The stimulated radiative corrections (or ac-Stark shift, or light shift...) of the energy levels of a hydrogenic atom irradiated by an intense, nonresonant, monomode laser field, are evaluated within the framework of the time-dependent perturbation theory, up to and including fourth order. The calculation is performed by using a Sturmian representation of the Coulomb Green's function. Whenever it is possible, comparison is made with other results, and several limiting cases are considered. If the laser frequency $\omega \to 0$, one recovers the results of the dc-Stark effect. If $2\omega$ becomes larger than the ionization energy of the atomic state considered, the fourth-order level shift acquires an imaginary part which may be connected, via an extension of the optical theorem, to the two-photon ionization cross section. We point out also the difficulties encountered, when trying to get sensible estimates from partial summation of the infinite sums entering the perturbative expression of the fourth-order amplitudes. Finally, the order of magnitude of these various corrections is discussed.

The effect of pump fluctuations on various coherent processes that arise in three-level systems interacting with two external fields is examined. Such coherent processes include the forward Hanle effect and various four-wave mixing effects such as the generation of phase-conjugate signals. A general formulation that enables one to calculate the influence of laser linewidth on the coherent signals produced in various directions is presented. Ensemble averages, over laser temporal fluctuations, of various physical quantities, such as atomic polarization, are calculated. The spectrum of polarization fluctuations is shown to consist of several new features which lead to coherent radiation in different directions depending on the resonant frequencies in the polarization fluctuations. The influence of pump linewidth on pressure-induced extra resonance (PIER) is treated in detail. The possibility of producing a laser-fluctuation-induced coherent signal at one of the atomic frequencies is examined. This new signal, which is produced in a direction different from that of the PIER signal, but has the same type of resonant character as PIER, is found to have significantly different pressure dependence than the PIER signal. The results of our numerical computations are qualitatively explained in terms of the convolutions of products of third-order susceptibilities and pump field-correlation functions.

A method for determining complementary energy functionals within a density-functional framework is derived. In particular, if $H\left[P\right]\mathrm{}$ is defined as a functional of the density equal to an energy functional $E_U\mathrm{}\left[P\right]\mathrm{}$ less a Coulomb energy term $\left(\frac{\nu }{2}\right)\int {1R^3}^{}\int {1R^3}^{}\times {\mathrm{}|x-y|\mathrm{}}^{-1\mathrm{}}P\left(x\right)P\left(y\right)\mathrm{}{d}^{3}y{d}^{3}x$ with $\nu$ a positive constant, then the functional $E_L\mathrm{}\left[P\right]\mathrm{}\equiv H\left[P\right]-\int \stackrel{}{1R^3}\frac{\delta H\left[P\right]\mathrm{}}{\delta P\left(x\right)\mathrm{}}P\left(x\right)\mathrm{}{d}^{3}x-\frac{1}{8\pi \nu }\int \stackrel{}{1R^3}{\left|\overrightarrow{\nabla }\frac{\delta H\left[P\right]\mathrm{}}{\delta P\left(x\right)\mathrm{}}\right|}^2{d}^{3}x+N\left[P\right]\mathrm{}limit\; of\frac{\delta H\left[P\right]\mathrm{}}{\delta P\left(x\right)\mathrm{}}\text{as}\mathrm{}\left|x\right|\mathrm{}\to \infty$ with $N\left[P\right]=\int {1R^3}^{}P\left(x\right)\mathrm{}{d}^{3}x$ is complementary to $E_U\mathrm{}\left[P\right]\mathrm{}$ whenever the second variation of $H\left[P\right]\mathrm{}$ is positive. Explicit forms of $E_L\mathrm{}\left[P\right]\mathrm{}$ for the Thomas-Fermi and the Thomas-Fermi—Dirac—von Weizsäcker theories are given and used to obtain both lower and upper bounds to the atomic energies of these theories. A discussion on the corresponding Hohenberg-Kohn complementary functional is also presented.

A linear algebraic method, based on an integral equations formulation, is applied to the excitation of atoms and molecules by electron impact. Various schemes are devised for treating the one-electron terms that sometimes cause instabilities when directly incorporated into the solution matrix. These include introducing Lagrange undetermined multipliers and correlation terms. Good agreement between the method and other computational techniques is obtained for electron scattering for hydrogenic and Li-like atomic ions and for $\mathrm{H}_2^{}{}_{}{}^{+}$ in two- to five-state close-coupling calculations.

Experimental studies of target ionization and electron capture have been carried out through measurements of charge-analyzed projectiles and target ions in coincidence for ${\mathrm{Au}}^{q+}$ projectiles at 100-keV/amu ($q=5-21\mathrm{}$) colliding with either helium or neon targets. Information about partial cross sections, where the charge state of both collision partners is specified both before and after the collision, is presented. For the low-charge-state projectiles, pure single-electron capture and pure single-target ionization are found to be dominating and of equal magnitude. At the highest-charge states, single-electron capture is found to dominate, whereas single ionization is small. However, single-electron capture accompanied by ejection of a second electron is found to be of significant importance with a cross section as large as ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$.

An accurate treatment is developed for the calculation of Compton defects and their physical interpretation. The case of atomic $K$ and $L$-shells analyzed here exhibits the strong dependency of Compton defects with overlapping properties of individual orbitals. For given azimuthal $l$ and magnetic $m$ quantum numbers, a simple generalization allows one to predict the sign of the Compton defect from the parity of $l+m$.

The gauge-invariant periodic quantization (GIPQ) method is applied within the complete Hilbert space of solutions of the exact time-dependent Schrödinger equation. The multiplicity of such GIPQ solutions is shown to exceed by far the number of eigenfunctions they are intended to analogize. However, time averaging (or the equivalent averaging over all values of the progressive phase) reduces in this space to a projection upon the exact eigenfunctions under which every one of these GIPQ solutions either vanishes identically or reduces precisely to one of the stationary (but unnormalized) eigenfunctions of the exact Hamiltonian. One concludes that the correspondence between the GIPQ solutions and exact eigenfunctions is well manageable in the complete Hilbert space, a result which encourages the further study of time-averaged GIPQ solutions in parametric subspaces, where time averaging projects not upon an eigenstate, but upon the constant component of the GIPQ periodic solution.

The excitation cross sections by electron impact from the Cd II ground state to the laser upper state $5s^2{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ (Beutler state) and the laser lower state $5p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ (resonance state) have been measured by using a crossed-beam method of electrons and ${\mathrm{Cd}}^{+}$ ions and a photoncounting method. The electron-energy region investigated was from the threshold energy (5.8 eV) for the excitation of the $5p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state to 20 eV. It has been shown that the excitation cross section for the ionic Beutler state $5s^2{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ is of the order of ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ and has a sharp peak near the threshold energy for the excitation. The excitation cross section for the resonance state $5p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ has also been of the order of ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ and has a relatively broad maximum.

The position and width of the lowest ${}_{}{}^2{}_{}{}^{}P$ resonance in electron-beryllium scattering are computed directly in configuration-interaction calculations with the use of the method of complex basis functions. These calculations make use of a reference wave function from a complex self-consistent-field calculation on ${\mathrm{Be}}^{-}$ with the use of complex Slater basis functions. The most extensive calculation performed includes 745 single, double, and triple excitations from the reference configuration and yields values for the position and width of 0.323 and 0.296 eV, respectively. Comparison is made with previous theoretical determinations. No experimental values are currently available.

Results of close-coupling calculations are reported, in which several models of the interaction potential are investigated. Cross sections for rotational transitions involving the lowest ten levels are obtained in the first detailed application of the MEAN approximation. The results are subject to a strong cooperative effect involving exchange and polarization. Rotationally elastic transitions are shown to be quite important at thermal energies and to dominate the total cross section above 4.0 eV. Transitions for which the angular momentum changes by two are found to be responsible for a broad resonance at ∼ 2.5 eV. No structure indicative of a resonance or virtual state at very low energies is, however, obtained. Total differential, momentum-transfer, and integrated cross sections are in satisfactory agreement with measured values.

The spectra of $K$ x rays emitted by thin targets of the alkali-metal and alkaline-earth fluorides under bombardment with 22-MeV carbon ions were measured with a curved crystal spectrometer. Comparison of the satellite intensity distributions with that obtained for neon under similar conditions revealed that electron transfer within the $K$-hole lifetime (∼ ${10}^{-13\mathrm{}}$ sec) is highly probable even for these highly ionic compounds. A detailed analysis of the satellite intensity distribution obtained for LiF yielded a rate constant for $K{L}^1-K{L}^0$ transfer equal to 30% that for $K$-vacancy decay. The spectra for KF, Sr${\mathrm{F}}_2$, and Ba${\mathrm{F}}_2$ show evidence of resonant electron transfer (RET) associated with the matching of the $2p$ binding energies of fluorine atoms in $K{L}^1$ states with the outer $\mathrm{np}$ binding energies of adjacent metal ions, in agreement with previous findings. Also, an anomalously low $K{L}^2$ intensity, indicative of RET in association with this double $L$-hole state, was observed for Ca${\mathrm{F}}_2$. An additional component contributing to the enhancement of the $K{L}^0$ peak was attributed to secondary-electron ionization.

We report calculations of the differential, integral, and momentum-transfer cross sections for elastic scattering for $e-\mathrm{H}\mathrm{e}$ collisions at 30-400 eV and $e-\mathrm{N}\mathrm{e}$ collisions at 50-400 eV. The calculations are based on static-exchange-plus-polarization-and-absorption model potentials. The static potentials are based on Hartree-Fock results, the exchange potentials are calculated with the semiclassical exchange approximation, and the absorption potentials are phenomenological ones previously adjusted to experimental total absorption cross sections. For polarization, we consider two approximations, both versions of the semiclassical polarization approximation of Valone and the authors. One of these, the low-energy semiclassical polarization approximation, is quite successful in all cases, although it does systematically overestimate the small-angle (10°) scattering by factors ranging from about 1.1 (at 30-100 eV) to 1.7 (at 400 eV) for He. (For Ne this model predicts the 10° scattering within 16% in all cases.) The integral elastic cross sections predicted by this model have a typical relative error of about 10% for both He and Ne. Another version of the model, the local-kinetic-energy semiclassical polarization approximation, is a little less successful. We also examined the differences between using perturbative and variational input for He and found that these differences are generally smaller than the differences between the low-energy and local-kinetic-energy models.

The classical-trajectory Monte Carlo method has been used to determine ionization and capture cross sections and stopping powers for collisions of negative muons with hydrogen atoms. The calculations were done for muon energies from about 3 eV to 150 keV. The uncertainty in the results is thought to be about 30%. Most muons are found to be captured in collisions at energies below the ionization potential of the target atom.

The elastic scattering of electrons with hydrogen atoms at incident electron energies of 200-680 eV is studied using a two-potential method and the variable-charge Coulomb-projected Born approximation. Effects of exchange and polarization are included. The results obtained are found to be in reasonable agreement with recent experimental measurements. Comparison is made with other available theoretical calculations.

Based on the first Born approximation and coupled-channel wave functions, a full three-dimensional treatment of state-to-state reactive scattering (rearrangement collision) has been made to derive explicitly the transition amplitude, differential cross section, and total cross section for atom-diatomic molecule systems. The present coupled-channel Born-approximation method will serve as a generalization of the distorted-wave Born-approximation method that we discussed elsewhere.

A series expansion of the Born propagator allows one to represent successive corrections to the impulse approximation and exhibits their relative dependence in momentum transfer $k$ and the Compton (target-structure) parameter $q$. The proposed treatment provides a physical interpretation of the observed Compton defects. It is shown here to be in close agreement with high-energy-electron-impact spectroscopy measurements obtained for helium atoms.

We complete the molecular results reported in a previous paper by presenting additional energies (for ${}_{}{}^{1,3}{}_{}{}^{}\Sigma$ states) and radial couplings (between ${}_{}{}^1{}_{}{}^{}\Sigma$ states) of the He${\mathrm{H}}^{+}$ system. These results are needed to treat elastic and inelastic charge-exchange processes when full account is taken of momentum-transfer problems. We also present a formalism to calculate radial couplings between wave functions computed with the use of different variational methods and basis sets. The detailed form of the radial couplings is discussed and related to the Barat-Lichten correlation diagram. The effect of using finite basis sets in calculating degenerate molecular energies is also discussed.

A treatment of the ${\mathrm{He}}^{+}$ -H collision is presented in an impact-parameter formalism for collision energies 0.5 - 30 keV. The origin dependence of the calculated total cross sections is studied in detail. It is shown that the branching ratio between reactions ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{He}}^{+}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$ and ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to \mathrm{He}\left(1s2p\right)+{\mathrm{H}}^{+}$ oscillates as a function of the origin of electronic coordinates chosen in the calculation. This oscillation is strong enough so that at nuclear velocity 0.5 a.u., either both reactions are competitive or one of them can have a cross section twice as large as that of the other. Likewise the cross section for the reaction $\mathrm{He}\left(1\mathrm{}{s}^2\right)+{\mathrm{H}}^{+}\to {\mathrm{He}}^{+}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ can either be negligible or comparable to those of the other reactions. We study the oscillatory behavior of the charge-exchange-transition probability as a function of $\frac{1}{v}$. We show the similarity, for high velocity, between non-resonant and resonant charge-exchange processes, the origin of the damping factor, and the influence of the rotational coupling on the transition probabilities as functions of $\frac{1}{v}$. A connection between Lichten's and Demkov's models is established.

Wave functions for doubly excited states of helium ${}_{}{}^{1,3}{}_{}{}^{}S_{}^e{}_{}{}^{}$ states calculated in the configuration-interaction (CI) method are examined in hyperspherical coordinates. It is shown that these wave functions are essentially identical to the wave functions calculated in the adiabatic approximation except in regions where the charge density is vanishingly small. This comparison establishes the connection between the classification of doubly excited states based upon the adiabatic approximation in hyperspherical coordinates and the classification of Herrick and Sinanoglǔ which is based upon the approximate CI wave functions. It is also shown that states calculated from the CI method which have similar quantum defects have the same correlation patterns except in regions where the charge density is small. This establishes the approximate channel classification of doubly excited states as implied in the adiabatic approximation in hyperspherical coordinates.

The singularity structure of the forward positron-atom scattering amplitude is studied within the framework of perturbation theory with the use of the Landau rules. The unphysical and anomalous regions in the positron-atom forward dispersion relations are discussed. It is shown that the unphysical region starts at $E_0=-\left|E\right(\mathrm{Ps}\left)\right|+\left|\mathrm{}{E}_1\right|$) and the anomalous region at $E_a=-[\sqrt{2\left|E\right(\mathrm{Ps}\left)\right|}-\sqrt{\left|E_1\right|}{]}^2$, where $E\left(\mathrm{Ps}\right)$ and $E_1$ are correspondingly the positronium and the atomic-electron binding energies. The anomalous region is on the physical sheet if $\frac{\left|E\right(\mathrm{Ps}\left)\right|}{2}>\left|E_1\right|$.