A direct solution of the Schrödinger equation for the 2 ${}_{}{}^1{}_{}{}^{}$S, 3 ${}_{}{}^1{}_{}{}^{}$S, 4 ${}_{}{}^1{}_{}{}^{}$S, and 5 ${}_{}{}^1{}_{}{}^{}$S states of the helium atom is obtained with the correlation-function hyperspherical-harmonic (CFHH) method. Given the proper correlation function chosen from physical considerations, the method generates wave functions accurate in the whole range of interparticle distances that lead, in turn, to precise estimates of the expectation values of the Hamiltonian and of different functions of interparticle distances. Our results show that even with the simplest correlation function, the accuracy of the CFHH method (which contains no adjustable parameters) for excited states is comparable to that of the ground state. The accuracy is also comparable to that of the most sophisticated variational calculations involving hundreds of variational parameters.

We present a calculation of the fourth-order gradient corrections to the noninteracting kinetic energy of a relativistic system of electrons and positrons. The basis of the calculation is a recently published algorithm for the generation of the gradient expansion of the Green’s function of a field-theoretical system characterized by a Lagrangian with an effective external potential.

The generalized Newton variational method is applied to the static-exchange approximation of the electron–hydrogen-atom scattering. Slater-type basis functions are employed to expand the amplitude density. Spurious singularities are encountered in both scattering processes. The width of the unphysical singularities is broader in the case of singlet scattering. Anomalous poles appear in narrow regions of the scale parameter and are in evident correlation with the zeros of the determinant of the free-particle Green’s operator. As a by-product, simple least-squares extension of the generalized Newton variational method is developed in order to avoid spurious singularities and to recognize whether or not the convergence is of secondary nature.

A coupled-channel optical method for electron-atom scattering is applied to electron-sodium scattering at energies of 10, 20, 22.1, 40, 54.4, and 100 eV. The 3 ${}_{}{}^2{}_{}{}^{}$S, 3 ${}_{}{}^2{}_{}{}^{}$P, and 3 ${}_{}{}^2{}_{}{}^{}$D channels are coupled explictly whereas the rest of the one-electron excited states of the atom are taken into account via the ab initio complex nonlocal polarization potential. The 3 ${}_{}{}^2{}_{}{}^{}$S–3 ${}_{}{}^2{}_{}{}^{}$S and 3 ${}_{}{}^2{}_{}{}^{}$S–3 ${}_{}{}^2{}_{}{}^{}$P differential cross sections are found to be in good agreement with recent experiments of Lorentz and Miller (unpublished). The effect of the polarization potential does not change the qualitative results of a standard coupled-channel calculation, but improves agreement with the experiment. Integrated and total cross sections are also presented.

Relative dielectronic-recombination cross sections for hydrogenlike argon are presented. The contributions of the KLL, KLM, KLN, KLO, and KLP groups of resonances are compared to theoretical calculations. The experimental method consists of the formation and interaction of ions with electrons in an ion trap followed by an analysis of the extracted ions to determine relative yields. Comparison with theory shows that the total cross sections agree within ±6%.

The multiconfiguration relativistic random-phase-approximation theory is applied to autoionizing levels of the neutral zinc atom between 4${\mathit{s}}_{1/2}$ and 4${\mathit{p}}_{3/2}$ ionization thresholds. There are five Rydberg series of doubly excited states that manifest themselves as autoionization resonances in the 4s photoionization cross section. Theoretical predictions for the positions and profiles of the autoionization resonances are in excellent agreement with experiment.

The polarization fraction P of the radiation emitted in the transitions 2 ${}_{}{}^1{}_{}{}^{}$P–1 ${}_{}{}^1{}_{}{}^{}$S of He-like ions and 2p-1s of H-like ones is studied theoretically. The calculation is made with the use of a distorted-wave method. The resulting P is found to be almost independent of nuclear charge, when expressed as a function of electron energy in threshold units and compared along an isoelectronic sequence. The degree of polarization approaches a threshold value very different from that of neutral atoms, due to the long-range Coulomb interaction.

L-shell x-ray production cross sections for L${\mathrm{\alpha }}_{1,2}$, L${\gamma }_1$, and L${\gamma }_{2,3,\left(6\right)\mathrm{}}$ have been measured for ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$, and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ on Yb and Au. The energy ranges for the incident ion species were 0.5–3.0 MeV/μ for Li, Be, C, and F, and 0.5–2.6 MeV/μ for N and Si. Comparisons of the L${\mathrm{\alpha }}_{1,2}$ and L${\gamma }_{2,3,\left(6\right)\mathrm{}}$ x-ray production-cross-section data have been made to the prediction of plane-wave Born-approximation theory and perturbed-stationary-state theory with energy-loss, Coulomb deflection, and relativistic corrections (ECPSSR). The comparison shows that for the L${\gamma }_{2,3,\left(6\right)\mathrm{}}$ x-ray production cross sections there are problems associated with the ECPSSR theory.

Z-dependent perturbation theory and the complex rotation method are utilized to calculate the resonance position and width for the 2s2p ${}_{}{}^{1,3}{}_{}{}^{}$P autoionizing states of two-electron atoms to high order. Use of the complex rotation method in Z-dependent perturbation theory simultaneously yields values of both the resonance position and width for all members of an isoelectronic sequence. It also simplifies the calculation by making the wave function of the resonance wave function square integrable while simultaneously rotating the interacting continuum away from the real energy axis, thereby eliminating any complications introduced by the presence of a degeneracy in zero order between the doubly excited states and the adjacent continuum. Knowledge of the exact second-order widths is used to increase the efficiency of the complex stabilization method. As the accuracy of the real and imaginary parts of the complex energy are generally related, the exact values of the second-order widths are also helpful in ascertaining the accuracy of the second-order results, and therefore the reliability of the total resonance position and widths. We believe the present values to be the most accurate results to date for Z≥3 for the singlet and Z≥2 for the triplet.

We report measurements of energy distributions of electrons emitted during interactions 10q-keV ${\mathrm{N}}^{6+}$, and ${\mathrm{Ar}}^{\mathit{q}+}$ (q=7,8,9) ions with Au(110) and Cu(001) surfaces at grazing angles. The electron energy distributions have been measured as a function of angle of incidence, observation angle, and target-crystal azimuth. For both Au and Cu targets, the projectile KLL Auger peak observed for the case of the ${\mathrm{N}}^{6+}$ projectiles is seen to consist of two components whose intensities have strikingly different dependences on incident perpendicular velocity. The main component of the KLL peak is attributed to subsurface electron emission and is modeled using a Monte Carlo simulation of the projectile trajectories in the bulk. The second component, observed only for the smallest incident perpendicular velocities, is attributed to above-surface KLL Auger electron emission and is modeled using computer simulations of the resonance neutralization-autoionization cascade that occurs prior to projectile penetration of the surface. In the case of the Au target, NNV and NVV transitions, attributed to vacancy transfer from the projectile K shell to the N shell of Au, are also observed. The Monte Carlo simulation of the subsurface contribution to the electron emission is able to reproduce the observed angle-of-incidence dependence of both the projectile and the target Auger electron intensities. In addition, it shows reasonable agreement with the observed dependences of the projectile KLL intensity on observation angle and crystal azimuth.

The screening effect in the projectile (target) ionization probability caused by the electrons that are attached to the target (projectile) during a collision process is studied using the time-dependent semiclassical approximation. The equivalence of the proposed approach with the plane-wave Born approximation is demonstrated and a simple procedure is suggested to obtain the impact-parameter-dependent ionization probabilities, when the screening is present, from calculations that do not take this effect into account.

Double-electron-excitation processes of He atoms by proton, antiproton, and ${\mathrm{C}}^{6+}$-ion impact have been theoretically investigated using the second-order Born approximation and the close-coupling method in the energy regime of MeV/u. The semiclassical impact-parameter method with a straight-line-trajectory approximation is employed to describe the collision processes. Hyperspherical wave functions are adopted to take full account of the strongly correlated motion of two atomic electrons in He. For proton and antiproton impact, it is found that the first-order mechanism dominates for excitation to the (2s2p) ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ excited state, while the second-order processes play a significant role in excitation to the (2s2s) ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}^{\mathit{e}}$, (2p2p${)}^1$${\mathit{S}}^{\mathit{e}}$, and (2p2p) ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{e}}$ excited states at a few MeV/u. It should be noted that the doubly excited (2s2p) ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ state plays an important role as an intermediate state in these second-order processes in addition to the singly excited 1s2p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ state. It is also found that the difference for the double-electron-excitation processes by proton impact and by antiproton impact is much smaller than that for the double-ionization processes in this energy range. For the ${\mathrm{C}}^{6+}$-ion impact, higher-order mechanisms play more important roles at a few MeV/u. The excitation mechanism is also discussed based on the classification scheme of the correlation quantum numbers, which enables us to obtain a more direct physical insight into the collision mechanism.

A theoretical study of electron emissions resulting from ionzation of light hydrogenlike projectiles in ion (atom)-atom collisions with heavy targets is presented with emphasis on backward observation angles. Angular and energy distributions of the ejected electrons have been calculated with various approximation methods, which agree with or can be traced to the impulse approximation with the exact off-energy-shell transition amplitudes. Comparisons with experimental data have been made for collisions of ${\mathrm{H}}^0$ and ${\mathrm{He}}^{+}$ with Ar. We find good agreement for both the electron angular distributions and the angular variation of the peak position. Our results show that electron loss at backward angles is dominated by elastic scattering of the projectile electron in the strong field of the heavy target. A reliable representation of the potential and a high-order theory for scattering at this potential are required to describe the experiment accurately.

K-shell x-ray production cross sections are reported for incident ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ions for elements with K-shell binding energies between 277 eV (C) and 1487 eV (Al). The data are compared with the first-order Born approximation (plane-wave Born approximation for direct ionization and Oppenheimer-Brinkman-Kramer approximation for electron capture) and to the energy loss and Coulomb deflection effects, perturbed stationary-state approximation with relativistic correction (ECPSSR) theory. The energy of the helium ions ranged from 0.5 to 6.0 MeV for ${\mathrm{He}}^{+}$ and 6.5 to 8.0 MeV for ${\mathrm{He}}^{2+}$. The targets used in these measurements were ${}_6{}^{}{}_{}{}^{}\mathrm{C}$,${\mathrm{}}_8$O, ${}_9{}^{}{}_{}{}^{}\mathrm{F}$, ${}_{11}{}^{}{}_{}{}^{}\mathrm{Na}$, ${}_{12}{}^{}{}_{}{}^{}\mathrm{Mg}$, and ${}_{13}{}^{}{}_{}{}^{}\mathrm{Al}$. Except for a systematic overprediction of the data at the lower projectile velocities, the ECPSSR theory is found to fit the data. The first-order Born theory is found to fit the data at higher energy, but greatly overpredicts the data at low energy.

The vibrational excitation mechanism has been included in the algebraic-eikonal approach to the electron–polar-molecule collision process. A dipole operator that can induce vibrational transitions has been used, and a technique for the evaluation of the matrix elements required for the calculation of the scattering amplitude in the Glauber approximation has been developed. In addition to the long-range dipole interaction, the quadrupole interaction has been included in the same framework in order to improve the potential description of the collision process. Numerical calculations are shown for electron-induced rotational-vibrational excitation through the dipole and dipole-plus-quadrupole interactions.

Collisions are treated by a method that has been very successful in calculating atomic spectra. Results of electron collisions with ${\mathrm{Be}}^{+}$, ${\mathrm{Mg}}^{+}$, and ${\mathrm{Ca}}^{+}$ are presented, showing extensive series of double excitation resonances of the collision complex. Convergence of the results to the limit of peripheral collisions, where the Born approximation holds, is displayed. Cross sections of optically allowed and forbidden excitations are evaluated, including cascade effects and distributions in the scattering angle. The polarization of emissions from the excited target is calculated successfully.

The transition amplitude for the inelastic scattering of a photon from a system of bound charged particles, with a single charge ejected, behaves at low-energy end of the scattered-photon spectrum as the inverse of the energy and is proportional to the on-shell matrix element corresponding to the process in which the soft photon is absent. The next term in the expansion in powers of the energy of the soft photon is derived here, and is expressed in terms of the same single-photon absorption amplitude. The correction takes the form of first-order momentum shifts in the arguments of the absorption amplitude; they enter in such a way as to leave this amplitude on the energy shell. This result is precisely what would be expected by analogy with Low’s theorem [Phys. Rev. 110, 974 (1958)] on spontaneous bremsstrahlung. A nonrelativistic version of the theorem on bound-state Compton scattering is obtained through an asymptotic analysis of the configuration-space matrix element for this process, with the effect of a long-range Coulomb tail accounted for. Relativistic versions are derived as well, appropriate to particles of zero spin, and with spin effects included, based on the same type of gauge-invariance argument employed by Low. Analogous results are obtained from an external-field formulation in the weak-field limit.

In 89-MeV ${\mathrm{Sc}}^{8+}$+He collisions, the light target atom He was used to ionize selectively the 2p shell of the scandium projectile. The subsequent L-shell Auger emission from Mg-like ${\mathrm{Sc}}^{9+}$ was measured with high resolution using the method of zero-degree Auger spectroscopy. The spectra are dominated by three peak groups that are attributed to transitions from the various initial states belonging to the configuration 1${\mathit{s}}^2$2${\mathit{s}}^2$2${\mathit{p}}^5$3${\mathit{s}}^2$3p to the final states 1${\mathit{s}}^2$2${\mathit{s}}^2$2${\mathit{p}}^6$3s ${}_{}{}^2{}_{}{}^{}$S, 1${\mathit{s}}^2$2${\mathit{s}}^2$2${\mathit{p}}^6$3p ${}_{}{}^2{}_{}{}^{}$P, and 1${\mathit{s}}^2$2${\mathit{s}}^2$2${\mathit{p}}^6$3d ${}_{}{}^2{}_{}{}^{}$D. The ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2\mathrm{-}}^2$${\mathit{P}}_{3/2}$ fine-structure splitting was resolved for the final configuration 1${\mathit{s}}^2$2${\mathit{s}}^2$2${\mathit{p}}^6$3p. The branching ratio for the transition to 1${\mathit{s}}^2$2${\mathit{s}}^2$2${\mathit{p}}^6$3d ${}_{}{}^2{}_{}{}^{}$D, which involves three electrons and, thus, must be ascribed to correlation, is compared to earlier results for the isoelectronic ions ${\mathrm{Al}}^{+}$ and ${\mathrm{Ar}}^{6+}$. Good agreement between observed and calculated branching ratios to the three final states is obtained by including only correlation in the initial state. A discrepancy for the branching to the 1${\mathit{s}}^2$2${\mathit{s}}^2$2${\mathit{p}}^6$3d ${}_{}{}^2{}_{}{}^{}$D term, which was observed already in the earlier investigation of ${\mathrm{Ar}}^{6+}$, has been removed by including correlation in the n=2 shell in addition to the correlation in the n=3 shell, which was the only correlation introduced previously.

The electron-capture process by protons impinging on different targets is calculated using the exact eikonal impulse approximation. Total cross sections are reported for a large variety of systems ranging from asymmetric systems (p-Ar) to a symmetric one (p-H). Alignment parameters for p-H and p-He processes are presented and compared with the experiments and other theoretical results. We conclude that the eikonal impulse approximation can be used with confidence to treat asymmetric collisions within the intermediate-high-energy range, and symmetric collisions for high-impact energy.

A pseudochannel extension of the coupled-reaction-channel (CRC) method is investigated formally and numerically as a means of simulating the effect of the breakup channel on the rearrangement amplitudes. The equations of the pseudostate-augmented CRC method are derived within a two-Hilbert-space approach. The connection of the effective CRC transition operators with the postform transition operators of the formal scattering theory is established. Alternative formulations of the method corresponding to different ways of treating the nonorthogonality interaction are given. Convergence with respect to the number and nature of the pseudostates are investigated numerically on a solvable three-particle model. It is observed that the results obtained with six distinct sets of pseudochannels that have considerably different threshold energies converge toward the exact ones.