In continuation of our previous work, charge transfer processes occurring in protons on rare-gas-atom collisions have been investigated. Diagonal and real off-diagonal coherence elements of the density matrix for H(n=3) atoms produced in 20–100-keV electron-capture collisions with Kr atoms are experimentally determined by analyzing the Balmer-α light from the decay of H atoms from the (n=3) state to the (n=2) state. The intensity and polarization of the emitted light are measured as functions of an axially symmetric electric field in the collision region. These data are fitted to a numerical model of the H atom in an electric field in order to extract density-matrix elements. The results are compared to previous studies of ${\mathrm{H}}^{+}$ on He and Ar. The collisionally produced dipole moment of the H(n=3) atom decreases for increasing atomic number of the rare-gas target atoms, which indicates that the final phase of the collision process is not essential for the formation of the dipole moment. This physical picture is further supported by our alignment data. Absolute cross sections for charge transfer to the 3s, 3p, and 3d levels are presented as well.

The zero-energy scattering in a particular partial wave by a potential V=${\mathit{V}}_{\mathit{s}}$+${\mathit{V}}_{\mathit{c}}$ that is a superposition of short range and attractive Coulomb components is characterized by the additional phase shift ${\mathrm{\delta }}_{\mathit{s}}$(0), due to ${\mathit{V}}_{\mathit{s}}$. It has been known for many years that ${\mathrm{\delta }}_{\mathit{s}}$(0)(modπ)=μ(∞)π, where μ(n) is the quantum defect of the nth energy level. In analogy with Levinson’s theorem for short-range potentials, one might expect that a more precise statement, based on an absolute definition of the phase shift, would be ${\mathrm{\delta }}_{\mathit{s}}$(0)=μ(∞)π, with the value of the largest integer contained in μ(∞) representing the number of additional bound states due to ${\mathit{V}}_{\mathit{s}}$. A simple derivation of this relation is presented here, based on variational principles for the binding energies and phase shifts, and on the property (fundamental to quantum-defect theory) that appropriately normalized bound-state wave functions for n→∞ merge smoothly into the energy-normalized regular continuum solutions at the continuum threshold.

Procedures are given for calculating relativistic distorted-wave collision strengths for producing optically allowed Δn=0 transitions between magnetic sublevels of highly charged ions by impact with directional electrons. For such transitions, which tend to have very small transition energies, difficulties arise because the contribution from extremely large angular momenta of the free electron is important. Illustrative numerical results are given for He-like ions, which have been of interest for electron-beam ion-trap experiments [Wargelin et al., Phys. Rev. Lett. 71, 2196 (1993)].

Absolute cross sections for ionization of 1.5–10.0 keV/amu Rydberg helium atoms in principal quantum states 12≤n≤15 due to collisions with potassium have been measured. The data are compared with the free-electron cross section at equal velocity. Our results for the collisional ionization cross sections (${\mathrm{\sigma }}_{\mathit{i}}$) agree both in shape and absolute magnitude with the data available for the total electron-scattering cross sections (${\mathrm{\sigma }}_{\mathit{e}}$) and support recent theoretical models for ionization of Rydberg atoms with neutral perturbers.

Charge-state dependence of M-shell x-ray production cross sections of ${}_{67}{}^{}{}_{}{}^{}\mathrm{Ho}$ bombarded by 2–12-MeV carbon ions, with and without K-shell vacancies, were measured using a windowless Si(Li) x-ray detector with a full-width-at-half-maximum resolution of 135 eV at 5.9 keV. Carbon ions of different charge states were produced using a postacceleration, nitrogen gas stripping cell. The carbon ions were then magnetically analyzed to select the desired charge state and energy before entering the target chamber. The total M-shell and Mζ, Mα,β, and Mγ x-ray cross sections were measured. The electron-capture (EC) contributions as well as the direct-ionization (DI) contributions can be determined by making a comprehensive study of the projectile-charge-state dependence of the target x-ray production cross sections for targets in which the single-collision realm is maintained. In this paper, both EC and DI contributions and the total M-shell x-ray production cross sections are compared to both the first Born theory and to the perturbed-stationary-state theory with energy-loss, Coulomb-deflection, and relativistic corrections.

In this paper, we describe collisions between high-energy (100-keV) fullerene ions (${\mathrm{C}}_{60}^{+}$, ${\mathrm{C}}_{60}^{2+}$, ${\mathrm{C}}_{70}^{2+}$, and ${\mathrm{C}}_{70}^{3+}$) and ${\mathrm{C}}_{60}$. The fast, forward-directed charged collision products are identified, leading to information on electron capture and loss as well as fragmentation. Similar studies are performed on rare-gas targets (He and Xe), and the fragmentation patterns and charge-exchange cross sections are compared and discussed. The electron-capture cross sections are two orders of magnitude larger for collisions with ${\mathrm{C}}_{60}$ as compared to Xe, while the smaller cluster-ion fragment peaks are only 3–6 times more intense. These observations are discussed in the light of the low ionization energy and the large mass and size of ${\mathrm{C}}_{60}$.

We have performed R-matrix calculations for the electron-impact excitation of a highly charged ion in which an optical potential is included to allow for radiative damping of intermediate resonance states. The present case considered is that of electrons incident on ${\mathrm{Ti}}^{20+}$ ions. Comparisons with undamped R-matrix calculations, distorted-wave calculations, and experimental measurement are made. The radiative optical potential accounts for significant damping of high-n resonances. Configuration interaction between resonances, which is automatically incorporated in the R-matrix method but usually omitted in the implementation of distorted-wave techniques, was found to increase the resonance contributions considerably. Our radiative-damped R-matrix cross sections show fairly good agreement with the resonance profile obtained from electron beam ion trap measurements [S. Chantrenne et al., Phys. Rev. Lett. 69, 265 (1992)]. This system demonstrates the necessity for simultaneously including radiative-damping and interfering-resonance effects within electron–highly charged ion scattering calculations.

In near-symmetric charge transfer at high-impact velocities and forward-scattering angles, the internuclear-scattering component of the second-order Faddeev representation of the generalized Thomas mechanisms, which, though generally associated with large-angle scattering, is valid at forward angles also, has been shown previously to agree with both the eikonal treatment in a continuum distorted-wave theory and the experimental data. A comparison of the multiple-scattering and eikonal methods using the same electronic amplitude is made in this paper. Significant differences are found between the results of the two methods, especially in the region where there is substantial cancellation among the partial amplitudes. At high velocities the Faddeev amplitude is a factor of 2 larger than the eikonal amplitude, a result attributable to the inclusion of two generalized Thomas channels in the former. The leading asymptotic form of the amplitude is also given.

The wave function for the collision of a proton with a hydrogen atom is obtained by direct solution of the time-dependent Schrödinger equation in a model two-dimensional Cartesian space using lattice techniques. The dimensional reduction from the full three-dimensional (3D) space allows the consideration of huge collision ‘‘volumes’’ with minimal computational expense, while still preserving the idea of an impact parameter. The probabilities for charge exchange and ionization are estimated for different projectile energies ranging from 10 to 100 keV/amu. Comparisons with full 3D calculations in smaller collision volumes show that the time-dependent behavior of the probability densities is quite similar for the 2D soft-core model interaction chosen here. The ionization dynamics are further analyzed in regard to the fate of that fraction of the probability density located near the saddle point between projectile and target potentials.

One of the problems associated with close-coupling calculations of electron-impact excitation is the occurrence of nonphysical pseudoresonances. These often arise from the (N+1)-electron bound states that are routinely kept within the close-coupling expansion. Within the R-matrix formalism, we describe a transformation and reduction of the bound portion of the (N+1)-electron basis to eliminate a class of pseudoresonances associated with approximate target wave functions. In order to explain the procedure and demonstrate its effectiveness, we include a variety of examples to show how this method is capable of eliminating those resonances not attached to one of the N-electron states included within the close-coupling expansion of the target.

The Kα and Kβ x ray spectra of zirconium, molybdenum, palladium, and praseodymium bombarded by 28-, 40-, 65-, and 100-MeV ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$ ions were measured with a high-resolution transmission curved crystal spectrometer. The Kα${\mathit{L}}^1$ and Kβ${\mathit{L}}^1$ satellite lines were observed and resolved from the parent diagram lines. The deduced satellite energy shifts are very well reproduced by multiconfiguration Dirac-Fock calculations. The experimental average L-shell ionization probabilities for nearly central collisions were obtained from the measured relative yields of the satellites. They are compared with theoretical predictions from the semiclassical independent particle approximation using hydrogenic wavefunctions (SCA-HWF) or Dirac-Hartree-Fock wave functions (SCA-DHF) and with n-body classical trajectory Monte Carlo (CTMC) calculations. A satisfactory agreement is obtained between the experimental probabilities and the SCA-DHF predictions. The variation of the probabilities in function of the projectile reduced velocity is also well reproduced by CTMC calculations although the predictions are in general smaller than the values deduced from our experiment. The same holds for the SCA-HWF calculations for which, in addition, an increasing discrepancy with the projectile reduced velocity is observed.

Electron capture from hydrogen molecules by protons is treated using the second-order Born approximation. Differential cross sections in an adiabatic-nuclei approximation for specific molecular orientations and for an equally weighted averaging over all orientations are presented for incident energies of 2.5 and 10 MeV. A Hartree-Fock molecular wave function and linearized-propagator approximation are employed to evaluate the amplitude. An approximate factoring of the amplitude into double scattering and diffraction (arising from the two target nuclei) components is shown to give a poor description of high-velocity molecular capture.

This paper presents an analysis of the energy distribution of the outgoing electrons in the double ionization of helium by photons with energies much larger than the ionization potential. The analysis improves on the one carried out by Amusia et al. [J. Phys. B 8, 1248 (1975)] in the framework of the special model for the wave function of helium. Now the energy distribution is expressed through certain expectation values averaged over the initial state described by the wave function of the general form Ψ(${\mathit{r}}_1$,${\mathit{r}}_2$). A larger interval of values of photon energies is considered. The limit equations for the angular distribution are obtained. The general features of the process with heavier atoms are also analyzed.

We develop an extension of a class of degenerate Gel’fand-Levitan and Marchenko equations previously used in the theory of isospectral Hamiltonians and in the theory of continuum bound states. The formalism allows the generation of new exactly solvable Schrödinger equations, whose potentials extend the class of Bargmann potentials. The scattering theory is developed using the Jost solutions of the new Schrödinger equations, leading to exact expressions for the Jost function and the scattering phase shifts. The theory is illustrated by a simple example.

We study the s-wave scattering produced by perturbing a family of potentials that support a single bound s state with energy embedded in the continuous spectrum. Such bound states were first studied by von Neumann and Wigner [Z. Phys. 20, 465 (1929)], and we refer to the class of potentials that we perturb as von Neumann–Wigner potentials. We solve the radial Schrödinger equation exactly for von Neumann–Wigner potentials which have been perturbed by a radial displacement. We analyze the Jost function and its zeros, including how the latter moves as the perturbation is changed. Depending on the amount of the displacement, the perturbation may produce a sharp resonance at an energy shifted from that of the unperturbed continuum bound state, a virtual state, or a conventional bound state with negative energy. In all cases, no physically acceptable solution of the perturbed Schrödinger equation has the energy of the unperturbed continuum bound state, and the scattering phase shift that is defined from the Jost function has a discontinuity of magnitude π at that energy. The continuum bound state is recovered in the limit as the perturbation goes to zero, but the limit is nonuniform, and we demonstrate a number of anomalies resulting from this.

The angular distribution of Auger electrons produced in the collision of 1634-eV electrons with ${\mathrm{N}}_2$ is reported. The angular distributions are measured relative to the internuclear axis of the molecule from 0° to 90° in 6° steps. When an Auger transition occurs to an unstable doubly ionized state the molecular ion dissociates into two ${\mathrm{N}}^{+}$ fragments. Because the time required for dissociation of the ${\mathrm{N}}_2^{2+}$ ion is much less than that for rotation of the ion, the axial recoil approximation holds to first order, and detecting one of the ${\mathrm{N}}^{+}$ ions determines the orientation of the target molecule at the time of the projectile-molecule collision. Therefore, a coincidence experiment between the Auger electrons of appropriate energy and the ${\mathrm{N}}^{+}$ fragments is devised. The rotation of the ${\mathrm{N}}_2^{2+}$ ions during the course of the dissociation process has been taken into account as a second-order approximation. As a result of this rotational effect, the predicted angular distribution function is smeared out by an amount depending on the different ${\mathrm{N}}_2^{2+}$ final states. The data are analyzed in terms of a two-center model in which prolate spheroidal coordinates are used.

Procedures for calculating the angular distribution of Auger electrons emitted by homonuclear diatomic molecules are presented. The calculation is performed in prolate spheroidal coordinates. A two-center effective potential is introduced to simplify the Schrödinger equation for an electron moving under the influence of the nuclei and other electrons. The effective potential is expressed by having equal fixed effective charges on each nucleus. The wave functions for the bound-state molecular orbitals and those for the Auger electron are obtained by solving the Schrödinger equation in which the appropriate experimental energies are used as the eigenvalues. The transition moments and the angular distribution of the Auger electron in the molecular frame are obtained by numerical integrations. For a specific Auger transition process, the distribution function is expressed in terms of the absolute square of a coherent sum of prolate spheroidal functions. In order to compare the predicted distribution function to our experimental results, corrections due to the rotation of the molecular ions during the course of dissociation are made.

We calculate the electronic stopping cross section of protons in solids using the linear-response dielectric theory, the semiclassical approximation, and the local-electron-density approximation. By introducing a local-field correction function in the dielectric function, the correlation and exchange interaction of the electron gas in solids has been taken into consideration. The calculation results are compared with experimental data, empirical results, and other previous theoretical results.

The electron emission yield induced by mega-electron-volt ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{2+}$, ${\mathrm{Li}}^{3+}$, ${\mathrm{B}}^{5+}$, and ${\mathrm{C}}^{6+}$ impact on aluminum, copper, and gold targets was measured. We found a significant deviation of the results from a simple proportionality to the stopping power, especially for heavier ions and low projectile velocities. Using a slightly modified model by J. E. Borovsky and D. M. Suszcynsky [Phys. Rev. A 43, 1433 (1991)] our experiments could be well represented. In this model the collective electric field generated along the projectile’s path was taken into account. Consequently, the positive ion channel appears to be the dominant mechanism that leads beyond a projectile-independent yield–to–stopping power ratio.

We study up to the sixth order of Bragg deflection of metastable neon atoms from a standing light wave, corresponding to a momentum transfer of 12ħk. We derive an analytical result for the scattering probability, suitable for arbitrarily high Bragg order, and demonstrate its agreement with experimental results. We investigate the effect of velocity distribution on the Bragg process and show that overlapping diffraction orders can be resolved in velocity space. The prospect of using Bragg scattering as the optics in a Mach-Zehnder style atom interferometer with large splitting is discussed.