phase approximation exactly, is used to calculate hyperfine constants and transition-matrix elements. We find agreement with experiment at the 0.5% level or better for ionization energies and dipole-matrix elements, and at the 1% level for hyperfine constants. Modifications of the method that have the potential of higher accuracy are discussed.

We use the techniques of dispersion theory to study the long-range behavior of the two-Coulomb-exchange potential acting between two atoms, or between an atom and a charged system such as an ion or electron, in the presence of open channels. In contrast to earlier work, we avoid the use of a multipole expansion. We focus on the case of atoms in initial S states. When one of the systems is in an excited state or the relative kinetic energy is large enough to allow excitation, the potential has an imaginary part that falls off exponentially with distance in the absence of degeneracy and as an inverse power in the presence of degeneracy of the initial state. The asymptotic form of the real part is unchanged from that found in the closed-channel case.

The classical and quantum theory of atom–symmetric-top collisions is developed by assuming that the medium- and long-range parts of the potential can be neglected and the short-range part replaced by an infinitely high (hard-core) barrier. The rotational energy transfer is analyzed for the He-${\mathrm{CH}}_4$, He-${\mathrm{CH}}_3$D, and He-${\mathrm{CDH}}_3$ systems.

Cross sections for radiative recombination of electrons with ground-state atomic oxygen ions to form oxygen atoms in the O[${(}^4$S)nl] ${}_{}{}^{3,5}{}_{}{}^{}$L states are calculated for nl up to (15,14) at 19 electron energies from 0.0345 to 2.585 eV based on Hartree-Fock wave functions of the bound and continuum states. By extrapolating the cross sections beyond n=15, the radiative-recombination rate coefficients are determined. The present cross sections are virtually identical to those obtained by using the hydrogenic approximation for l≥3, but entirely different for the ns and np series. For the nd series the agreement is good at low energies, but the discrepancy becomes larger at higher energies. The present calculation agrees with a calculation based on the quantum-defect method to within 10% for the nd series, but some discrepancy is found for the np series. In the case of the ns series these two sets of calculations disagree entirely.