Various versions of a statistical model of atoms are developed in which the numbers of electrons in different regions of an atom are fixed by certain postulates. It is assumed that the electron density can be represented by a sum of exponentially decreasing functions. The electronic energies and electronic densities of these new models are found to be comparable to the corresponding Hartree-Fock results and are substantial improvements over the original Thomas-Fermi statistical model and its various extensions. Densities of the new models are improvements over the modified statistical models of Wang and Par [Phys. Rev. A 16, 891 (1977)]. Some corrections to this reference are included.

Boundary conditions are derived for the interfaces of a conductor moving across an external magnetic field in an ambient medium (vacuum or nonconductor), which consider the emission of electromagnetic waves from the conductor surface as a result of electromagnetic induction. These boundary conditions are applied to the initial-boundary-value problem for the electromagnetic induction in a conducting slab, which is accelerated across a homogeneous magnetic field to a nonrelativistic velocity. Fourier-series solutions are presented for the transient electromagnetic fields in the moving conductor and the discontinuous electromagnetic waves in the ambient space. It is shown that the transient electromagnetic fields inside and outside the conductor are due to two mechanisms, i.e., "velocity induction" (ordinary induction) and "acceleration induction" [$\frac{d\overrightarrow{\mathrm{v}}\mathrm{}\left(t\right)\mathrm{}}{\mathrm{dt}}\ne \overrightarrow{0}$]. The latter result cannot be explained by means of the Lorentz transformation, which is valid only for constant conductor velocities (inertial frames).

With the development of ion-storage techniques, it has become possible to study the hyperfine interactions of alkaline-earth positive ions which are isoelectronic with alkali-metal atoms. As part of a program to study the available experimental values of the hyperfine constants and the relative importance of various contributing mechanisms in these systems, we have investigated the singly ionized barium ion using relativistic many-body perturbation theory. The one-electron contribution to the hyperfine constant in ${}_{}{}^{137}{}_{}{}^{}\mathrm{Ba}_{}^{+}{}_{}{}^{}$ is found to be 3476 MHz composed of direct and exchange core-polarization contributions of 3055 and 421 MHz, respectively. The many-electron correlation contribution is found to be 727 MHz. The net calculated hyperfine constant of (4203± 200) MHz agrees satisfactorily with the experimental value of 4018.2 MHz. The ratios of the exchange core-polarization and correlation contributions to the direct contribution are both found to be smaller than the corresponding ratios in the isoelectronic cesium atom. This can be ascribed to the lesser deformability of the core of ${\mathrm{Ba}}^{+}$ as compared to that of the neutral cesium atom.

Linked-cluster many-body perturbation theory has been used to calculate the Sternheimer hexadecapole antishielding factor ${\eta }_{\infty }$ in ${\mathrm{Pr}}^{3+}$. This parameter is a measure of enhancement of a possible nuclear electric hexadecapole (16-pole) moment due to polarization of the core electrons in an atom or ion. Large and predominant contributions due to the angular mode of excitations neglected in earlier works have been found. Self-consistency contributions to ${\eta }_{\infty }$ are found to be small (about 3%), similar to those in the quadrupole antishielding factor ${\gamma }_{\infty }$. These contributions in the case of quadrupole polarizability ${\alpha }_q$ and the crystal-field shielding parameter ${\sigma }_2$ in ${\mathrm{Pr}}^{3+}$ were found to be larger (about 17% but of opposite sign in both cases).

Absolute $K$-shell x-ray-production cross sections have been measured for thin-foil targets of Ti, Cr, Co, Ni, Cu, and Zn at incident proton beam energies from 300 to 2400 keV. Particular care was necessary in the control of experimental conditions in order to determine the x-ray-production cross sections with high precision (∼5%). The x-ray-production cross sections were determined from x-ray yields normalized to simultaneous measurements of particle scattering yields at 90°. The values of $K$-shell vacancy-production cross sections were determined to range from 0.133 b for 300-keV protons on Zn to 1230 b for 2400-keV protons on Ti. The overall agreement of these total cross sections with recent data obtained by other workers generally is to within 10% and frequently is to within the 5% accuracy of our results. The $K$-shell ionization cross sections inferred from these results are compared with the predictions of energy-loss Coulomb-deflection perturbed-stationary-state relativistic theory which reproduces the data with good accuracy. In addition, these results also show good agreement when compared with a more fundamental formulation based on perturbed-stationary-state theory.

We report several calculations of the differential, integral, and momentum-transfer cross sections for elastic scattering, and of the absorption cross sections (for the sum of all electronically inelastic and ionization processes) for electron-He collisions at 30-400 eV. We consider two basically different approaches to include the effect of absorption, i.e., loss of flux from the initial channel. The first is the matrix effective potential (MEP) based on a variational calculation of the polarization potential; this models absorption by including a pseudochannel whose properties are based on a variational adiabatic polarization potential. This method predicts both the absorption and elastic cross sections. The second method involves phenomenological absorption ($A$) potentials, calibrated against experimental absorption cross sections. These potentials, when combined with static ($S$), exchange ($E$), and real polarization ($P$) potentials form an SEPA optical model potential that is used to predict the elastic cross sections. The MEP model based on the variational polarization potential predicts the absorption cross sections with an average absolute error of 28% at 30 and 50 eV, and 5% at 100-400 eV. It predicts the elastic integral cross sections with an average absolute error of 8% over the whole energy range. The SEPA models, including a nonadiabatic polarization potential, predict the elastic integral cross sections with average absolute errors of 12 or 6%, depending on the shape function (i.e., $r$ dependence) of the absorption potential. The adiabatic approximation for polarization is less accurate than the nonadiabatic one, even when absorption effects are included. Five new calculations of the differential cross sections at each of five impact energies are compared to experimental results in detail.

A virtual state of an electron interacting with a molecule indicates that a new bound state with a large $s$-wave component is about to appear. In the picture of fixed nuclei, the bound state is caused to appear or disappear by a small displacement of the nuclei. When the nuclear vibrations are taken into account, it is shown, for the example of $e+\mathrm{HCl}$, that nuclear-excited Feshbach resonances occur at energies just below the vibrational thresholds.

An application of the time-dependent Hartree-Fock (TDHF) theory of charge transfer in atomic collisions is presented. Probabilities for elastic and double symmetric charge exchange are calculated for a fixed laboratory scattering angle and for collision energies from 10 to 70 keV. The TDHF equations are solved using finite difference techniques and propagated in time using the Peaceman-Rachford alternating-direction implicit method. Plots of time-evolved charge densities are presented also.

Absolute charge-transfer cross sections for collisions of protons with hydrogen and deuterium atoms have been measured within the energy range 0.1 to 150 eV using the merging-beams technique. The results are in excellent agreement with a fully quantum-mechanical treatment of this reaction. Earlier measurements which extended down to about 10 eV lie somewhat above the present values.

We have studied the transfer of electronic and nuclear spin polarization from the $5{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state of Rb to the $5{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ state caused by quenching collisions of Rb atoms with ${\mathrm{N}}_2$ molecules. We evaluate the dependence of such polarization transfer upon the strength of the hyperfine interaction in the excited state. The nuclear spin independent relative probabilities connecting $J$, $m_J$ sublevels of the $5{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state with the $S$, $m_S$ sublevels of the ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ state are $K_1({}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{},m_J=\pm \frac{1}{2}\to {}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{},m_S=\pm \frac{1}{2})=0.33\mathrm{}\pm 0.15,$

$K_2({}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{},m_J=\pm \frac{1}{2}\to {}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{},m_S=\mp \frac{1}{2})=0.67\mathrm{}\pm \mathrm{0.15.}$

The results suggest that the quenching interaction is a sudden perturbation in which the orientation of the electronic spin is preserved. The experiment provides a determination of the cross section for the destruction of orientation within the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state, ${\Lambda }_{\frac{1}{2}}^1$:

${\Lambda }_{\frac{1}{2}}^1(\mathrm{Rb}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{},{\mathrm{N}}_2)=(105\mathrm{}\pm 25)\times {10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$.

The value of ${\Lambda }_{\frac{1}{2}}^1$ for Rb in ${\mathrm{N}}_2$ is considerably larger than corresponding values for Rb in the noble gases. The experimental and theoretical results provide insight into the influence of quenching collisions on the efficiency of optical-pumping processes. They show why a small amount of ${\mathrm{N}}_2$ added to an optical-pumping cell improves pumping efficiency, whereas a large amount of ${\mathrm{N}}_2$ reduces it.

Crossed beams of electrons and ${\mathrm{Ga}}^{+}$ ions have been used to measure the absolute emission cross section for the process $e^{-}+{\mathrm{Ga}}^{+} \left(4\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)\to e^{-}+{\mathrm{Ga}}^{+} \left(4\mathrm{}{}_{}{}^1{}_{}{}^{}P\right)$ from below thresh-old (8.77 eV) to 400 eV. Total uncertainties at 68% confidence level are typically 16%. The cross section exhibits the sharp onset at a threshold characteristic of positive-ion excitation processes. Evidence of structure is observed from just above threshold to 15 eV. The semiempirical Gaunt-factor formula is in reasonable agreement with the measurements over the energy range measured. A lower limit for the lifetime of the $4{}_{}{}^3{}_{}{}^{}P_{0,2}^{}{}_{}{}^{} {\mathrm{Ga}}^{+}$ metastable state has been established at $\tau \ge 0.4$ sec.

A local approximation to the second-order optical potential for elastic scattering of low-energy electrons from ground-state atoms is expressed in terms of the imaginary-frequency susceptibilities of the atom due to a point charge and to modified perturbing potentials. This provides a basis for the physically appealing concept of regarding the perturbation due to the projectile as having a position-dependent effective frequency associated with it. The result is extended to higher energies with the use of the concept of a local kinetic energy. With a semiclassical approximation the result reduces to a simple general form that should be useful for model potential studies of electron-atom and electron-molecule scattering. Alternatively, variational functionals for the susceptibilities can be used to calculate the approximate optical potential most rigorously without making effective-frequency, average-kinetic-energy, or semiclassical approximations. Intermediate levels of rigor are also possible.

Velocity spectra of electrons emitted into the forward direction have been measured for 0.7 - 8.5-MeV/u projectile ions transversing He, Ne, and Ar targets, ploycrystalline solids (C, Al, Ag, Au), and axial channels in gold. Spectral shapes and yields are compared and contrasted with one another and with theories which seek to account for the cusp-shaped peaks observed in terms of electron capture and loss to low-lying projectile-centered continuum states. We report the results of both singles and coincidence measurements, where the dependence of cusp shapes and yields on the emergent-ion charge state are examined. For electron capture to the continuum (ECC), variance is noted with respect to the simple, first-order theory of Dettmann, Harrison, and Lucas. The ECC yields are compared to experimental and theoretical studies of bound-state capture, especially to high Rydberg states. For electron loss to low-lying continuum states (ELC), variance is noted with respect to the corresponding theories of Briggs, Drepper, and Day, and ELC cross sections are compared to total electron-loss cross sections. For convoy electron production in solids, no known theory accounts for the results. As in ELC processes, convoy cusp widths are observed to be velocity independent. Convoy electron yields are also observed to be independent of the emergent-ion charge state.

Simple models suggest that the momentum-transfer ($q$) dependence of inelastic electron scattering is sensitive to the difference between collective and single-particle behavior in atomic dynamics. We measured the energy centroid of the $4d$ continuum peak for $0<q\le 1.4$ ${\mathrm{\AA }}^{-1\mathrm{}}$ in the following solids having complete $4d$ shells: Sb, Te, and Ba${\mathrm{F}}_2$, and find that a single-particle description is favored.

We apply two methods to predict integral and differential elastic and absorption cross sections for electron-neon scattering at 150-700 eV: a matrix-effective-potential (MEP) formalism and an optical-potential formalism. For the optical potential we use the absorption potential that Green, Rio, and Ueda adjusted to give accurate absorption cross sections, and we show that the real part of the potential can be chosen so that the calculated elastic-scattering cross sections also agree with experiment. The MEP model, with no parameters adjusted to experiment, is even more successful. The agreement with available experimental elastic differential cross sections is better than 10% in many cases and is about 40% at worst; agreement with experimental total inelastic cross sections averages 3% at four energies. An interesting conclusion from the optical-potential calculations is that when the absorption potential is included in the optical potential, accurate elastic cross sections can be calculated even at high energy by using an adiabatic polarization potential.

The theoretical description of double ionization followed by the emission of a single photon is critically examined. Some numerical calculations based on existing models are carried out and the results obtained subjected to an experimental test in a suitably designed experiment. Some doubt is cast on the accuracy with which the existing theoretical models describe the process.

Resonant two-photon transition rates from the ground state of atomic hydrogen to ns excited states have been computed as a function of photon frequencies in the length and velocity gauges in order to test the accuracy of the calculation and to discuss the rate of convergence over the intermediate states. The dramatic structure of the transition rates produced by intermediate-state resonances is exhibited. A two-photon transparency is found in correspondence to each resonance.

A semiclassical core-polarization-penetration model has been used to parametrize energy-level and energy-interval data for He I. Various contributions to the energy of the form $〈\gamma r^{-s}〉$ with $s\le 10$ were tested in attempts to account for different types of polarizabilities, dynamical correlations, and relativistic and retardation effects, which are all exactly calculable for the hydrogenlike core. Penetration effects were simulated by replacing expectation values by time averages over classical Kepler orbits that penetrate a parametrized hollow shell of core charge. It was found that the best fits were obtained if only dipole, quadrupole, lowest-order dynamical correlations, and relativistic mass corrections to the gross energy were included, and that higher-order polarizabilities and retardation effects worsened the fit. The approach generally reproduces observed $J=L$ singlet-triplet averages to within experimental uncertainties for $n\ge 5$ and $l\ge 2$. Three free parameters each are necessary to describe the $D$ and $F$ Rydberg series, whereas the $l\ge 4$ series can be described with no free parameters. The model can be very precisely tested with the use of available microwave-optical resonance data for the $\Delta n=0\mathrm{} F-G-H-I$ intervals, for which the relativistic and polarization energies have been observed directly.

We implement the Raman echo for the first time in collision studies to measure the noble-gas-induced broadening of the $6P_{\frac{1}{2}}-6\mathrm{}{P}_{\frac{3}{2}}$ transition of atomic thallium. Except in the case of He, the measured broadening cross sections He 59(2), Ne 67(2), Ar 124(4), Kr 167(5), and Xe 204(6) ${\mathrm{\AA }}^2$ ($T=840\mathrm{}$ K), agree with those calculated assuming a pure van der Waals collisional interaction. Our measurements, sensitive to collisionally induced changes in axial velocity of ≳ 300 cm/sec, reveal that collisional velocity changes of that magnitude are not important in T1-noble-gas collisions.

The production of $\mathrm{Ne} K$ Auger electrons is investigated in fast heavy-ion—atom collisions with the use of gas target and ${\mathrm{Ne}}^{9+}$ and ${\mathrm{Ar}}^{9+}$ ions ranging in energy from 3 MeV/amu to about 15 MeV/amu. In particular, the projectile energy dependence of multiple $L$-shell ionization in Ne is compared to previous results from heavy-ion—atom collisions covering a projectile energy range from 1.2 MeV/amu to about 3 MeV/amu with atomic numbers varying between 8 and 18. The proposed linear relationship between the mean number of multiple ionized outer-shell electrons and the centroid energy of the corresponding Auger spectra is confirmed. The scaling behavior of the multiple ionization in Ne as a function of projectile energy and atomic number is investigated. It is found that the degree of multiple outer-shell ionization can be represented by a universal curve over a wide range of projectile energy and species.