The exact exchange-correlation functional ${\mathit{E}}_{\mathrm{xc}}$[n] must be approximated in density-functional theory for the computation of electronic properties. By the coupling-constant integration (adiabatic-connection) formula we know that ${\mathit{E}}_{\mathrm{xc}}$[n]=${\mathcal{F}}_0^1$(${\mathit{V}}_{\mathit{e}\mathit{e}}^{\mathrm{\alpha }}$[n]-U[n])dα, where ${\mathit{V}}_{\mathit{e}\mathit{e}}^{\mathrm{\alpha }}$[n] is the electron-electron repulsion energy of ${\mathrm{\Psi }}_{\mathit{n}}^{\mathrm{m}\mathrm{i}\mathrm{n},\mathrm{\alpha }}$, which is that wave function that yields the density n and minimizes 〈T^+αV${\mathrm{^}}_{\mathit{e}\mathit{e}}$〉. Here α is the coupling constant. Consequently, knowledge of the behavior of ${\mathit{V}}_{\mathit{e}\mathit{e}}^{\mathrm{\alpha }}$[n] as a function of α ensures knowledge of ${\mathit{E}}_{\mathrm{xc}}$[n]. With this in mind and for the purpose of approximating ${\mathit{E}}_{\mathrm{xc}}$, it was previously established that (∂${\mathit{V}}_{\mathit{e}\mathit{e}}^{\mathrm{\alpha }}$/∂α)≤0. The present paper reveals that ${\mathit{V}}_{\mathit{e}\mathit{e}}^{\mathrm{\alpha }}$[n]=α${\mathit{V}}_{\mathit{e}\mathit{e}}^1$[${\mathit{n}}_{1/\mathrm{\alpha }}$], where ${\mathit{n}}_{\mathrm{\beta }}$(x,y,z)=${\mathrm{\beta }}^3$n(βx,βy,βz), and where β is a coordinate scale factor.

In other words, knowledge of ${\mathit{V}}_{\mathit{e}\mathit{e}}^1$[n] implies knowledge of ${\mathit{V}}_{\mathit{e}\mathit{e}}^{\mathrm{\alpha }}$[n] for all α. Alternatively, knowledge of ${\mathit{V}}_{\mathit{e}\mathit{e}}^{\mathrm{\alpha }}$[n] for some small α implies knowledge of all of the ${\mathit{V}}_{\mathit{e}\mathit{e}}^{\mathrm{\alpha }}$[n]. In any case, any viable approximation to ${\mathit{V}}_{\mathit{e}\mathit{e}}^{\mathrm{\alpha }}$[n] should be made to satisfy the above displayed equality. Analogous conclusions hold for the second-order density matrix, the pair-correlation function, the exchange-correlation hole, and the correlation component of the exchange-correlation hole, etc. For example, ${\mathrm{\rho }}_{\mathrm{xc}}$([n,α];${\mathbf{r}}_1$,${\mathbf{r}}_2$)=${\mathrm{\alpha }}^3$${\mathrm{\rho }}_{\mathrm{xc}}$([${\mathit{n}}_{1/\mathrm{\alpha }}$,1]; α${\mathbf{r}}_1$,α${\mathbf{r}}_2$), where ${\mathrm{\rho }}_{\mathrm{xc}}$([n,α]; ${\mathbf{r}}_1$,${\mathbf{r}}_2$) is the exact exchange-correlation hole of ${\mathrm{\Psi }}_{\mathit{n}}^{\mathrm{m}\mathrm{i}\mathrm{n},\mathrm{\alpha }}$.

(A corresponding expression holds for the correlation hole alone.) Further, when n belongs to a noninteracting ground state that is nondegenerate, then ${\lim }_{\mathrm{\alpha }\to 0}$ ${\mathrm{V}}_{\mathit{e}\mathit{e}}^{\mathrm{\alpha }}$[n]=A[n]+${\mathit{f}}_{\mathit{n}}$(α)B[n]+..., where ${\mathit{f}}_{\mathit{n}}$(α) must vanish at least as rapidly as α, and ${\lim }_{\lambda \to \mathrm{\infty }}$ ${\mathrm{E}}_{\mathit{c}}$[${\mathit{n}}_{\lambda }$]>-∞, where ${\mathit{E}}_{\mathit{c}}$[n]=${\mathit{E}}_{\mathrm{xc}}$[n]- ${\lim }_{\gamma \to \mathrm{\infty }}$ ${\gamma }^{\mathrm{-}1}$${\mathit{E}}_{\mathrm{xc}}$[${\mathit{n}}_{\gamma }$], and where ${\mathit{E}}_{\mathit{c}}$ is a familiar exact density-functional ‘‘correlation energy.’’ In contrast, in the local-density approximation and in certain nonlocal approximations, ${\mathit{f}}_{\mathit{n}}$(α) is replaced by a function that goes as α[ln(${\mathrm{\alpha }}^{\mathrm{-}1}$)], α→0, and ${\mathit{E}}_{\mathit{c}}$ is replaced by a functional that is unbounded as λ→∞. Further, ${\lim }_{\lambda \to \mathrm{\infty }}$ ${\mathrm{E}}_{\mathrm{xc}}$[${\mathit{n}}_{\lambda }^{\mathit{x}}$]>-∞ and ${\lim }_{\lambda \to \mathrm{\infty }}$ ${\mathit{E}}_{\mathit{x}}$[${\mathit{n}}_{\lambda }^{\mathit{x}}$]>-∞, which are also not generally satisfied by common approximations. Here ${\mathit{n}}_{\lambda }^{\mathit{x}}$(x,y,z)=λn(λx,y,z) and ${\mathit{E}}_{\mathit{x}}$ is a familiar exact density-functional ‘‘exchange energy.’’ Finally, comparison is made between ${\mathit{E}}_{\mathit{c}}$ and the traditional quantum-mechanical correlation energy, which is expressed exactly as a functional of the Hartree-Fock density.

A new type of ‘‘intermediate’’ state, ‖Ψ${\mathrm{̃}}_{\mathit{J}}$〉, is introduced in the representation of many-body propagators and related resolvent matrix elements. A simple algebraic procedure is presented for constructing the unitary transformation matrix Q that relates the intermediate states and the exact energy eigenstates, ‖${\mathrm{\Psi }}_{\mathit{n}}$〉, of the interacting system. Here the starting point is the matrix X of generalized spectroscopic amplitudes 〈${\mathrm{\Psi }}_{\mathit{n}}$‖C${\mathrm{^}}_{\mathit{J}}$‖${\mathrm{\Psi }}_0^{\mathit{N}}$〉, where C${\mathrm{^}}_{\mathit{J}}$ denotes a physical excitation operator and ‖${\mathrm{\Psi }}_0^{\mathit{N}}$〉 is the N-electron ground state. A block QR decomposition [G. H. Golub and C. F. von Loan, MatrixB Computations (Johns Hopkins University, Baltimore, 1989)] of X according to the equation X=Q F allows one to determine explicit expressions for the subblocks of Q and the intermediate propagator representations constituted by a nondiagonal effective interaction matrix C and an effective spectroscopic matrix f. These effective quantities f and C are formulated entirely in terms of ground-state density-matrix elements and related energy expectation values. The relevance of the intermediate representations as a means for deriving computational schemes is based on the regularity and compactness of the perturbation expansions for the effective matrices f and C. These basic properties also establish that the intermediate representations are closed-form versions of the algebraic-diagrammatic construction approximation schemes derived previously as a reformulation of the original diagrammatic propagator perturbation series. The intermediate representations represent a link between algebraic and diagrammatic approaches in the field of propagator methods and are expected to be useful also in the development of nonperturbative approximations.

Relativistic configuration-interaction calculations have been made for the 6${\mathit{p}}^2$ resonances of Hgi using a relativistic version of the Fano theory. Pair-correlation effects associated with the 5d and valence electrons are important, contributing ∼1.5 eV to the positions of the resonances. Relative to Hg 6${\mathit{s}}^2$, the theoretical positions of the resonances (in ${\mathrm{cm}}^{\mathrm{-}1}$) are 90654, 94595, 97066, 106257, and 111609 for ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{0,1,2}$, ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$, and ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$. The experimental values are 90096, 93980, 96185, and (tentatively) 103232, 109286 ${\mathrm{cm}}^{\mathrm{-}1}$. The theoretical values for the width (in eV) are 0.002, 0.0, 0.215, 0.914, and 0.298. The experimental value for the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$ width is 0.272±0.074 eV.

The improved adiabatic representation is used in calculations of elastic and hyperfine-transition cross sections for symmetric collisions of pμ, dμ, and tμ with bare p, d, and t nuclei and with H, D, and T atoms, respectively. The cross sections for dμ+d and tμ+t are in excellent agreement with other recent determinations, while those for pμ+p are about 30% larger at low energies. The electronic screening is calculated nonperturbatively and found to be about 30% smaller in magnitude than the previously calculated value at large internuclear distances, and to deviate considerably from the asymptotic form in the molecular region. The resulting screened elastic cross sections are up to 60% smaller than those obtained using the old screening potential. The reactance matrices, needed for calculations of molecular-target effects, are given in tables.

Calculations of the photoionization cross sections for the excited (6s6p) ${}_{}{}^{3,1}{}_{}{}^{}$P state of ytterbium have been performed at the Hartree-Fock and Hartree-Slater levels. The results for ${}_{}{}^3{}_{}{}^{}$P show reasonable agreement (at the edge of error bars) with a recent experiment at a single energy. Significant differences between the triplet and singlet cases exist and arise primarily due to the effects of exchange on the initial-state wave functions.

In this report, a follow-up to our earlier paper [Theodosiou, Manson, and Inokuti, Phys. Rev. A 34, 943 (1986)] on comprehensive calculations of various properties of all atomic ions in all stages of ionization with nuclear charge Z≤50, we investigate, within the Hartree-Slater approximation, inner-shell properties including orbital binding energies, x-ray transition energies and rates, photoionization cross sections, and expectation values of powers of electron radial coordinates. Throughout we concentrate on enumerating general trends of the properties as functions of the nuclear charge Z and the total electron number N. The systematics thus found for highly stripped ions (i.e., for ions in which Z-N is appreciable) are interpreted in terms of the outer-shell screening and the hydrogenic shell structure in which complete shells occur at N=n(n+1)(2n+1)/3 =2,10,28,60,..., for principal quantum numbers n=1,2,3,4,..., respectively.

A multiple-electron-emission process for atoms with one or more inner-shell vacancies is treated using the radiative- and Auger-electron-emission cascade model, in which inner-shell holes are assumed to decay by sequentially emitting radiations and/or Auger electrons. Such hollow ions are produced by synchrotron irradiation of atomic targets and in ion-surface interactions with multiple-electron transfers. The final charge-state distribution is determined by the Auger and radiative branching ratios at each stage of the decay sequence. At intermediate stages of cascade, hollow ions with more than one hole in different ionization stages are created. The Ne, Mg, and ${\mathrm{Fe}}^{14+}$ ions with the initial 1s, 2s, and 2p vacancies are considered in detail, and the core charge dependence of the maximum charge state is studied. The hollow Mg ion with double initial 1s holes is analyzed, and the result compared with that for the case of one 1s hole. The peak is shifted more than two units to a higher degree of ionization. The correlated shake-off and shake-up multiple-electron processes are not considered, but they are expected to cause further shifts.

Double-resonance spectroscopy is used to study transitions between autoionizing levels of atomic oxygen. The first laser is used to produce oxygen atoms in the 1${\mathit{s}}^2$2${\mathit{s}}^2$2${\mathit{p}}^4$ ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$ level by photodissociation of ${\mathrm{N}}_2$O and to excite two-photon transitions from the ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$ level to the long-lived ${(}^2$D°)3p ${}_{}{}^1{}_{}{}^{}$${\mathit{F}}_3$ autoionizing level. The second laser is used to probe transitions from the ${}_{}{}^1{}_{}{}^{}$${\mathit{F}}_3$ level to higher-energy autoionizing levels as well as to the ${\mathrm{O}}^{+}$ ${}_{}{}^2{}_{}{}^{}$D° direct-ionization continuum. The transitions are detected by using a magnetic bottle electron spectrometer to monitor photoelectrons selectively with the kinetic energy specific to the process of interest. New transitions to the ${(}^2$D${\mathrm{°}}_{5/2,3/2}$)ns’ and nd’ Rydberg-series members with n=16–31 are observed. The intensity dependence of these results has also been studied, and the implications of this relatively low-power measurement for above-threshold ionization are discussed.

The multiconfiguration Hartree-Fock method has been applied to study low-energy scattering of electrons from argon atoms. The polarization of the argon atoms due to the scattered electron and the electron-correlation effects that are very important in the calculation are taken into account in the ab nitio way more accurately through the configuration-interaction procedure. Phase shifts for various partial waves calculated in this approximation have been used to calculate elastic differential, total elastic, and momentum-transfer cross sections. The present results are compared with the experimental and other theoretical results. It is found that the present results are in very good agreement with the experimental results and compare well with the other theoretical results.

Single and double ionization of helium in relatively small-impact-parameter collisions with 0.5–2.5-MeV/u ${\mathrm{O}}^{6,7+}$ ions is studied by associating target ionization with single-electron loss from the projectile. Double ionization is considerably enhanced (4–6 times) and found to deviate substantially from the energy and charge-state behavior observed for double ionization without accompanying electron loss from the projectile. The results are considered in terms of one- and two-step processes of double ionization.

Cross sections have been calculated for excitation of the (2${\mathit{s}}^2$) ${}_{}{}^1{}_{}{}^{}$S, 2 ${}_{}{}^1{}_{}{}^{}$S, and 2 ${}_{}{}^1{}_{}{}^{}$P states and ionization of helium by MeV-energy protons. The sensitivity to couplings among these excitation and ionization channels is studied using the Sturmian-pseudostate approach applied previously by Winter [Phys. Rev. A 35, 3799 (1987)] to one-electron systems. The inclusion of many states greatly lowers the 2${\mathit{s}}^2$ cross section and brings it closer to the recent experimental result of Giese et al. [Phys. Rev. A 42, 1231 (1990)].

The alignment and orientation parameters of excited states are theoretically studied for the electron collision with H-like and He-like ions. With the use of the distorted-wave method, those parameters are calculated for the excitation of the 2 ${}_{}{}^1{}_{}{}^{}$P and 2 ${}_{}{}^3{}_{}{}^{}$P states of He-like ions with Z=3,8,∞ and the 2p state of H-like ions with Z=2,6,∞. Here Z is the nuclear charge of each ion. The dependence of the parameters on the scattering angle and the collision energy is examined along the isoelectronic sequences. When compared at the same collision energy in threshold units, the parameter as a function of the scattering angle is not much changed along each isoelectronic sequence.

The multiconfiguration relativistic random-phase approximation is applied to photoionization of the Be atom. Angular distribution and spin polarization of photoelectrons from subshells 2${\mathit{s}}_{1/2}$, 2${\mathit{p}}_{1/2}$, and 2${\mathit{p}}_{3/2}$ are presented and compared with other theories. Subshell cross sections near the 2${\mathit{p}}_{3/2}$ threshold are found to be sensitive to the initial-state correlations.

Positron-lithium scattering has been investigated using the three-state [Li(2s), Li(2p), and Ps(1s)] close-coupling approximation. Calculations have also been carried out by using the static, coupled static, and Born approximations. Elastic (2s-2s), excitation (2s-2p), and Ps-formation cross sections are reported up to an incident energy of 100 eV. The effect of the Ps-formation channel on elastic scattering is found to be pronounced at low incident energies, and this effect is not negligible even up to 50 eV. The positronium formation cross section is reduced appreciably in the energy region 1.0–20.0 eV when the 2p state is included in the expansion scheme.

Symmetric (homonuclear) charge transfer between completely stripped projectiles and hydrogenlike atoms is studied by means of the second-order Born approximation (CB2) with the correct boundary conditions. Along the integration path, the transition amplitude ${\mathit{T}}_{\mathit{i}\mathit{f}}^{\mathrm{CB}2\mathrm{}}$ exhibits so-called movable singularities, such as branch points and poles. A powerful method is presented which demonstrates that these singularities are integrable, not only for the resulting cross sections, but also for every individual matrix element. The resulting algorithm is very efficient, since the exact differential cross sections of the CB2 method are readily obtained through only two-dimensional numerical quadratures. The present theory is applied to symmetric resonant charge exchange in ${\mathrm{H}}^{+}$+H(1s)→H(1s)+${\mathrm{H}}^{+}$ collisions at several impact energies, and the results are found to be in satisfactory agreement with the experimental data of Martin et al. [Phys. Rev. A 23, 3357 (1981)] and Vogt et al. [Phys. Rev. Lett. 57, 2256 (1986)].

An analysis of the L x-ray spectra, induced by ∼50 keV electron impact and recorded with a curved crystal spectrometer, has been performed based on a calculation model that takes into account all physical events taking place during the initial ionization and inner-vacancy processes. The L-subshell fluorescence yields ${\mathrm{\omega }}_1$, ${\mathrm{\omega }}_2$, and ${\mathrm{\omega }}_3$ for ten elements with atomic number Z=73–83 were obtained. They are all in good agreement with recent measurements but display an appreciable disagreement with the semiempirically compiled data for the elements around Z=80. These experimental values of ${\mathrm{\omega }}_1$ are approximately 20% larger than the compiled data and 55% larger than the latest theoretical calculation for the elements with Z≊80.

An analytical formula for the electronic stopping power S of atoms with atomic number ${\mathit{Z}}_2$ and mean excitation energy I can be obtained, on the basis of Bethe theory, for fast hydrogenlike (${\mathit{Z}}_{\mathit{p}}$=${\mathit{Z}}_1$, ${\mathit{N}}_{\mathit{e}}$=1) and heliumlike (${\mathit{Z}}_{\mathit{p}}$=${\mathit{Z}}_1$-5/16, ${\mathit{N}}_{\mathit{e}}$=2) projectiles with atomic number ${\mathit{Z}}_1$ and velocity v. The resultant expression is S=(4π${\mathit{e}}^4$/${\mathit{mv}}^2$)${\mathit{NZ}}_2$L(${\mathit{Z}}_1$,${\mathit{Z}}_2$,v), where L(${\mathit{Z}}_1$,${\mathit{Z}}_2$,v)=(${\mathit{Z}}_1$-${\mathit{N}}_{\mathit{e}}$${)}^2$ln(2${\mathit{mv}}^2$/I)+(2${\mathit{Z}}_1$${\mathit{N}}_{\mathit{e}}$ -${\mathit{N}}_{\mathit{e}}^2$)ln(v/${\mathit{Z}}_{\mathit{p}}$${\mathit{v}}_0$)+${\mathit{Z}}_1$${\mathit{N}}_{\mathit{e}}$-11/12${\mathit{N}}_{\mathit{e}}^2$.

The frequencies of five Doppler-free ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}_2^{}{}_{}{}^{}$ transitions at 486 and 488 nm have been measured interferometrically with reference to an iodine-stabilized 633-nm He-Ne laser. These frequencies are useful as transfer standards for 1S-2S transitions in deuterium, hydrogen, positronium, and muonium. A comprehensive study of the reproducibility of such tellurium reference standards has been made. Under the conditions specified, the frequencies of components ${\mathit{d}}_4$, ${\mathit{b}}_2$, ${\mathit{b}}_1$, ${\mathit{e}}_3$, and ${\mathit{i}}_3$ in tellurium were found to be 613881 149.1, 616 513 894.9, 616 678 855.8, 616 803 544.7, and 616 806 134.5 MHz, respectively. The overall standard deviation of frequency measurements on FM saturated tellurium spectra was 0.47 MHz across several cells, with 0.18 MHz day-to-day reproducibility for each cell. A comparison has also been made between the results reported here and our earlier measurements on tellurium [J. R. M. Barr, J. M. Girkin, A. I. Ferguson, G. P. Barwood, P. Gill, W. R. C. Rowley, and R. C. Thompson, Opt. Commun. 54, 217 (1985)].

The spectrum of doubly ionized neon (Neiii), emitted from hollow-cathode and θ-pinch discharges, has been photographically recorded in the 430–12 000-Å wavelength range. The number of classified lines has been increased from about 100 to about 750, and the number of experimentally established energy levels from 60 to 230. The level scheme comprises levels in the 2${\mathit{s}}^2$2${\mathit{p}}^4$, 2s2${\mathit{p}}^5$, 2${\mathit{p}}^6$, 2${\mathit{s}}^2$2${\mathit{p}}^3$3s-8s, 3p-5p, 3d-5d, 4f-8f, and 5g-7g configurations. The experimentally observed level distributions are compared with the results of Hartree-Fock calculations and least-squares fits.

Stimulated Raman spectroscopy has been used in a fast ion beam to measure the hyperfine structure in the 4${\mathit{d}}^2$ configuration of Y ii. A simple theory is provided for the line shape of the coherent two-photon transition which gives a transit-time limited linewidth of 0.9/T, comparable to the resolution of the laser–radio-frequency double-resonance technique. The hyperfine structure is compared with a multiconfiguration Dirac-Fock calculation and with that of the homologous Sc ii ion. This comparison confirms the role of core polarization as a significant factor in the hyperfine structure of these ions.