Hyperspherical coordinates are used to study properties of Coulombic three-body systems of arbitrary masses. Consider a system ABA, which consists of two identical particles A and a third particle B, each with one unit of charge. We examine the evolution of the approximate quantum numbers that are used for classifying bound and resonance states of the system as the mass ratio λ=${\mathit{m}}_{\mathit{A}}$/${\mathit{m}}_{\mathit{B}}$ changes from the atomic limit (λ→0 as in ${\mathrm{H}}^{\mathrm{-}}$) to the diatomic molecular limit (λ≫1 as in ${\mathrm{H}}_2^{+}$). It is shown that for states which exhibit rovibrational behaviors in the atomic limit (λ→0), a single set of approximate quantum numbers can be used to describe three-body systems of any λ’s. For states that display independent-particle behavior in the atomic limit, such as singly excited states, it is shown that these states display rovibrational behaviors only in the large-λ limit. The evolution of the spectroscopy of the three-body systems from the shell model of atoms to the rovibrational model of molecules is thus analyzed. Calculations of potential curves in hyperspherical coordinates were carried out for ${\mathrm{Ps}}^{\mathrm{-}}$ and ${\mathit{d}}^{+}$${\mathrm{\mu }}^{\mathrm{-}}$${\mathit{d}}^{+}$ that serve as the intermediate steps for the study of the evolution of the approximate quantum numbers from ${\mathrm{H}}^{\mathrm{-}}$ to ${\mathrm{H}}_2^{+}$.

A method based on supersymmetric quantum mechanics is given for obtaining exact solutions of the potential V(r)=α/r+${\mathit{p}}_1$r+${\mathit{p}}_2$${\mathit{r}}^2$+${\mathit{p}}_3$${\mathit{r}}^3$+${\mathit{p}}_4$${\mathit{r}}^4$ where α and the p’s are parameters, provided certain relations are satisfied between the parameters. Detailed results are given for three specific cases. The potential in question gives rise to some very interesting shapes (double-well, etc.). The applicability of the shifted 1/N expansion method to such potential shapes is examined by comparing eigenenergies obtained by this method with the exact ones obtained from supersymmetric considerations. It is found that in certain situations, the shifted 1/N expansion method may give poor or erroneous results. Applicability of the proposed method to potentials involving higher powers of r is also discussed.

Formally exact formulas are generated for the exchange-correlation energy of an electronic system, of Xα type, of Wigner-like form, and gradient-corrected versions of each. Parameters in the several alternative formulas are determined by least-squares fitting of the actual exchange-correlation energies for ten atoms, from He to Ar.

The local virial theorem is derived within the exact density-functional theory. Special forms of the local virial theorem valid within the local-density approximation and the local thermodynamic description are also presented.

We have calculated L-shell cross sections for the process of resonant transfer excitation followed by x-ray stabilization (RTEX) in collisions of ${\mathrm{Nb}}^{\mathit{q}+}$ ions (q=28–32) with ${\mathrm{H}}_2$. The LMn plateau cross section is nearly constant [(4.5–5.2)×${10}^{\mathrm{-}20}$ ${\mathrm{cm}}^2$] for q=29–32 and is consistent with the results of the recent experiment by Bernstein et al. [Phys. Rev. A 40, 4085 (1989)] for q=31 and 32, but our results for q=28–30 are substantially larger than experiment. For Ne-like niobium (q=31), the inclusion of RTEX contributions from higher transitions (LNn, LOn, etc.) leads to good agreement with the experiment by Bernstein et al. in the high-energy tail. This implies that only a small contribution is possible from the uncorrelated transfer excitation process.

We have calculated K-shell cross sections for the process of resonant transfer excitation followed by x-ray stabilization (RTEX) in collisions of ${\mathrm{Ca}}^{\mathit{q}+}$ (q=10–12,16–19) ions with ${\mathrm{H}}_2$. Our KLn intermediate-coupling results are in excellent agreement with the experimental results of Tanis et al. [Phys. Rev. A 34, 2534 (1986)] for q=16–18, particularly when supplemented by our LS-coupling results for the KMn transitions. The comparison for q=19 is hampered by the nonresonant background, but our results are consistent with experiment. Our LS-coupling results for KLn-plus-KMn transitions are in good agreement with experiment for q=11 and 12. But for q=10 our KMn RTEX cross sections are much smaller than the sparse experimental results, indicating a large nonresonant experimental background.

We have measured cross sections for single capture, transfer ionization, single ionization, double ionization, ionization excitation, and transfer excitation for fully stripped oxygen projectiles at energies between 8 and 20 MeV on ${\mathrm{D}}_2$ molecular targets. Coincidences between charge-analyzed projectiles and recoil ${\mathrm{D}}^{+}$ and ${\mathrm{D}}_2^{+}$ products were measured. The time of flight (TOF) of the recoil, collected by applying an extraction electric field, was used to separate the ${\mathrm{D}}^{+}$ from ${\mathrm{D}}_2^{+}$ ions. TOF spectra taken with no field were used to distinguish the ${\mathrm{D}}^{+}$ ions from different dissociative channels, including the electronically excited 2p${\mathrm{\sigma }}_{\mathit{u}}$,2s${\mathrm{\sigma }}_{\mathit{g}}$,2p${\mathrm{\pi }}_{\mathit{u}}$ channels and the double-ionization channel. The results are compared with two model calculations.

The Mg 3pnd J=3 autoionizing spectra have been studied for n values ranging from 9 to 40, using an isolated-core excitation technique with ion detection. The measured spectra are found to be in generally excellent agreement with results from a calculated reaction matrix. The observed spectra exhibit strong interseries interactions between the 3${\mathit{p}}_{1/2}$${\mathit{nd}}_{5/2}$ and 3${\mathit{p}}_{3/2}$${\mathit{nd}}_{\mathit{j}}$ series, and, for n≤15, interferences between the amplitudes for excitation of the core electron to the 3${\mathit{P}}_{1/2}$ and 3${\mathit{P}}_{3/2}$ ion states. Classifications of states for n≤29 are tabulated. We discuss the difficulties in deducing autoionization rates for Mg from the experimental and theoretical data, the implications of which could have relevance to dielectronic recombination rate calculations.

We present a calculation of the cross sections for two-photon free-free transitions of an electron colliding with a Coulomb center of force. The calculation is based on second-order perturbation theory, in the nonrelativistic dipole approximation. The matrix elements for absorption and emission were integrated analytically in momentum space, following a method developed earlier by one of us. This makes use of the Schwinger integral representation for the Coulomb Green’s function. The result was expressed in terms of integrals over hypergeometric functions of the Gauss type. Simple limiting forms of these complicated expressions were found in the first Born approximation, and at low and high photon energies. The results derived agree with those obtained by direct calculations done for these limits. Finally, concluding remarks on the analytic part of our work are made. The numerical computation of the two-photon free-free transition cross sections for absorption and emission in various geometries is planned to be presented at a later time.

Differential excitation cross sections for the transitions from 1 ${}_{}{}^1{}_{}{}^{}\mathrm{S}$ to 2${\mathrm{}}^3$S, 2${\mathrm{}}^1$S, 2${\mathrm{}}^3$P, and 2${\mathrm{}}^1$P in He-like ${\mathrm{Li}}^{+}$ are calculated in the distorted-wave and close-coupling approximations in order to study their sensitivity to continuum coupling effects. Comparisons are made between nonunitarized distorted-wave, 5-state unitarized distorted-wave, 5-state close-coupling, and 11-state close-coupling calculations. The results indicate that the shape of the cross sections, as a function of scattering angle, can be significantly different for the various levels of approximation, even when the total cross sections are in reasonably close agreement.

A complex resonance-scattering theory is developed to obtain partial widths and branching ratios for full scattering experiments. A new formula for the partial widths which is useful in atomic, molecular, nuclear, and particle physics is obtained. The formalism provides a simple relationship among the previously proposed different methods for calculating partial widths. Illustrative numerical examples are given, showing the stability (lack of oscillations) of the partial widths obtained by this formula.

M-shell x-ray production cross sections for selected heavy elements, namely, ${}_{72}{}^{}{}_{}{}^{}\mathrm{Hf}$, ${}_{73}{}^{}{}_{}{}^{}\mathrm{Ta}$, ${}_{74}{}^{}{}_{}{}^{}\mathrm{W}$, ${}_{75}{}^{}{}_{}{}^{}\mathrm{Re}$, ${}_{76}{}^{}{}_{}{}^{}\mathrm{Os}$, ${}_{77}{}^{}{}_{}{}^{}\mathrm{Ir}$, ${}_{78}{}^{}{}_{}{}^{}\mathrm{Pt}$, ${}_{79}{}^{}{}_{}{}^{}\mathrm{Au}$, ${}_{83}{}^{}{}_{}{}^{}\mathrm{Bi}$, and ${}_{90}{}^{}{}_{}{}^{}\mathrm{Th}$, were measured for protons of energy 0.6–4.0 MeV. The experimental results are compared with the predictions of the first Born and semiclassical approximations for M-shell ionization; these data are also compared with the theory that accounts for the projectile’s energy loss and Coulomb deflection as well as for the target’s M-shell electron perturbed stationary state and relativistic nature (ECPSSR). Generally, fair agreement between the data and the ECPSSR theory is found. Some systematical discrepancies observed for the lightest elements (Hf, Ta, and W) are explained as possible ambiguities in the M-shell Coster-Kronig factors and fluorescence yields, which were used to convert theoretical M-subshell ionization cross sections to the total M-x-ray production cross sections. The experimental total M-shell ionization cross sections were obtained from measured M-x-ray cross sections using the proposed approximate average fluorescence yield ω${\mathrm{¯}}_{\mathit{M}}$ that relies on two fluorescence yields and the Coster-Kronig factor for only ${\mathit{M}}_4$ and ${\mathit{M}}_5$ subshells.

The ionization of He atoms, prepared in a well-defined (n=14) ${}_{}{}^1{}_{}{}^{}$P Rydberg state, in collisions with electron-attaching molecules like ${\mathrm{SF}}_6$ and ${\mathrm{NO}}_2$, is studied in a crossed-beam experiment at thermal energies. The ionization cross section is observed to be large for ${\mathrm{SF}}_6$, reaching 4.2×${10}^{\mathrm{-}13}$ ${\mathrm{cm}}^2$, and to be smaller for ${\mathrm{NO}}_2$, close to ${10}^{\mathrm{-}15}$ ${\mathrm{cm}}^2$. The dependence of these two cross sections on the relative velocity of the reactants exhibits a characteristic behavior with a saturation at low velocities, a dependence that is completely different from that obtained with polar molecules. The observation of such a dependence for ${\mathrm{NO}}_2$ indicates that, for this molecule, the reaction product is an ion pair, as for ${\mathrm{SF}}_6$, and that ionization is not due to rotational energy transfer even though ${\mathrm{NO}}_2$ has a dipole moment. This dependence cannot be explained by the ‘‘free-electron model’’ usually used in Rydberg-atom–molecule collisions; it clearly shows that the interaction of the molecule with the ion core cannot be neglected.

Dielectronic recombination cross sections for several H-like atomic ions are calculated in an isolated-resonance, distorted-wave approximation. Fine-structure and configuration-interaction effects are examined in detail for the ${\mathrm{O}}^{7+}$ cross section. Hartree-Fock, intermediate-coupled, multiconfiguration dielectronic recombination cross sections for ${\mathrm{O}}^{7+}$ are then compared with the recent experimental measurements obtained with the Test Storage Ring in Heidelberg. The cross-section spectra line up well in energy and the shape of the main resonance structures are comparable. The experimental integrated cross sections differ by up to 20% from theory, but this may be due in part to uncertainties in the electron distribution function.

Total photoabsorption cross sections have been calculated for the Ba, ${\mathrm{Ba}}^{+}$, ${\mathrm{Ba}}^{2+}$, Xe, and Kr atoms, and also for barium plasma at kT=20 eV temperature. The calculations are based on a self-consistent Dirac-Slater model of the atom with the option of including the effect of the vacancy hole created by the ejected electron following photoionization from an inner shell. We investigate the effect of the vacancy hole together with the use of the dipole-length and dipole-velocity forms of the transition matrix elements and also the effect of polarization in the final state of the ion. We present calculations for photoabsorption at photon energies in the regions of inner-shell photoionization.

In a system consisting of an electron and a highly charged ion, interaction with the radiation field is strong, and radiation-damping effects must be accurately taken into account. The present work provides a numerical method to study the radiation-damping effect in the processes of photoionization, radiative recombination, and electron scattering. A simple calculation is made for ${\mathrm{Fe}}^{24+}$, ${\mathrm{Xe}}^{52+}$(1s2s)+hν⇆${\mathrm{Fe}}^{25+}$, ${\mathrm{Xe}}^{53+}$(1s)+e. Special emphasis is placed on the nonapplicability of conventional first-order perturbation theory to photoinduced autoionization of a highly charged ion. The interference effect between the resonant and the nonresonant parts is found to be negligible in the present cases.

A single-center coupled-channel code based on an expansion in terms of atomic wave functions that includes dynamic curved projectile trajectories is applied to the calculation of stopping powers. Stopping powers and differential ionization cross sections are evaluated for p¯, ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{2+}$, and ${\mathrm{Li}}^{3+}$ projectiles penetrating atomic H and He targets at energies of 10–500 keV/u. The results are compared to experimental data, to predictions of the first-order plane-wave Born approximation, and to results of calculation for excitation of a harmonic oscillator including Barkas corrections. The improvement of the present model to first-order or second-order perturbative treatments as well as the effect of polarization on the projectile trajectories is discussed.

In a previous paper [J. C. Straton, Phys. Rev. A 41, 71 (1990)] an integro-differential transform was introduced and utilized to obtain the analytically reduced form for multicenter integrals composed of general-state hydrogenic orbitals, Yukawa or Coulomb potentials, and plane waves. The present paper extends this result to include Coulomb waves.

The van der Waals potential of the H-He interaction and the hyperfine frequency shift of H in He are predicted using the Tang-Toennies model. This model damps the long-range ab initio dispersion terms individually using a universal damping function and adds to this a simple Born-Mayer repulsive term. The Born-Mayer parameters are derived from self-consistent-field calculations. The resulting potential is found to be in good agreement with two molecular-beam experiments and its well parameters, in excellent agreement with the complete configuration-interaction calculation. In order to compare with experiment, the hyperfine frequency shift is thermally averaged over the potential both quantum mechanically and classically. The thermally averaged results are in excellent agreement with experiment in the high-temperature range but there are some discrepancies with the measurements at 0.5 and at 1.15 K. These discrepancies may be due to the fact that the long-range coefficient ${\mathit{K}}_{10}$ used is too small. The quantum and classical results are practically identical for temperature above 40 K. The classical statistics fails completely only for temperature below 5 K. Also in the quantum calculation, the isotope effect between ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is found to show up only for temperature below 10 K. The theoretical isotope effect is in qualitative agreement with experiment.

Infinitesimal propagators have been used in quantum-mechanical problems to establish ordering rules for classical quantities. Ambiguities arise in operator ordering as a result of the freedom of choice in evaluating the classical action over a short-time interval. The primitive quadrature rule employed in a short-time propagator establishes the quantum system associated with the classical Hamiltonian. Normal propagators are constructed from products of infinitesimal propagators and represent a compound quadrature in which the path is broken into line segments and a separate quadrature rule is applied to each line segment. It is demonstrated for Hamiltonians involving the vector potential that higher-order quadratures of the infinitesimal propagator all give a unique and proper ordering. Similarly, Hamiltonians that are products of powers of position x and momentum p, i.e., ${\mathit{p}}^{\mathit{l}}$${\mathit{x}}^{\mathit{m}}$, show some preference for Born-Jordon ordering as higher quadrature rules are applied. Unique orderings can be obtained in some cases by solving for the normal propagator. This is done for the Hamiltonian ${\mathit{p}}^{\mathit{l}}$${\mathit{x}}^{\mathit{m}}$ by using a Fourier representation for the phase-space propagator. This formalism requires that both the momentum and position coordinates be represented by Fourier series. These results show that care must be taken when generating quantum-mechanical operators by using primitive quadrature rules in conjunction with a short-time propagator. These ambiguities are eliminated when the compound quadrature is performed to generate the normal propagator.