Pair-correlated energies are reported for the ground states of a series of Be-like ions and, in particular, an assessment is made of the influence which individual pair correlations alone have on various one-particle expectation properties. The small changes which occur were, generally, heavily dominated by the $L$-shell effect, which became more pronounced as $Z$ became larger.

We have developed an analytic perturbation theory for screened Coulomb radial wave functions, based on an expansion of the potential of the form $V\left(r\right)=-\left(\frac{a}{r}\right)[1+V_1\lambda r+V_2{\left(\lambda r\right)}^2+V_3{\left(\lambda r\right)}^3+\cdots ]$, where $\lambda \simeq \alpha Z^{\frac{1}{3}}$ is a small parameter characterizing the screening. The coefficients $V_k$ may be chosen such that the above form converges rapidly and gives a good approximation to realistic numerical potentials, such as those of Herman and Skillman, in the interior of the atom. The screened radial wave functions are obtained as a series in $\lambda$ with simple analytic coefficients, owing to the special symmetries of the unperturbed Coulomb problem. Both bound and continuum shapes are correctly treated in the region $\lambda r<\mathrm{}1\mathrm{}$. For inner bound states, this includes all of the region where the wave function is large. Similarly, high-energy continuum wave functions will have completed several oscillations in this interval so that by $r\simeq {\lambda }^{-1\mathrm{}}$ one has reached the asymptotic region. Consequently, expressions for bound-state normalizations can be given as series in $\lambda$, which are accurate, in general, for the $K$ shell and for other low-lying levels of high-$Z$ elements. The continuum normalizations which we obtain are valid for energies on the order of the $K$-shell binding energy above threshold. Bound-state energies and continuum phase shifts are also obtained in these circumstances.

The energy results of an extensive configuration-interaction calculation of the ground state of ${\mathrm{Li}}^{-}$ are reported. A quantitative assessment of all sources of truncation errors leads to a nonrelativistic energy estimate of -7.5004 ± 0.0002 a.u. An $r_{ij}$ calculation on the ground state of ${\mathrm{Li}}^{-}$ yields a rigorous upper bound to the nonrelativistic energy of -7.500 186 a.u., in excellent agreement with the estimate from the configuration-interaction calculation. Consideration of relativistic contributions to the electron affinity of Li leads to an estimate of the electron affinity of Li of 0.609 ± 0.007 eV.

The coincidence spectra of molecular orbital x rays produced in the scattering of a beam of 26.85-MeV I ions by Au at laboratory angles of 1.5, 3.5, and 10.5 deg have been measured. Analysis of the data gives the energy dependence and approximate cross section for the molecular-orbital x rays for the combined system with $Z=132\mathrm{}$ as a function of impact parameter. The results confirm and extend the conclusions drawn from previous measurements of the x-ray singles spectrum.

We have measured electron energy distributions in the angular range 0°-6° for ion energies in the energy range 0.175-1.0 MeV/amu. A predominant group of electrons whose velocities are centered about the ion velocity is always observed. For this group of electrons, angular distributions have been deduced. Dependence on foil thickness and ion configuration, ${\mathrm{H}}^{+}$ or ${\mathrm{H}}_2^{+}$, have been investigated. Our results are consistent with a charge-exchange process being the dominant mechanism for producing these electrons.

$K$-shell ionization cross sections for Al and Si by proton and ${}_{}{}^3{}_{}{}^{}\mathrm{H}\mathrm{e}-\mathrm{i}\mathrm{o}\mathrm{n}$ impacts have been measured with thin targets and a proportional counter over the projectile energy range 0.75-4 MeV/amu. The results, together with others on light elements, are compared with theoretical predictions based on the plane-wave Born approximation and the binary-encounter approximation, and it is found that the scaling law, taking into account the effects of the Coulomb deflection of the projectile and the increase of binding energy of $K$-shell electrons, gives a good fit to the experimental results over the entire energy range measured. Ratios of the $K$-shell ionization cross sections for helium-ion impact to those for proton impact show deviations from the $Z_1^2$ dependence predicted by the Coulomb interaction theory. Possible reasons for this deviation are discussed.

The cross section for x-ray characteristic fluorescence excited by 950-keV protons has been measured for 12 elements: Cl, K, V, Cr, Fe, Ni, and Cu for $K$-shell emission and Rb, Y, Ag, Sm, and Gd for $L$-shell emission. The results for Cl, K, V, Rb, and Y are new data. We obtain ${\sigma }_K^{\mathrm{X}}=260\mathrm{}\pm 15\%$ for Cl, ${\sigma }_K^{\mathrm{X}}=121\mathrm{}\pm 15\%$ for $K$, ${\sigma }_K^{\mathrm{X}}=22.7\mathrm{}\pm 10\%$ for $V$, ${\sigma }_L^{\mathrm{X}}=405\mathrm{}\pm 15\%$ for Rb, and ${\sigma }_L^{\mathrm{X}}=350\mathrm{}\pm 15\%$ for Y, all cross sections (in barns) having been measured at 950-keV proton energy. Moreover, we deduce for Y a new value of ${\overline{\omega }}_L=0.14\mathrm{}\pm 15\%$. The results for the remaining elements are compared with the results of similar measurements. The experimental values are also compared with the predictions of the binary-encounter approximation and of the binding-energy-corrected plane-wave Born approximation. Both theories predict higher $K$-shell ionization cross sections than observed.

We report high-resolution differential cross-section measurements for the systems H-Ar and D-Ar at a relative energy of 67 meV. The primary beam is velocity selected (FWHM 10%) and the secondary beam is produced by a low-temperature source. The experimental resolution allows us to resolve the "fast-oscillation" structure of the cross section. Our experimental results are compared with the effective cross sections obtained from potentials recently proposed for these systems. The present data cannot accommodate the potential forms deduced from two separate measurements of the energy dependence of the total cross section, but are not in disagreement with the recent theoretical results of Wagner, Das, and Wahl. The sensitivity of the measured properties to the attractive and to the weakly repulsive parts of the potential is discussed, and we show that a compensation effect between the two does not allow a unique determination of the potential.

The classical path treatment of a collision between an excited atom and another atom with a nearly resonant energy level leads to coupled differential equations which have been discussed previously by many workers. Here we present an elementary procedure for solving this system of equations in the case of no crossing point and in the limit where $\Delta E\tau \gg \hslash$, with $\Delta E$ being the energy discrepancy and $\tau =\frac{b}{v}$ being a measure of the time of collision. Even though the method is designed to take advantage of the slowness of the collision, it is also shown to be exact if $\Delta E=0\mathrm{}$. The form of the solution is very similar to that of Vainshtein et al., but the present derivation avoids several of their approximations which individually are not as accurate as their final result. It is also pointed out that the coupled equations which arise for the energy-transfer problem also arise in connection with the interaction of laser pulses with atoms. Hence, the method has application to a wide class of multistate problems. A simple laser-interaction problem is discussed as a second example of the method.

X rays emitted by a thin target bombarded with C, N, and O ions with energies between 1 and 2.5 MeV are observed at an angle of 135° with a Bragg crystal spectrometer having a resolution of 3 eV. The $\mathrm{KL}$ and $K{L}^2$ satellite lines of the carbon target are observed, as well as the diagram $K$ line. These peaks are superimposed on a broad x-ray distribution extending from 265 to 290 eV. The $K{L}^2$ line appears for N at low energies, but not for C. Projectile and target spectra involve the $K$ and $\mathrm{KL}$ lines in approximately equal amounts for C. These observations are interpreted as evidence for a molecular-orbital theory involving promotion of $L$ electrons of the colliding atoms, in which the momentum change of the promoted electron is taken into account. Cross sections for production of carbon $K$ x rays at energies below the carbon absorption edge in the Bragg pseudocrystal are obtained from the data. The cross sections rise monotonically with energy in the range studied and are smallest for oxygen ions, which have the largest atomic number.

Absolute total electron detachment and relative elastic differential cross sections for the scattering of${\mathrm{Cl}}^{-}$ by Ne, Ar, Kr, and Xe have been measured at energies ranging from near detachment threshold to 180 eV. The experimental results have been analyzed by using semiclassical expressions for the cross sections which involve localized complex potentials. Reasonable potentials have been deduced which yield calculated cross sections that are in good agreement with the experimental observations.

Absolute total electron-detachment cross sections and relative elastic-scattering cross sections are presented for collisions of ${\mathrm{H}}^{-}$ (${\mathrm{D}}^{-}$) + He, Ne, Ar, ${\mathrm{N}}_2$ for collision energies ranging from about 2 eV up to 100 eV. Special emphasis has been given to the effect of isotopic substitution. It was found that, with the exception of the helium target, the results cannot be in accord with a model using a localized complex potential. On the other hand, the results for ${\mathrm{H}}^{-}$ (${\mathrm{D}}^{-}$) + He are in excellent agreement with predictions based upon a previous (local complex potential) analysis of differential elastic-scattering measurements.

A recently proposed anomaly-free averaged Kohn parameter-variation method has been used for calculations of the two lowest ${}_{}{}^1{}_{}{}^{}S$ resonances in $e^{-}\mathrm{H}$ scattering. Calculated phase shifts at a number of points spanning each resonance can be fitted rather closely with a one-level resonance formula, and the resulting widths are in reasonable agreement with results of other workers.

In an earlier paper a general formulation of differential cross sections for electron-impact ionization of atomic systems, in the Born approximation, was presented. The present work uses this formulation, with simple correlated wave functions, to evaluate various differential cross sections for electron-impact ionization of helium. The results are compared with previous experimental and theoretical data. The favorable agreement obtained with experiment for high incident-electron energies and low ejected-electron energies in both double- and single-differential cross sections is indicative of the agreement which can be expected when the same procedure is applied to the electron-impact ionization of other atoms.

Within the one-configuration molecular-orbital scheme, diabatic molecular states of the molecular ion ${\mathrm{HeD}}^{+}$ involved in the collisional process ${\mathrm{He}}^{+}$ + D are determined by the shielded diatomic orbitals (SDO's) method. These SDO's are exact solutions of the one-electron-two-center problem with an effective parametric potential. This potential, which preserves the separability in prolate spheroidal coordinates of the Schrödinger equation, is obtained by classical electrostatic considerations. Differential cross sections for the ${\mathrm{He}}^{+}$D colliding system are determined by a semiclassical collisional method. Good agreement is found with recent experimental results in the keV energy range.

The carbon $K$ x-ray emission cross section of methane molecules bombarded by 1- to 5-MeV nitrogen ions has been measured for incident charges +2 to +5 under single-collision conditions. Only x rays with energies which penetrate the polypropylene window of a proportional counter are counted. The cross sections increase monotonically with ion energy. Above 2 MeV they also increase with ion charge, to a maximum of nearly ${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$.

The eikonal-Born-series method, developed recently to analyze elastic scattering of electrons by atomic hydrogen and helium, is extended to inelastic scattering. In this paper we investigate the excitation of atomic hydrogen to the $2s$ or $2p$ state by electron bombardment. Important differences from the elastic case are discussed and a careful comparison with the Glauber method is made. Also, for angles greater than 20° comparison is made with recent experimental data on the sum of the differential cross sections for $2s$ and $2p$ excitation. Very good agreement is found.

We derive a new criterion for determining an accurate description of the total wave function at the energy of a resonance in the elastic scattering region from a bound-state representation. The criterion is based on an extension of the stabilization and Harris phase-shift methods. We construct the theoretical framework for a bound-state description of the resonance wave function and exhibit its connection to calculations of the bound-state Green's function.

The multiple-linear-time-scale method is used to construct a perturbation theory for $N$-level quantum systems subjected to time-dependent perturbations. The secular and small-denominator terms which plague conventional time-dependent perturbation theory are avoided; consequently, the theory is useful for treating long-term behavior and resonant interactions. The introduction of a self-energy operator allows the shifts in energy levels to be displayed explicitly. When the perturbation is the dipole interaction with an electromagnetic field, the successive approximations yield the well-known rotating-wave approximation, corrections due to counter rotating terms, and the Bloch-Siegert frequency shift. The formalism is applicable to arbitrary pulse shapes, provided that $\parallel H_1\parallel \ll \hslash \overline{\omega }$, where $\parallel H_1\parallel$ represents the inter-action strength and $\overline{\omega }$ is a characteristic frequency of the field. Rabi oscillations induced by multiphoton resonances are automatically included, and this effect is demonstrated in the case of a square pulse with frequency approximately one half the resonance frequency for a transition between two vibrational levels of a molecule. These calculations are compared to an exact numerical solution in order to find the limits of validity of the approximation. Even at high intensities ($I\sim {10}^{14}$ W/${\mathrm{cm}}^2$) the shifted resonance frequency is quite accurate; however, the approximate and exact solutions are slightly out of phase, so that the approximate solution can only be trusted for a few Rabi cycles. For much lower intensities ($I\sim {10}^{10}$ W/${\mathrm{cm}}^2$), the approximate solution is valid for many thousands of Rabi cycles.

Our earlier measurements of $K$-shell photoelectric cross sections for intermediate-$Z$ elements at 37 and 74 keV have been extended to energies in the range of $18\le E\le 44$ keV. The difficulty of nonavailability of clean and strong x-ray sources encountered earlier has been overcome by using external- instead of internal-conversion x rays. The present technique gives relative rather than absolute cross-section values, but is simpler and more accurate. The experimental results show fairly good agreement with theory, and no discrepancy between theory and experiment similar to the one reported for the $L$ shell has been found for photons in this energy region also.