A detailed study of the bound-state properties of the Hulthén potential is presented. Accurate eigenenergies are obtained for the Hulthén potential by numerical integration of the Schrödinger equation. One-parameter variational calculations are carried out. The variational results are practically identical to the exact energies, except in the high-screening region. The critical screening parameter is calculated for various values of l for n≤10 by a numerical solution of the wave equation. The energy eigenvalues obtained by a variety of methods are compared and discussed. The variational wave functions are employed to calculate absorption oscillator strengths for 1s→2p, 1s→3p, and 2p→3d transitions.

We have calculated the total energy of 3d, 4d, and 5d transition elements by a local-spin-density approximation with a ‘‘fully relativistic’’ treatment for core levels and a ‘‘scalar-relativistic’’ approximation for valence levels. This work improves the agreement of the previous nonrelativistic calculation on s→d promotion energy with experiment. A table for the energy difference between spin-restricted and spin-polarized 3d, 4d, and 5d atoms is provided that is useful for obtaining the cohesive energy of solids.

Using an asymptotic expansion and the hyperspherical adiabatic approximation, we obtain a representation of the Scrhödinger equation for the helium atom and its isoelectronic ions for large values of the hyper-radius. We solve the lowest-order equation for the channel wave functions with boundary conditions imposed by exchange symmetry. Diagonalization of the potential matrix, keeping only terms through second order in the symmetrized basis set, gives potential curves that show avoided crossings essential for the interpretation of atomic dynamics.

A method is developed that gives compact closed analytical formulas for the evaluation of pseudopotential matrix elements in the full Gaussian case. It has the advantage of working with normalized spherical harmonics of any angular momentum and is based upon the Löwdin α-function decomposition technique. It leads to final formulas that make use only of the well-known Dawson function and of its integral.

The applicability of multireference many-body perturbation theory is considered by numerically investigating the practical convergence properties of a common variant. Perturbation energies through 20th order are reported for ${\mathrm{BeH}}_2$ at geometries near the Be→${\mathrm{H}}_2$ symmetric-insertion transition state and for BH in its equilibrium region. The recursive perturbation-theory equations are solved using a computationally intensive, but conceptually simple, configuration-based algorithm. In the study of diverse regions of molecular potential-energy surfaces, the difficulties involved in selecting appropriate zeroth-order models, which consist of the choice of reference functions, orbitals, and zeroth-order Hamiltonian, are addressed. We also consider convergence-acceleration techniques such as series resummation using Padé approximants.

We consider how externally coupled (e.g., dc-field-coupled) autoionizing states can be useful in producing gain without population inversion. The dc fields produce new absorption minima that enable one to obtain laser action in different frequency regions depending on the strength of the coupling. We calculate absorption and emission profiles assuming that one of the autoionizing states is incoherently pumped as in most conventional laser models. We present numerical results that demonstrate gain regions without population inversion.

We consider laser action on a transition involving an autoionizing state ‖a〉 and an initially unpopulated state ‖f〉, the population of which builds up because of spontaneous emission and Raman processes. The autoionizing state is pumped by a coherent field. We discuss the transient amplification of the probe field on the lasing transition for a range of parameters. The coherent field on the pumping transition leads to minima in the absorption spectra if the atomic population were in the state ‖f〉. Such regions of minima can be used for obtaining gain even for long times.

Static-exchange, plus correlation-polarization-potential calculations are performed for elastic low-energy electron scattering from Sr atoms while paying attention to the low-lying shape resonances. The correlation potential is calculated both with and without a scaling factor. A ${}_{}{}^2{}_{}{}^{}$D-shape resonance is produced at 1.0 eV with a parameter-free, and at 1.25 eV with a scaled, correlation potential. No ${}_{}{}^2{}_{}{}^{}$P-shape resonances are predicted, but evidence to support the existence of a stable negative ion ${\mathrm{Sr}}^{\mathrm{-}}$ in the 5${\mathit{s}}^2$5p electron configuration is given from the viewpoint of electron scattering. The bound energy of the extra electron in the negative ion is estimated by transforming the phase shift of the corresponding partial wave into the polarization quantum-defect number and extrapolating the number from positive to negative energies.

First-order many-body theory was modified to include correlation effects in the target description and used to calculate differential cross sections, coherence, and correlation parameters for the electron-impact excitation of the 3${\mathrm{}}^1$P and 3${\mathrm{}}^3$P states of magnesium at incident energies of 20, 30, 40, 50, and 100 eV. The results are analyzed and compared with available theoretical and experimental results.

The L-shell ionization cross sections of Si, P, S, Cl, and Ar have been obtained for incident ${\mathrm{He}}^{+}$ ion energies 0.4–2.1 MeV in steps of 0.2 MeV. The cross sections were obtained from the Auger electron yields measured for ${\mathrm{SiH}}_4$, ${\mathrm{PH}}_3$, ${\mathrm{H}}_2$S, ${\mathrm{CH}}_3$Cl, and Ar gaseous targets. The present experimental L-shell ionization cross sections are compared to existing experimental L-shell ionization cross sections as well as to previous theoretical predictions.

Direct and resonance excitation rate coefficients have been calculated for transitions between states with principal quantum number n=3 in Ne-like selenium. A relativistic distorted-wave method was used to compute the direct excitation rate coefficients and the resonance excitation rate coefficients were obtained using a multiconfiguration Dirac-Fock method. The effect of autoionizing resonances has been found to be significant for most transitions, especially at low temperatures. The resonances enhance the rate coefficients for some electric-dipole-allowed transitions by as much as a factor of 2. For strongly forbidden transitions, resonances can increase the rate coefficients by more than an order of magnitude.

The electron emission spectra observed following collisions of heavy ions with heavy atoms is often dominated by electrons with a continuous range of energies. The impact-parameter dependence for the emission of these electrons from Kr-Kr and Kr-Xe collisions has been measured for collision energies from 0.1 to 3.2 MeV and for scattering angles from 3° to 10° by measuring the emitted electrons in coincidence with the scattered ions. These data indicate that most of the ionization (often 20 to 25 electrons from the collision system) resulting from these heavy-ion–atom collisions occurs during the collision on a time scale of ${10}^{\mathrm{-}16}$–${10}^{\mathrm{-}17}$ sec, as opposed to Auger decay in the separated atoms following the collision. For each combination thresholds were observed for electron production as a function of the collision’s distance of closest approach. These excitation thresholds agree well with promoted molecular orbitals calculated within the framework of the Fano-Lichten model and indicate that this model is useful beyond its expected range of applicability.

Double-excitation cross sections of helium atoms by bare heavy-ion projectiles at high energies are calculated within the one-center atomic-orbital expansion method including the electron-electron interaction between correlated helium wave functions. The resulting excitation cross sections to 2${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}^{\mathit{e}}$, 2${\mathit{p}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{e}}$, 2s2p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$, and 2${\mathit{p}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}^{\mathit{e}}$ states are analyzed. We conclude that double excitations at high energies by low-${\mathit{Z}}_{\mathit{p}}$ projectiles are dominated by a first-order process in which the two-electron transition proceeds through one electron-projectile interaction in conjunction with shakeup or rearrangement due to electron-electron interactions. For high-${\mathit{Z}}_{\mathit{p}}$ projectiles at a given velocity, on the other hand, the excitation is dominated by a second-order process in which the transition proceeds through two successive electron-projectile interactions.

A formulation of collision theory is presented to analyze the process by which ${\mathrm{H}}^{\mathrm{-}}$ and ${\mathrm{H}}^{+}$ ions are produced from charge exchange in H(1s)+H(1s) and H(2s)+H(1s) collisions in the energy range of 100 eV to 100 keV. A simple closure approximation to the full Green’s function allows an analytic evaluation of the amplitudes. The anomalously large cross sections observed experimentally around 0.5 keV, one maximum near 10–20 keV, and the interference feature around 2–4 keV are reproduced, respectively, in the theory by the excitation-exchange amplitude, the direct amplitude, and their interference. The same theoretical procedure is employed in the treatment of both the 1s and 2s initial projectile states, providing a unified picture of the H+H collision system at low and intermediate energies.

In this work the muon transfer process A+μB→Aμ+B is treated in a similar way to that used in chemical reactions. Two processes were considered: the exothermic reaction d+pμ→dμ+p and the thermoneutral reaction d+dμ→dμ+d, where the two deuterons are treated as distinguishable particles. Energy-dependent (0.5≤E≤10 eV) reaction probabilities and integral cross sections were calculated by solving the three-body Schrödinger equation using the mass-scaled Jacobi coordinates (R,r) and the orientation angle γ. After the γ eigenvalue problem is solved at fixed (R,r), the scattering matrix is calculated. It is shown that the contribution of closed vibrational states (so-called ‘‘nonadiabatic’’ corrections) changes the behavior of the muon transfer cross section.

Absolute state-selective electron-capture cross sections for charge transfer into the 3l state of ${\mathrm{C}}^{3+}$ in collisions of ${\mathrm{C}}^{4+}$ on H and ${\mathrm{H}}_2$ have been measured in the impact energy range of 0.05–1.33 keV/amu. The low-energy beams have been produced by retarding a 1.33-keV/amu ${\mathrm{C}}^{4+}$ beam (16 keV) by means of a five-element electrostatic lens system. The experimental results are compared with calculations based on molecular and atomic basis-set expansions. It turns out that especially for energies below 200 eV/amu there are considerable differences between experiment and theory both in relative and absolute 3l state-selective cross sections.

Total cross sections for charge transfer and electron detachment for collisions of ${\mathrm{H}}^{\mathrm{-}}$ and ${\mathrm{D}}^{\mathrm{-}}$ with atomic hydrogen have been separately determined for collision energies that range from a few electron volts up to several hundred electron volts. The experiments are performed with an apparatus that utilizes a crossed-beam configuration with a radio-frequency discharge as the source of atomic hydrogen. The experimental results are compared with several calculations and with other measurements that overlap the present results at the highest collision energies.

The energy distribution of binary-encounter electrons (BEE) produced in collisions of 1–2 MeV/amu ${\mathrm{H}}^{+}$ and bare C, N, O, and F ions with ${\mathrm{H}}_2$ and He gas targets is reported at 0° with respect to the beam direction. These electrons result from ionization of the target due to hard collisions with the projectile and can thus be considered to be produced in a process analogous to elastic scattering of a free electron from a highly charged ion. An impulse-approximation (IA) model has been developed to describe this process in which ‘‘quasifree’’ target electrons undergo 180° Rutherford scattering in the projectile frame. The measured BEE double-differential production cross sections for bare ions were well described by this model and were found to scale with ${\mathit{Z}}_{\mathit{p}}^2$ and ${\mathit{E}}_{\mathit{p}}^{\mathrm{-}(\mathrm{\sim }2.6–2.7)}$ where ${\mathit{Z}}_{\mathit{p}}$ and ${\mathit{E}}_{\mathit{p}}$ are the charge and energy of the projectile, respectively. An energy shift of the BEE below 4t, where t is the cusp electron energy, is observed and is also predicted by the IA treatment. A plane-wave Born approximation (PWBA) calculation for BEE production is also found to be in overall agreement with our data. However, the energy shift of the BEE peak could not be fully accounted for within this PWBA calculation.

Results are reported of a translational energy spectrometric study of state-selected electron-capture reactions between metastable ${\mathrm{CO}}^{2+}$ ions and ${\mathrm{H}}_2$, He, ${\mathrm{O}}_2$, and Kr. The experimental data are interpreted within the framework of recent ab initio calculations of the potential-energy curves of low-lying electronic states of ${\mathrm{CO}}^{2+}$. Electron capture is found to occur predominantly into moderately exoergic channels corresponding to avoided crossings of seams of potential-energy surfaces in the range of internuclear separations between 3 and 5 a.u. Some evidence is found that the ${\mathrm{CO}}^{2+}$ projectile beam may comprise not only the ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ ground electronic state but may also possess a not-insignificant long-lived excited-state ${(}^3$Π) component.

Charge-state distributions of slow recoil ions produced in the single-electron-capture reaction ${\mathrm{H}}^{+}$+Ar→H+${\mathrm{Ar}}^{\mathit{q}+}$ have been measured in the energy range 800–3500 keV to supplement and confirm previous measurements in the energy range 500–1750 keV. The observed singly charged recoil ions, ${\mathrm{Ar}}^{+}$, originate almost exclusively from capture in the M shell. The M-shell-capture cross section deduced from the measured fractions of ${\mathrm{Ar}}^{+}$ ions and well-established total-capture cross sections taken from the literature exhibits a pronounced structure. It is suggested that this structure is due to one or two radial nodes of the wave functions that describe the M shell.