The asymptotic form of the radial wave function for positive-energy states is calculated for the case of a repulsive Coulomb field. The cases of a pure Coulomb potential and a modified Coulomb potential are considered. Second-order analytic solutions for the amplitudes and phases are obtained when the modifications to the pure Coulombic potential take the form α${\mathit{r}}^{\mathrm{-}2}$+β${\mathit{r}}^{\mathrm{-}3}$+γ${\mathit{r}}^{\mathrm{-}4}$, using the Jeffreys or WKB method. For the case of a pure Coulomb field, numerical results obtained from this method were compared with ‘‘exact’’ numerical results that were obtained using the analytic properties of the Coulomb wave functions. Tables are presented to show the conditions under which the method is accurate.

The R-matrix formalism is applied to the study of resonance properties. We present an iterative method that provides the energy and width of a resonance without the usual Breit-Wigner parametrization. The validity of the method is checked on a microscopic study of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$${+}^{13}$C scattering at low energies, and on the hydrogen atom in a strong magnetic field. For this latter system, the method is also applied to the study of two-channel resonances.

We present an approximate analytic expression for the low-frequency ground-state relativistic Rayleigh scattering matrix elements for hydrogenic atoms, including the possibility of electron spin flip as a result of the elastic photon atom scattering. Our expression is obtained by taking the long-wavelength approximation in the relativistic Coulomb matrix elements, without neglecting the photon frequency dependence in the Coulomb Green operator. By comparison with existing exact numerical calculations, we demonstrate that our approximation is appropriate for photon frequencies below the photoelectric threshold, at least for the non-spin-flip amplitude. Using our expressions, we investigate two issues: (i) the comparison of static and dynamical polarizabilities, and (ii) the behavior of the electron spin-flip amplitude, related to magnetic scattering.

We present measurements of absolute differential cross sections for the scattering of 10-eV electrons by ground-state sodium, with no calibration needed. Results for 3S→3P have been obtained in the angular range 1°–20°. From these results the total cross section is estimated to be 23×${10}^{\mathrm{-}16}$±30% ${\mathrm{cm}}^2$. Comparisons with computational results and other (normalized) measurements are made.

The semiclassical impact-parameter method, based on a 14-state molecular expansion, is employed to calculate the charge-transfer cross sections for ${\mathrm{He}}^{2+}$-Na(3s) collisions. Electron translation effects have been taken into account. Selective capture into the n=3 manifold of ${\mathrm{He}}^{+}$ is found to occur in the low kilo-electron-volt energy region. The total capture cross section also exhibits an oscillatory energy dependence in the low-energy region.

Ionization in H(1s)+${\mathrm{H}}^{+}$ collisions is studied near the threshold and at relative collision energies in the range 5–25 keV. Based on the analytic continuation of the adiabatic potential-energy curves in the complex plane of the internuclear distance, the transition probabilities are calculated in the WKB approximation by evaluating the phase integral around the branch points connecting the potential curves. Two different ionization mechanisms are identified: one is the propagation on a ridge of the centrifugal core of the electronic potential when the nuclei approach each other, and the other is associated with the saddle point of the two-center Coulomb potential. The two mechanisms give about equal contributions to the total ionization cross section in the relative energy range 5.0–25.0 keV. Near threshold the second mechanism dominates. The analytical threshold energy-dependence behavior differs from the Wannier law.

Semiclassical coupled-state model calculations have been performed for L-shell ionization of gold induced by protons and antiprotons in the energy range 0.15–3 MeV. The results of the calculations have been compared with the predictions of a simple approach suggested by Brandt and Basbas for description of antiparticle excitation of atomic inner shells. Apart from the range of very low collision velocities, a reasonable agreement has been found between the two models. In addition to the binding and Coulomb-distortion effects discussed by Brandt and Basbas [Phys. Rev. A 27, 578 (1983); 28, 3142(E) (1983)], for the L shell a further effect due to dynamical couplings between the L-substate ionization amplitudes also contributes to the particle-antiparticle differences. While the latter processes have only a negligible effect on the energy dependence of the cross sections, their inclusion has been shown to be unavoidable when ratios of the subshell ionization cross sections are analyzed for the two kinds of excitation.

Highly charged Ar (up to 18+), Xe (up to 48+), and U (up to 71+) ions produced through electron-impact ionization and excitation in an electron-beam ion trap have efficiently been extracted from the trap, and mass and charge analyzed. Charge-state distributions for Ar and Xe ions following electron-impact ionization and excitation have been measured. Relative yields for the production of ${\mathrm{Ar}}^{16+}$ and ${\mathrm{Xe}}^{44+}$ ions have been deduced as a function of electron-beam energies. Ar K and Xe L x-ray emission following ${\mathrm{Ar}}^{17+}$, ${\mathrm{Ar}}^{18+}$ and ${\mathrm{Xe}}^{44+}$, ${\mathrm{Xe}}^{45+}$ and ${\mathrm{Xe}}^{48+}$ ion impact on a Cu surface was measured. The observed line positions demonstrate electron capture into high-n states and a fast radiative decay in the neutralization process at the surface.

It is shown that in a Born treatment of excitation, ionization, and pair production in relativistic atomic collisions, cross-section calculations are not affected by the presence or absence of explicitly imposed Coulomb boundary conditions. On the other hand, in relativistic single- or two-center coupled-channel calculations, the results are strongly affected. For ${\mathrm{U}}^{92+}$+${\mathrm{U}}^{91+}$ collisions at 1 GeV/u, it is illustrated that in all calculations unperturbed atomic basis sets lead to long-range couplings along the trajectory while for basis states satisfying boundary conditions the couplings among states are localized around the distance of closest approach. The necessity of imposing Coulomb boundary conditions for relativistic direct reactions is emphasized.

A combined optical-pumping–laser-induced-fluorescence method was developed to determine the fraction of metastable-state ions in a ${\mathrm{Ba}}^{+}$ beam. This allowed us to measure the ratio of the charge-exchange cross sections for collisions of ${\mathrm{Ba}}^{+}$(6s) and ${\mathrm{Ba}}^{+}$(5d) ions with a sodium vapor for impact energies ranging from 3 to 29 keV. For a collision energy of 5 keV, the ratio of the cross sections for ${\mathrm{Ba}}^{+}$(5d ${}_{}{}^2{}_{}{}^{}$${\mathit{D}}_{3/2}$) and ${\mathrm{Ba}}^{+}$(5d ${}_{}{}^2{}_{}{}^{}$${\mathit{D}}_{5/2}$) was measured. All results are compared to theoretical near-resonance predictions.

The spin-dependent cross sections for electron excitation of the 3p level of sodium at energies just above threshold are studied using the R-matrix approach. In addition to the total cross section for excitation, we present results for the excitation cross sections as a function of the change in the spin and orbital angular-momentum projection of the target. Calculations were made in the four- (3s,3p,4s,3d), five- (+4p), and six-state (+4p,4d) approximations, for electron energies ranging from threshold to 4.0 eV. The results are compared with other calculations and with the recent experimental results of Han, Schinn, and Gallagher [Phys. Rev. A 38, 535 (1988)].

An alternative method for taking into account correlation effects in the calculation of Auger decay rates is presented here. This approach, which generalizes a technique recently proposed by the authors [Phys. Rev. A 39, 6247 (1989)], is based on the coupling of final ionic states and decay channels and has been applied to the construction of a ‘‘theoretical’’ Auger spectrum of the LiF molecule in which transitions also due to shakeoff and shakeup processes are taken into account.

A three-dimensional quantum-mechanical study of vibrational, state-resolved differential cross sections (DCS) for the direct inelastic and for the charge-transfer scattering channels has been carried out for the ${\mathrm{H}}^{+}$+${\mathrm{O}}_2$ system. The collision energy considered was ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.\mathrm{}}$=23.0 eV, which is the same as that examined by Noll and Toennies in their experiments [J. Chem. Phys. 85, 3313 (1986)]. The scattering treatment employed was the charge-transfer infinite-order sudden approximation (CT IOSA) with the vibrational states correctly expanded over the relevant adiabatic basis for each of the two electronic channels. The state-to-state DCS are found to follow closely the behavior of the experimental quantities, both in the inelastic and the charge-transfer channels. Moreover, a careful comparison between the measured relative probabilities and computed values allows us to test in minute detail the efficiency of the scattering model and the reliability of the potential-energy surfaces employed. It is found that vibrational energy transfer is overestimated in the vibrational inelastic channels while in the charge-transfer inelastic channels the same energy transfer is slightly underestimated by the calculations. The total flux distribution, however, is found to be in very good accord with experiments. Angular distributions are also well reproduced both by the DCS and by the average energy-transfer values. The study of some of the CT IOSA quantities also allows us to establish clearly the importance of nonadiabatic transitions in enhancing vibrational inelasticity in the present system.

The classical dynamics of a hydrogen atom in a generalized van der Waals potential is investigated. In order to carry out the analytical and numerical investigations for a range of parametric values, we removed the singularity of the problem using Levi-Civita regularization and converted the problem into that of two coupled sextic anharmonic oscillators. We identify the integrable choices of the oscillator system using the Painlevé singularity analysis, and the associated second integrals of motion are derived using the extended Lie transformations. Numerical investigations are carried out for other nonintegrable regions and we observe chaos-order-chaos type of transition regions when one of the system parameters is varied.

A theoretical derivation of the differential photoionization cross section taking into account the spin polarization of photoelectrons is presented. This cross section corresponds to rotationally resolved transitions from an initial rotational level of the neutral molecule to a final rotational level of the ion. The final-state wave function of the ion-plus-electron system is written in the Hund’s-case (c) coupling scheme, and the parities of this state and of the initial-state wave functions are explicitly introduced. Two equivalent expressions for the cross section are obtained that correspond to two coupling schemes of the angular momenta involved in the problem. One is a transferred-momentum-coupling scheme, and the other is the final-state (ion-plus-electron) total-angular-momentum-coupling scheme. Their respective advantages in analyzing the experimental results are highlighted. Each term in the transition moment and cross-section expressions contains a multiplicative factor of a simple form that determines if a contribution to these expressions is zero or not, thus playing the role of a selection-rule factor. Our expressions apply to the single-photon process as well as to multiphoton processes in cases in which only the last (one-photon) ionization step is considered explicitly. The paper ends with derivation of explicit formulas for the total cross section and the angle-integrated spin-polarization parameter in a particular case. The photoionization of the HI molecule was the model for these particular formulas.

The time-dependent Schrödinger equation for a central collision between a heavy point charge and a harmonically bound electron is solved numerically. This is done in a basis of energy eigenfunctions of the undisturbed electron. Our numerical method also provides the coefficients of the Born series for the collision. We compare the Born expansion with the exact results. In agreement with other calculations we find a significant Barkas effect for some collision parameter values. At low velocities the Barkas correction is shown to be very large, but at higher velocities it becomes very small even for ions with high charges.

Post-collisional effects on the electronic distribution of autoionization processes are studied. A formulation including both the long range of the projectile Coulomb potential and the polarization potential is presented. The latter potential mixes close lying levels of autoionizing states with equal magnetic quantum number, giving rise to a significant perturbation of the angular and energy distribution of the electron spectra. Particular attention is paid to the mixing of autoionizing levels of helium 2s2p ${}_{}{}^1{}_{}{}^{}$P and 2${\mathit{p}}^2$ ${}_{}{}^1{}_{}{}^{}$D. Deviation from 90° symmetry is studied, and comparison with experiments is presented.

Decay of double-K-shell-vacancy states in xenon atoms, created in the decay of ${}_{}{}^{131}{}_{}{}^{}\mathrm{Cs}$, was investigated. The measurements were performed with a pair of germanium detectors, a fast-slow coincidence system, and a three-parameter pulse-height analyzer. In the analysis of the two-dimensional ${\mathit{E}}_1$-${\mathit{E}}_2$ spectrum, improved least-squares routines were applied. The following results were derived: the probability of creation of a double K-shell vacancy per ${}_{}{}^{131}{}_{}{}^{}\mathrm{Cs}$ decay, ${\mathit{P}}_{\mathit{K}\mathit{K}}$=(1.48±0.35)×${10}^{\mathrm{-}5}$; the hypersatellite energy shifts ${\mathrm{\Delta }}^{\mathit{h}}$(Kα)=(653±20) eV, ${\mathrm{\Delta }}^{\mathit{h}}$(K${\mathrm{\beta }}_1$)=(834±39) eV, and ${\mathrm{\Delta }}^{\mathit{h}}$(K${\mathrm{\beta }}_2$)=(903±81) eV; the average values of the satellite energy shifts due to the presence of an ${\mathit{L}}_3$- or ${\mathit{L}}_2$-shell spectator vacancy ${\mathrm{\Delta }}^{\mathit{s}}$(Kα${\mathit{L}}^{\mathrm{-}1}$)=(80±15) eV, ${\mathrm{\Delta }}^{\mathit{s}}$(K${\mathrm{\beta }}_1$${\mathit{L}}^{\mathrm{-}1}$)=(169±34) eV, and ${\mathrm{\Delta }}^{\mathit{s}}$(K${\mathrm{\beta }}_2$${\mathit{L}}^{\mathrm{-}1}$)=(261±81) eV; the intensity ratios of the hypersatellite transitions, I(K${\mathrm{\alpha }}_2^{\mathit{h}}$)/I(K${\mathrm{\alpha }}_1^{\mathit{h}}$)=0.94±0.18, I(K${\mathrm{\beta }}_1^{\mathit{h}}$)/I(K${\mathrm{\alpha }}_1^{\mathit{h}}$)=0.36±0.06, and I(K${\mathrm{\beta }}_2^{\mathit{h}}$)/ I(K${\mathrm{\alpha }}_1^{\mathit{h}}$)=0.09±0.04; the intensity ratios of the satellite transitions I(K${\mathrm{\alpha }}_2$${\mathit{L}}^{\mathrm{-}1}$)/I(K${\mathrm{\alpha }}_1$${\mathit{L}}^{\mathrm{-}1}$)=0.44±0.10 and 0.44±0.09 for an ${\mathit{L}}_3$ and ${\mathit{L}}_2$ spectator vacancy, respectively; and the intensity ratios of some other satellite transitions.

An algebraic Hamiltonian for two coupled anharmonic (Morse-type) oscillators admits an exact symmetry at a finite value of the coupling constant. The two symmetry-adapted modes are neither local nor normal, yet are independent. The explicit discussion is given for two coupled stretch modes but the same symmetry is found also when the two stretches are in addition coupled to the bend mode.

This paper presents an extended spectroscopic analysis of Na-like titanium, Tixii, based on spectra recorded using the beam-foil method. About 30 new lines have been classified that have established ten new terms with high n and l quantum numbers. The new terms and combinations improve the established energy levels and allow for an accurate determination of the ionization limit from Ritz and polarization formulas. By comparison with a very elaborate relativistic calculation, the QED contribution to the ionization potential is estimated to be 849±20 ${\mathrm{cm}}^{\mathrm{-}1}$. An isoelectronic study of the ionization limit along the Na sequence is also presented.