The relativistic K${\mathrm{\alpha }}_3$ (${2\mathrm{s}}_{1/2}$-${1\mathrm{s}}_{1/2}$) x-ray transition induced by photoionization was observed in ${\mathrm{Xe}}_{54}$, ${\mathrm{Pr}}_{59}$, ${\mathrm{Gd}}_{65}$, ${\mathrm{Ho}}_{67}$, ${\mathrm{Ta}}_{73}$, and ${\mathrm{Au}}_{79}$. The transitions were measured with a transmission curved-crystal spectrometer. I(K${\mathrm{\alpha }}_3$)/I(K${\mathrm{\alpha }}_1$) as well as I(K${\mathrm{\alpha }}_2$)/I(K${\mathrm{\alpha }}_1$) intensity ratios are presented and compared with multiconfiguration Dirac-Fock and Dirac-Hartree-Slater predictions. A good agreement is obtained. No systematic deviation as a function of Z is observed.

The position- and momentum-space entropies of the isotropic harmonic oscillator and the hydrogen atom in D dimensions are shown to be related to some entropy integrals which involve classical orthogonal polynomials. These integrals are exactly calculated for Chebyshev polynomials and only in an approximate way for Gegenbauer polynomials. The physical entropies are explicitly obtained in the ground state and in a few low-lying excited states. Finally, the dimensionality dependence of the ground-state entropies of the two above-mentioned quantum-mechanical systems is analyzed (numerically) and the values of the entropies in a large class of excited states of the D-dimensional (D=1,2,3) harmonic oscillator and hydrogen atom are tabulated and discussed.

A new isotope shift program, part of the multiconfiguration Hartree-Fock (MCHF) atomic structure package, has been written and tested. The program calculates the isotope shift of an atomic level from MCHF or configuration-interaction (CI) wave functions. The program is specially designed to be used with very large CI expansions, for which angular data cannot be stored on disk. To explore the capacity of the program, large-scale isotope shift calculations were performed for the 1${\mathit{s}}^2$2${\mathit{s}}^2$2p ${}_{}{}^2{}_{}{}^{}$P, 1${\mathit{s}}^2$2${\mathit{s}}^2$3s ${}_{}{}^2{}_{}{}^{}$S, and 1${\mathit{s}}^2$2s2${\mathit{p}}^2$ ${}_{}{}^2{}_{}{}^{}$D levels in boron. From the isotope shifts of these levels the transition isotope shifts were calculated for the two resonance transitions. The calculated transition isotope shifts are in very good agreement with experimental shifts. As an additional test of the quality of the CI wave functions, the hyperfine structure was calculated for all levels.

We discuss the formal basis and general advantages of magnetic-field-and-density functional theory (BDFT) for the ground-state magnetic properties of many-electron systems. The ground-state density ρ(r) and the magnetic field B(r) are the variables appearing in the energy functionals that are the fundamental elements of BDFT. This is in contrast to the energy functionals of current-and-density functional theory (CDFT), the most general density-functional way of treating systems in a magnetic field, where the variables are ρ(r) and the ground-state paramagnetic current ${\mathbf{j}}_{\mathit{p}}$(r). Explicit calculations of magnetic properties have already been made that can be recognized as belonging to the BDFT paradigm, which this work therefore puts on a formal foundation. There are also aspects of BDFT discussed here that may make it an attractive alternative to the more general CDFT in some situations. In particular, we show that Kohn-Sham equations may be derived that use purely real orbitals and for which the energy does not separate into para- and diamagnetic contributions. We also show that in BDFT the zero-field electron density alone is sufficient to calculate the energy to second order in the magnetic field. Thus calculation of, e.g., diamagnetic susceptibilities or chemical shifts can in principle be made directly from zero-field electron distributions, without any need for the calculation of first-order corrections.

The retarded long-range potentials for the dispersion interaction arising from induced multipole moments of two ground-state alkali-metal atoms are evalulated as functions of the separation R for Li, Na, K, Rb, and Cs. Accurate atomic properties, determined using published model potentials, are utilized. Values for the potentials are given over a wide range of R. Results for H are also given. For small R the results reproduce the accepted values for the unretarded dispersion dipole-dipole (van der Waals), dipole-quadrupole, quadrupole-quadrupole, and dipole-octupole coefficients, while for R→∞ the Casimir-Polder potentials, due to retardation or effects due to the finite speed of light, are obtained. The overlap between the retardation potentials and terms arising from the Breit-Pauli Hamiltonian is explored.

A systematic study of collision strengths for the electron-impact excitation of ions along an isoelec- tronic sequence is presented. 105 excitation transitions between 15 fine-structure levels of the eight LS terms 2${\mathit{s}}^2$2p${(}^2$${\mathit{P}}^{\mathit{o}}$), 2s2${\mathit{p}}^2$${(}^4$P${,}^2$D${,}^2$S${,}^2$P), and 2${\mathit{p}}^3$${(}^4$${\mathit{S}}^{\mathit{o}}$${,}^2$${\mathit{D}}^{\mathit{o}}$${,}^2$${\mathit{P}}^{\mathit{o}}$) in boronlike ions are considered. The calculations include O iv, Ne vi, Mg viii, Al ix, Si x, S xii, Ar xiv, Ca xvi, and Fe xxii in an eight-term close-coupling expansion, using the R-matrix method [H. L. Zhang, M. Graziani, and A. K. Pradhan, Astron. Astrophys. 283, 319 (1994)]. An 11-term expansion, including some n=3 states, is also carried out for Ne vi to study the effect of the coupling to higher-n complexes. The results were compared with those with a fully relativistic distorted-wave method by Zhang and Sampson [At. Data Nucl. Data Tables 56, 41 (1994)]. The study shows that the coupling effects and the resonance effects are still pronounced for highly charged ions, even up to Fe xxii. The relativistic effects, which are incorporated into the R-matrix calculations through the term-coupling method [W. Eissner, M. Jones, and H. Nussbaumer, Comput. Phys. Commun. 8, 270 (1974)], begin to manifest themselves for Z≥16. This study should provide some guidelines for future R-matrix calculations for other isoelectronic sequences.

The method of projectile electron spectroscopy was used to measure the ${\mathrm{Ne}}^{8+}$ Auger decay of the configurations 3lnl′ and 4lnl′ (n⩾4) created by double electron capture in 150-keV ${\mathrm{Ne}}^{10+}$+He collisions. Auger yields were evaluated to convert the experimental cross sections for Auger-electron emission into the corresponding cross sections for double electron capture. It is found that the cross sections attributed to the configurations 3lnl′ follow a ${\mathrm{n}}^{\mathrm{-}3}$ law, while the excitation of the configurations 4lnl′ is rather selective for n=5. It is shown by means of model calculations that the electron correlation plays a decisive role in the capture mechanisms producing the configurations 3lnl′.

Studies of collisions between Rydberg atoms with values of principal quantum number n in the range 100≲n≲400 and ${\mathrm{H}}_2$S and ${\mathrm{C}}_6$${\mathrm{H}}_5$${\mathrm{NO}}_2$ are reported. These targets were selected because they have very different dipole moments: 0.97 and 4.22 D, respectively. Analysis of the data using the essentially-free-electron model shows that at micro-electron-volt energies the cross sections for rotationally inelastic electron scattering by these targets have very different energy dependences. This difference suggests that, in the case of ${\mathrm{C}}_6$${\mathrm{H}}_5$${\mathrm{NO}}_2$, dipole-supported states might be important in the scattering. To examine this further, the data are compared with the results of calculations using a free-electron cross section that assumes the presence of dipole-supported states, and it is demonstrated that, with a reasonable choice of parameters, it is possible to reproduce the experimental observations.

The energy dependence of the positronium (Ps) formation cross section for positrons colliding with all the stable inert atoms is analyzed near threshold. Using R-matrix and threshold theories, the corresponding variations with energy of the elastic-scattering and total cross sections are predicted and compared to experiment where possible. As the target atomic number increases from He to Xe, Wigner cusps are predicted to develop in the elastic cross section near the Ps formation threshold, reflecting the progressive increase of the interaction strength between the positron and the atoms.

In the case of He-like ions, dielectronic recombination ends in the population of Li-like core excited states. Likewise the charge-exchange collision process involving long-lived metastable He-like ions ends in Li-like core excited states. The observation of satellites 1s2l2l’→1${\mathit{s}}^2$2l’’ and 1${\mathit{s}}^2$3l’’ leaves open a certain number of questions. The case of ${\mathrm{O}}^{6+}$(1s2s${)}^3$${\mathit{S}}_1$+${\mathrm{H}}_2$, ${\mathrm{C}}^{4+}$(1s2s${)}^3$${\mathit{S}}_1$+${\mathrm{H}}_2$, and ${\mathrm{N}}^{5+}$(1s2s${)}^3$${\mathit{S}}_1$+${\mathrm{H}}_2$ is considered. The satellites are seen, unpolluted by parent transitions on the one hand, and on the other hand the parent transitions are observed. But a further test of the capture process is significant: the ${}_{}{}^4{}_{}{}^{}$L to ${}_{}{}^4{}_{}{}^{}$L optical transitions in the vacuum ultraviolet range. The n=4 satellites in oxygen and nitrogen coincide with the n=3 parent transitions.

The first-order functional sensitivity densities δ ln${\mathrm{\sigma }}_{1/2\to 3/2}$(E)/δ ln${\mathit{W}}_{\mathrm{\Vert }\mathrm{\Lambda }\mathrm{\Vert }}$(R) are employed to assess the role of structure in the potential-energy curves ${\mathit{W}}_0$${(}^2$Σ) and ${\mathit{W}}_1$${(}^2$Π) mediating the fine-structure transition Na${(}^2$${\mathit{P}}_{1/2}$)+He→Na${(}^2$${\mathit{P}}_{3/2}$)+He and Na${(}^2$${\mathit{P}}_{1/2}$)+Ar→Na${(}^2$${\mathit{P}}_{3/2}$)+Ar. The sensitivity density profiles δ ln${\mathrm{\sigma }}_{1/2\to 3/2}$(E)/δ ln${\mathit{W}}_{\mathrm{\Vert }\mathrm{\Lambda }\mathrm{\Vert }}$(R) for the two systems reveal that regions of significance differ widely for the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }$ and ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }$ curves. The results suggest that prevalent mechanistic explanations from adiabatic analyses have limitations in terms of the ultimate significance of the identified kinematic coupling over well demarcated radial and angular coupling regions. The functional sensitivity analysis is shown to permit a full deconvolution of the collision cross section’s dependence on the features in the individual ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }$ and ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }$ curves as opposed to the adiabatic analysis where only the features in [${\mathit{W}}_0$(R)-${\mathit{W}}_1$(R)] are deemed critical to the collisional outcome.

Quenching rates have been measured for selected metastable levels of ${\mathrm{Ar}}^{\mathit{q}+}$ ions (q=2, 3, 9, and 10) stored in a Kingdon ion trap, with mean energies of 262q eV and 181q eV. Effective quenching cross sections derived from these rates are found to be comparable to electron-capture cross sections of ${\mathrm{Ar}}^{\mathit{q}+}$-Ar collisions studied independently using ion-beam techniques. This implies that quenching is dominated by electron-capture collisions which change the ion charge state.

Photoionization cross sections and asymmetry parameters of photoelectrons resulting from ionization in the 2p subshell of excited-state 2${\mathit{p}}^6$3p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ and ground-state 2${\mathit{p}}^6$3s ${}_{}{}^2{}_{}{}^{}$${\mathit{S}}_{1/2}$ sodium atoms have been calculated using the multiconfiguration Hartree-Fock method over a large photon energy range. Calculations of relative intensities and branching ratios for leaving the positive ions in various final states corresponding to the main and satellite lines have been made and are compared with the available experimental measurements. It is found that there is a strong enhancement of the relative intensity of the shake-up satellite in the excited atom, in agreement with experimental observation. The asymmetry parameter β in the excited state agrees well with a recent experimental measurement made at a single photon energy. Further experimental work is needed to verify the theoretical results over a large photon energy range.

The data obtained by Rapp, Englander-Golden, and Briglia [J. Chem. Phys. 42, 4081 (1965)] on the dissociative-ionization fractions and cross sections for electron impact on ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and ${\mathrm{O}}_2$ molecules have been reanalyzed. Trajectories of the atomic ions produced in the crossed electric and magnetic fields within their target cell were computed as functions of ion energy and angular distribution, leading to a determination of how their ion-collection efficiencies depended on these parameters. Relative ion-energy and angular distributions as functions of incident electron energy from a variety of experimental studies were then incorporated into the calculations to yield total collection efficiencies, to be compared with the value of 40% estimated during the original measurements. For 100-eV electrons, the comparisons indicate that the reported dissociative-ionization fractions and cross sections should be increased by about 15% for ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ targets, but by almost 70% for ${\mathrm{H}}_2$ targets, with all corrections increasing markedly at lower electron energies.

The cross sections for double and single photoexcitation and -ionization of helium are calculated in the acceleration gauge assuming a totally asymmetric energy and angular momentum partitioning between two electrons. The electron-electron correlation is taken into account in the ground-state wave function. By extrapolating single-ionization differential oscillator strengths to n→∞, where n is the excited ${\mathrm{He}}^{+}$ principal quantum number, an estimate of the double-ionization cross sections is obtained. Comparison with other calculations is made.

A simple and easily implemented highly accurate method to compute the scattering length and effective range for a diatomic potential is presented. It combines the numerical solution for small internuclear distances R with analytical corrections for large R. The method provides upper and lower limits to the exact values, to any desired precision. A numerical example and discussion are given for the case of the Cs-Cs ground-state interaction.

In the reflection approximation, the dissociative cross sections of ${\mathrm{H}}_2$ by electron impact for production of H(1s) and H(2s) are accurately computed in the Bethe approximation using highly correlated electronic wave functions. It is found that the calculated Bethe cross sections, expected to be valid only for high-incident electron energies, agree surprisingly well with other theoretical values for low impact energies, where electron exchange must surely be included. The discrepancy between theory and experiment reported for total production of H(2s) at incident energies above 500 eV may be attributed to lack of inclusion in the theoretical model of double excitations, particularly those corresponding to optically forbidden transitions.

The relationship between the plane-wave Born approximation (PWBA) and the impulse approximation (IA) for the antiscreening contribution to electron loss is studied. It is shown that the IA can be obtained from the PWBA in the case of fast, asymmetric collisions. In this collision regime, it is shown that the broadening of the ‘‘free’’ electron beam velocities, taken into account by the Compton profile of the target within the IA framework, can be considered to simulate the sum over the final continuum target states in the PWBA. Thus, these two different theoretical approaches are reconciled. The derivation also brings out some important features of the antiscreening mechanism not easily seen in either approximation.

We present calculations of the electronic stopping power for hydrogen molecular ions ${\mathrm{H}}_2^{+}$ in solids. These calculations include contributions from both valence electrons and inner-shell electrons of target atoms with the linear dielectric theory and the local-density approximation method. The screened Coulomb potential is used to describe the repulsion process of the two protons. The values of the stopping-power ratio Q for ${\mathrm{H}}_2^{+}$ at the high velocities are decreased, obviously due to the contributions of the inner-shell electrons. The theoretical results are compared with some experimental data.

Rigorous expressions have been derived for the mean energy loss of ions penetrating through foils, specified into entrance and exit charge states. These expressions allow extraction of partial stopping cross sections and charge-exchange cross sections in solids from measured energy losses versus foil thickness. Particular attention is given to thin penetrated layers and the opposite limit of charge-state equilibrium which may be easier to deal with experimentally. Sum rules to be obeyed by measured parameters have been derived. Explicit results have been listed for the two-state case.