Detailed theoretical calculation of the dielectronic recombination rate coefficient ${\alpha }^{\mathrm{DR}}$ has been carried out for the Be and Ne sequences, and the scaling properties of ${\alpha }^{\mathrm{DR}}$ in the nuclear core charge are examined. Based on these results an improved semiphenomenological formula is then constructed.

Narrow threshold peaks are observed in the excitation functions for high-Rydberg states of the rare-gas atoms. They are considered to be evidence for the direct excitation of high-orbital-angular-momentum ($l$) states.

The space part of a general spin-spin interaction is expanded in a complete orthonormal set of irreducible tensors constructed from spherical harmonics of the interacting particles. With this expansions, the $m$-scheme matrix element of the spin-spin interaction is represented as a sum of weighted radial integrals along with its graphical representation. The graphical form of the $m$-scheme matrix element enables one to obtain graphically matrix elements between many-particle configurations in any coupling scheme.

The Sternheimer equation for atomic polarizability is modified to account for the self-consistent field. The equations are quite simple for closed-shell ions. Numerical results are presented.

The approximation method introduced by Keldysh is revised and extended. The technique is applicable to the photodetachment by a plane-wave field of an electron bound by a short-range potential. The approximation is to neglect the effect of the binding potential as compared to the field effects on the final state of the detached electron. By choice of a different gauge than that used by Keldysh, the formalism becomes very simple and tractable. A general basis for the formalism is developed, and it is then applied to find transition probabilities for any order of interaction for both linearly and circularly polarized plane-wave fields. The low-intensity, first-order limit and the high-intensity, high-order limit yield the correct results. Two intensity parameters are identified. The fundamental one is $z=\frac{e^2{a}^2}{4m\omega }$, where $a$ is the magnitude of the vector potential (in radiation gauge) of the field of circular frequency $\omega$. The second parameter is $z_1=\frac{2z\omega }{E_B}$, where $E_B$ is binding energy, and it becomes important only in the asymptotic case. With the assumption that the field leaves the neutral atomic core relatively unaffected, the formalism is applied to the example of the negative hydrogen ion irradiated by circularly or linearly polarized 10.6-μm radiation. Photodetachment angular distributions and total transition probabilities are examined for explicit intensity effects. It is found that total transition probability $W$ is not sensitive to intensity since $\frac{d\left(logW\right)}{d}$ ($logz$) retains low-intensity straight-line behavior up to quite high values of $z$. An important intensity effect is the major significance of higher-than-lowest-order terms when $z$ is large, especially for circular polarization. A sensitive indicator of intensity is the ratio of photodetachment probabilities in circularly and linearly polarized fields, which increases sharply with intensity. An investigation of the convergence of perturbation expansions gives the upper limit $z<\left[\frac{E_B}{\omega }\right]-\frac{E_B}{\omega }$, where the square bracket means "smallest integer containing" the quantity in brackets. This limit is $z<\mathrm{}0.59\mathrm{}$ for ${\mathrm{H}}^{-}$ in 10.6-μm radiation. The failure of perturbation theory is not necessarily manifest in qualitative ways. For example, it is not apparent in total photoelectron yield as a function of intensity.

The classical spin of a particle is essentially its angular momentum of rotation about an axis passing through its center of mass. The classical Poisson brackets are generalized to include spin for any system for which the rate of change of spin is given by $\frac{d\overrightarrow{s}}{\mathrm{dt}}=-\overrightarrow{s}\times \left(\frac{\partial H}{\partial \overrightarrow{s}}\right)$ where $H$ is the Hamiltonian. In a previous paper, we showed that this equation is satisfied by the Breit-Pauli Hamiltonian for a molecular system of electrons and nuclei interacting with an electromagnetic field. This Hamiltonian contains all of the fine-structure terms with the exception of the Lamb shift. Thus, our generalized Poisson brackets should apply to almost all molecular problems. Our generalized Poisson brackets are the same as those which Sudarshan and Mukunda derived by group-theoretic arguments for the direct product of a pure spin group with the group of transformations of generalized coordinates and their conjugate momenta.

A coupled-channel approach with complex rotated coordinates and boundary conditions identical to those used for bound states is shown to lead to an accurate determination of the widths of resonances in the heavy particle motion of molecular systems.

We present a perturbation theory for an arbitrary bound state of a Dirac particle in a central field by reducing the Dirac equation to a Ricatti equation, following a method first introduced by Mikhailov and Polikanov. All corrections to the energies and wave functions, including corrections to the positions of the nodes in excited states, are expressed in quadrature in a hierarchical scheme, without the use of either the Green's function or the sum over intermediate states.

The correct treatment of strongly bound electrons is grafted smoothly onto the Thomas-Fermi computation of the total binding energy of neutral atoms. This provides a clearcut demonstration of the leading correction of relative order $Z^{-\frac{1}{3}}$ which, with effects of relative order $Z^{-\frac{2}{3}}$, gives an accurate account of the binding energy over a wide range of $Z$ values. There is a brief discussion of relativistic corrections, with results that are somewhat at variance with previous numerical estimates.

Separation equations in parabolic coordinates are written in terms of the logarithmic derivative of the wave function. It is shown that for the ground state of the hydrogen Stark problem the $n$ th order of the perturbation expansion is a polynomial of order $n$ with integer coefficients. The energy coefficients. The energy coefficients, suitably defined, are integers and the calculation of the first 30 coefficients is listed.

A radiatively assisted inelastic collision (RAIC) is one in which two atoms collide in the presence of a radiation field to produce a reaction of the form $A^{*}+B+\hslash \Omega \to A+B^{*}$. In this paper, a general theory of RAIC is developed with special attention given to the final-state coherences produced by RAIC. These final-state coherences can be monitored by standard experimental techniques (polarization of fluorescence, quantum beats), enabling one to use such studies to gain information on the interatomic potentials that are relevant to the RAIC under consideration.

A theoretical calculation of the final-state coherences produced by a radiatively assisted inelastic collision (RAIC) is presented. Two atoms, $A$ and $A^{\prime }$, collide in the presence of an external radiation field to produce the RAIC reaction $A_i+A_{i^{\prime }}^{\prime }+\hslash \Omega \to A_f+A_f^{\prime }$, where $|{\mathrm{ii}}^{\prime }〉$ is the initial state, $|{\mathrm{ff}}^{\prime }〉$ is the final state, and $\Omega$ is the frequency of the external field. It is assumed that the final states consist of a number of nearly degenerate levels and the coherences produced in these levels by the RAIC reaction is calculated. These final-state coherences can be monitored by standard techniques (polarization of fluorescence, quantum beats) enabling one to use the final-state coherences as a probe of the RAIC reaction. The calculation is limited to the weak-field (perturbation-theory) limit and is valid only in the impact core of the RAIC profile.

For a symmetric potential barrier with two turning points there exists an inversion procedure which is closely related to the inversion of scattering phase shifts. The inversion formulas correct to first order in ${\hslash }^2$ are derived in the WKB approximation. To illustrate the applicability and limitation of the proposed procedure, we construct the quartic potential barrier $U\left(X\right)=-X^4$, from its transmission coefficients.

Total scattering cross sections have been measured in the same apparatus for positrons and electrons of well-defined energies (0.35-100 eV) colliding with krypton and xenon using a beam-transmission technique. The positron total cross sections are largest at the lowest energies studied, and decrease in a manner very similar to the elastic scattering cross-section calculations by Schrader and by McEachran et al. The total cross sections for positron-krypton, xenon collisions experience abrupt changes in their slope at the respective positronium-formation thresholds indicating that positronium formation may be an important contributor to the total cross section above the formation threshold. The present electron measurements are in good agreement with the recent measurements of Wagenaar. Estimates of potential errors in the present measurements due to incomplete discrimination against small-angle forward elastic scattering are made.

Cross sections have been calculated for photoionization of the first excited $s$, $p$, and $d$ states of the heavier rare gases (neon, argon, krypton, and xenon). A semiempirical, central-field approximation has been used in which an effective core polarizability was adjusted to fit the computed eigenvalues to the known excited-state binding energies for each atom. The calculations have revealed interesting features in many of the cross sections, and these are described and analyzed. In addition, the role of excited-state photoionization processes in short-pulse raregas-halide lasers is briefly discussed.

$K$-shell vacancy fractions have been measured for B, C, N, O, and Ar projectiles traversing thin carbon foils. The equilibrium vacancy fractions were determined by measuring Auger electron yields from the projectiles emerging from the foils. Projectile energies ranged from 50 to 500 keV. The fractions increase as energy increases, up to saturation values. The measurements are interpreted in terms of vacancy creation and filling events, using previously measured cross sections and vacancy sharing ratios. Collisional vacancy filling cross sections for projectile-carbon atom collisions are extracted, and the mechanisms responsible for saturation are delineated. These cross sections are compared to available theoretical estimates and are found to be much larger than those predicted by modified Brinkman-Kramers theory. This is attributed to quasimolecule-formation effects. Tentative values for dynamical projectile vacancy lifetimes are obtained.

$K$-shell x-ray production cross sections were measured for ${}_{28}{}^{}{}_{}{}^{}\mathrm{Ni}\mathrm{}\left(K\right)\mathrm{}$ in collision with ${}_1{}^1{}_{}{}^{}\mathrm{H}$ ions of kinetic energies 55 to 300 keV, ${}_1{}^2{}_{}{}^{}\mathrm{H}$ ions of 100 to 300 keV, and ${}_2{}^4{}_{}{}^{}\mathrm{He}$ ions of 200 to 300 keV; for ${}_{46}{}^{}{}_{}{}^{}\mathrm{Pd}\mathrm{}\left(K\right)\mathrm{}$ with ${}_1{}^1{}_{}{}^{}\mathrm{H}$ ions of 215 to 300 keV, and for ${}_{47}{}^{}{}_{}{}^{}\mathrm{Ag}\mathrm{}\left(K\right)\mathrm{}$ with ${}_1{}^1{}_{}{}^{}\mathrm{H}$ ions of 200 to 300 keV. $L$-shell x-ray cross sections were measured for ${}_{47}{}^{}{}_{}{}^{}\mathrm{Ag}\mathrm{}\left(L\right)\mathrm{}$ in collision with ${}_1{}^1{}_{}{}^{}\mathrm{H}$ ions of kinetic energies 35 to 300 keV, with ${}_1{}^2{}_{}{}^{}\mathrm{H}$ ions of 60 to 300 keV, with ${}_2{}^4{}_{}{}^{}\mathrm{He}$ ions of 110 to 300 keV, and for ${}_{79}{}^{}{}_{}{}^{}\mathrm{Au}\mathrm{}\left(L\right)\mathrm{}$ with ${}_1{}^1{}_{}{}^{}\mathrm{H}$ ions of 140 to 300 keV. The collisions conditions were such that the effect of the projectile energy loss during the ionizing collision became significant for the $K$-shell ionizations, but remained unimportant for the $L$-shell ionizations. The measurements extend the experimental range of the Coulomb-deflection variable $d{q}_{0S}$ over previous measurements for the shells $S=K$ by a factor ∼ 1.2, and for $S=L$ by a factor ∼ 2. This permits a decisive test of current theories for the effect of the deflection of the projectile in the Coulomb field of the target nucleus on inner-shell ionization cross sections.

Cross sections for electron capture from inner shells by fully stripped ions are calculated and compared with data for $K$-shell vacancy production. A procedure for inclusion of the relativistic effect is developed, and the scheme of calculations is illustrated through sample evaluations of electron-capture cross sections.

Time-of-flight spectra of $\mathrm{H}\mathrm{}\left(2S\right)\mathrm{}$ and $\mathrm{D}\mathrm{}\left(2S\right)\mathrm{}$ fragments from electron-bombardment dissociated ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ have been observed. Kinetic energy distributions of "fast" metastable fragments were obtained for electron-bombardment energies ranging from near the threshold for fast metastable production (less than 29 eV) to 100 eV. At low bombarding energies previously unreported structure is observed in the fast peaks for both isotopes. At high bombarding energies also there is evidence of unresolved structure in the fast peaks. The present data are compared with the results of earlier investigations. At low bombarding energies there are significant discrepancies between the present results and previous measurements. At high bombarding energies there is significant disagreement with a calculation that assumes a single dissociating state. The observed shift of the fast peak as a function of the bombarding electron energy is compared to predictions incorporating a form of the Wannier law. This comparison tends to confirm the presence of more than one dissociation channel yielding fast metastables. Several excited states of ${\mathrm{H}}_2$ and $\mathrm{H}_2^{}{}_{}{}^{+}$ are discussed as possible dissociation channels contributing to the observed kinetic energy distributions.