The authors present a self-consistent approximation scheme for the calculation of the dynamical polarizability $\alpha (\overrightarrow{\mathrm{k}},\omega )$ at long wavelengths in strongly coupled one-component plasmas. Development of the scheme is carried out in two stages. The first stage follows the earlier Golden-Kalman-Silevitch (GKS) velocity-average approximation approach, but goes much further in its application of the nonlinear fluctuation-dissipation theorem to dynamical calculations. The result is the simple expression for $\alpha (\overrightarrow{\mathrm{k}},\omega )$, ${\alpha }_{\mathrm{GKS}}(\overrightarrow{\mathrm{k}},\omega )={\alpha }_{\mathrm{RPA}}(\overrightarrow{\mathrm{k}},\omega )[1+v(\overrightarrow{\mathrm{k}},\omega \left)\right]$, where the dynamical screening function $v(\overrightarrow{\mathrm{k}},\omega )$ is expressed in terms of quadratic polarizabilities, and RPA stands for random-phase approximation. Its zero-frequency limit $v(\overrightarrow{\mathrm{k}},0)$ has already been established and analyzed in the earlier GKS work. At high frequency, ${\alpha }_{\mathrm{GKS}} (\overrightarrow{\mathrm{k}},\omega \to \infty )$ exactly satisfies the $\frac{1}{{\omega }^4}$ moment sum rule. In the second stage, the above dynamical expression is made self-consistent at long wavelengths by postulating that a decomposition of the quadratic polarizabilities in terms of linear ones, which prevails in the $k\to 0$ limit for weak coupling, can be relied upon as a paradigm for arbitrary coupling. The result is a relatively simple quadratic integral equation for $\alpha$. Its evaluation in the weak-coupling limit and its comparison with known exact results in that limit reveal that almost all important correlational and long-time effects are reproduced by our theory with very good numerical accuracy over the entire frequency range; the only significant defect of the approximation seems to be the absence of the "dominant" $\gamma \ln {\gamma }^{-1\mathrm{}}$ ($\gamma$ is the plasma parameter) contribution to $\mathrm{Im} \alpha (\overrightarrow{\mathrm{k}},\omega )$.

Energy levels and lifetimes are calculated for the resonant states that are important in radiative single charge transfer in ${\mathrm{He}}^{2+}$-He collisions at thermal energies. The resonant contribution to the charge-transfer rate decreases with increasing temperature and is approximately 12% of the total rate at 300 K.

The authors determine $K$ x-ray production cross sections and $K$-shell fluorescence yields in solid Si and gaseous Si${\mathrm{H}}_4$ as a function of incident-projectile charge state for a F beam at 1 and 2 MeV/amu. Discrepancies between solid- and gas-target results are observed in both the x-ray production cross section and fluorescence yield. It is found, however, that the ionization cross section (x-ray production cross section divided by fluorescence yield) is independent of target physical state for each incident-projectile charge state.

A remarkably consistent ordering of excited atomic states with the quantity $k=n+l$, for small values of the orbital angular momentum $l$, was pointed out by Sternheimer. This fact is readily interpreted in terms of the variation of the quantum defects with $l$, and simple rules for the $k$ ordering are given. The reasons for the observed variation of the quantum defects can be understood in terms of the accumulation of zero-energy scattering phase shifts with $l$ and with $Z$, as calculated by Manson from a realistic atomic potential.

A classical model for fluorescent and Raman scattering by molecules embedded in small spherical particles has been formulated recently by Chew, McNulty, and Kerker, on the assumption that the dominant transitions are electric dipole transitions. In this Addendum results are given for those cases where the dominant transitions are magnetic dipole.

The heating of electrons in the stochastic electric field of a collisionless turbulent plasma by the multiphoton absorption of a laser beam is described from a quantum-mechanical viewpoint. A kinetic equation is derived and the change in kinetic energy of the electrons is calculated. The effective interaction frequency is found and compared to the effective collision frequency of multiphoton inverse bremsstrahlung for the strong laser beam. It is found that the rate of energy absorption is proportional to the inverse square root of the intensity of the laser beam and the average of the square of the turbulent electric field when the laser frequency is approximately equal to the electron plasma frequency.

Recoil corrections of order ${\left(Z\alpha \right)}^2\frac{m}{M}$, where $m$ and $M$ are muon and nuclear masses, to the ratio $R$ of free- to bound-muon lifetimes are calculated by means of an expansion in $Z\alpha$. As in the case of ${\left(Z\alpha \right)}^2$ corrections there are cancellations, but their physical interpretations are different in the two orders. The net result is $R=1-\frac{1}{2}{\left(Z\alpha \right)}^2-0.06\mathrm{}{\left(Z\alpha \right)}^2\frac{m}{M}$.

Calculations of the electronic energy of the Be-atom ground state are performed using a configuration-interaction technique and a nondegenerate formulation of diagrammatic many-body perturbation theory. Both methods are applied within the algebraic approximation defined by three finite-basis sets. One of the basis sets contains only $s$ functions, and it defines an algebraic problem without degeneracies where agreement between the two methods is excellent. The other two basis sets, although more complete, both contain $p$ functions, and they define algebraic problems involving a near degeneracy where agreement between the two methods is found to be less satisfactory. It is concluded that either a degenerate formulation of perturbation theory is required, or certain diagrams in the model perturbative scheme need to be summed to high order through denominator shifts in order to properly handle the nondynamic-correlation effect found in the Be atom.

Effective radial parameters of the magnetic dipole hyperfine interaction and $g_J$ values have been determined from atomic beam magnetic-resonance measurements in five metastable states of W. The contact-interaction parameters $a_{6s}$, important for hyperfine anomaly and Knight shift, are analyzed and tabulated for the $5d^{N}6s$ configurations.

The aim of this paper is to test a simple method for converting accurate nonrelativistic predictions of atomic properties into accurate relativistic predictions with a minimum of additional computational effort. The method connects smoothly the exact nonrelativistic $\mathrm{LS}$-coupling results appropriate at small $Z$ with the relativistic $\mathrm{jj}$-coupling results appropriate at large $Z$. For the processes stated in the title, the method appears to offer a significant improvement in accuracy over relativistic Hartree-Fock or random-phase-approximation calculations, particularly in the low and intermediate range of nuclear charge. For large $Z$, the present results agree well with the relativistic random-phase approximation.

We show that the usual Foldy-Wouthuysen reduced (to order $\frac{1}{c^3}$) and additive expression for the external electromagnetic interaction of a composite system of two weakly bound charged particles does not lead to relativistically invariant results to relative order $\frac{1}{c^2}$ for the one-photon radiative transitions, even when it is used with the relativistic c.m. variables. We also show how the interaction Hamiltonian should be modified so that it does lead to relativistically correct results (again to relative order $\frac{1}{c^2}$) at least in the first order of perturbation theory. The new interaction Hamiltonian $H_I$ can be obtained by the replacement of ${\overrightarrow{\mathrm{p}}}_{\mu }$ by [$({\overrightarrow{\mathrm{p}}}_{\mu }-(\frac{e_{\mu }}{c}){\overrightarrow{\mathrm{A}}}_{\mu }$] in the Breit Hamiltonian of the composite system. Consequences of the modified Hamiltonian in the calculation of relativistic corrections to the electric dipole transition amplitudes of the hydrogenlike mesic and electronic atoms and of the charmonium are discussed. We also compare our results with those of other comparable works. The new Hamiltonian $H_I$ can also be justified by considerations based on quantum electrodynamics.

Cross sections for the electron-impact excitation of the $2p_{\frac{1}{2}}$ and $2p_{\frac{3}{2}}$ states of the lithiumlike ions ${\mathrm{C}}^{3+}$, ${\mathrm{Fe}}^{23+}$, ${\mathrm{Mo}}^{39+}$, and ${\mathrm{W}}^{71+}$ are calculated in the relativistic Coulomb-Born approximation. A range of incident electron energies from the $2p_{\frac{1}{2}}$ threshold to (approximately) ten times the $2p_{\frac{3}{2}}$ threshold is considered. The most significant relativistic effects result from the spin-orbit splitting of the $2p$ states. An interpolation formula is presented which permits the estimation of these cross sections for similar ions of intermediate charges.

Thin solid Al targets ranging in thickness from ∼ 1 to 30 μg/${\mathrm{cm}}^2$ were bombarded by ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ions wih incident energies from 0.25 to 2.25 MeV/amu. The effects of target thickness on the measured A1 $K$ x-ray yield for ions incident without an initial $K$-shell vacancy were determined. Comparisons of the data for Al $K$ x-ray production in vanishingly thin targets (and 29-μg/${\mathrm{cm}}^2$ targets) were made to perturbed-stationary-state calculations (PSS) for O ions on Al targets. The PSS calculations contained corrections for Coulomb deflection and binding energy [PSS(CB)] and for Coulomb deflection, binding energy, and polarization [PSS(CBP)]. Further, two different PSS calculation procedures were employed: calculations without radial cutoffs employed in the binding-energy contribution (PSS), and calculations with radial cutoffs employed in the binding-energy correction (NPSS). The PSS(CBP) calculations agree with the measured A1 $K$ x-ray production cross section for data taken in the limit of a vanishingly thin target. The NPSS(CBP) calculations agree with the data taken for a 29-μg/${\mathrm{cm}}^2$ Al target. The latter agreement is fortuitous, as the increase observed in the measured target x-ray yield for the 29-μg/${\mathrm{cm}}^2$ target, in comparison to the yield extracted as $\rho x\to 0$ at each bombarding energy, is due to $K$-shell-to—$K$-shell charge exchange. Comparisons are made with previously published data for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ions incident on finite-thickness Al targets.

The $L_1-L_2{M}_{4,5}$ and $L_1-L_3{M}_{4,5}$ Coster-Kronig transition thresholds in the atomic-number region $37\le Z\le 56$ are determined by bombardment of these elements with 2.5-MeV ${\mathrm{H}}^{+}$ ions, and detection of the resulting $L$ x rays with a curved-crystal spectrometer. The intensities of both the $L\alpha$ and $L{\beta }_1$ satellites, along with the total intensities of the $L\alpha$, $L{\beta }_1$, and $L{\beta }_{3,4}$ x rays which are produced during these collisions, are dependent upon the energetic permissibility of these Coster-Kronig transitions. The discontinuous nature of the intensity ratios as functions of atomic number indicates that the $L_1-L_2{M}_{4,5}$ and $L_1-L_3{M}_{4,5}$ transitions are energetically allowed for the elements with atomic numbers in the regions $Z\le 39 or 40$ and $Z\le 49 or 50$, respectively.

In this paper the effects of nuclear scattering on the polarization of a beam of spin-½ particles are calculated. These first-order results include the effects of nuclear recoil and apply to elastic scattering by light, spin-0 nuclei at moderate energies. The net effect of the scattering is that the polarization vector is rotated through an angle $\beta$ about the normal to the scattering plane, in the same direction in which the momentum is rotated. The rotation of the polarization vector is less than that of the momentum by an angle given by $cos (\theta -\beta )=\frac{[1-{\left(\frac{m}{\epsilon }\right)}^2{tan}^2(\frac{\theta }{2}\left)\right]}{[1+{\left(\frac{m}{\epsilon }\right)}^2{tan}^2(\frac{\theta }{2}\left)\right]}$, where $\theta$ is the scattering angle and $\epsilon =E+\frac{(E^2-m^2)}{\tilde{E}}$, with $m$ and $E$ denoting the mass and energy of the scattered particle and $\tilde{E}$ the energy of the recoiling nucleus. The magnitude of this effect is illustrated for the scattering of muons from helium at several incident energies.

For 50-300-keV ${\mathrm{He}}^{+}$ and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}_{}^{+}{}_{}{}^{}$ in C, Al, Cu, Ag, and Au, the applicability of the simplified stopping function is investigated. Using the same targets for ${\mathrm{He}}^{+}$ and ${\mathrm{Li}}^{+}$ the electronic stopping power $S_e$ in 400-800-Å foils is measured by means of a magnetic spectrometer. The resulting stopping fractions $\frac{S_e\left(\mathrm{Li}\right)}{S_e\left(\mathrm{He}\right)}$ can be evaluated to an error of 2%. At energies above 20 keV/amu they are found to be independent of the target material. Applied to our experimental data, the simplified stopping function is shown to be a good approximation in connection with the fits of Andersen-Ziegler for $S_e$ (H) and the stopping ratios.

Absolute total cross sections for single- and double-electron capture by ${\mathrm{H}}^{+}$ in collisions with Mg and Ba have been measured for energies between 1 and 100 keV. The single-electron-capture cross section has also been calculated with the Gryzinski formalism of the classical binary-encounter approximation. The measured cross sections exhibit both high- and low-energy structure. The high-energy behavior is in accord with the Brinkman-Kramers results and classical predictions for the energy at which inner-shell capture becomes important. The low-energy behavior is discussed in terms of a molecular picture of the collision. The cross sections are shown to be critically dependent on curve-crossing effects which occur at avoided crossings between potential curves. At low energies the double-electron-capture cross section in Mg shows pronounced structure consistent with a description of the collision in terms of transitions via the intermediate H ($1s$) state. It is shown that this mechanism is not important in Ba, since curve crossings are expected to take place at internuclear separations too large for transitions to occur. A possible explanation for the decrease in single-electron-capture cross section in Ba at low energies is suggested in terms of competition from direct target-excitation collisions. For single-electron capture in Mg, recent low-energy perturbed-stationary-state calculations and high-energy classical-trajectory Monte Carlo calculations by Olson and Liu are in good agreement with experiment. The present classical binary-encounter approximation results for single-electron capture in both Mg and Ba agree with experiment to within a factor of 2 over the entire energy range. Measurements of single- and double-electron capture are also reported for Ar targets. A pronounced second maximum in the double-electron-capture cross section is found.

This work presents a multifaceted experimental and theoretical study of collisions of ${\mathrm{Na}}^{+}$ ions in the energy range 0.2-12 keV with Ne atoms. Four different collision experiments are reported here. With one, doubly differential cross sections in scattering angle and energy loss were obtained by electrostatic analysis for direct collisions in the energy range 0.5-3.0 keV. With a second, energy-loss spectra for the neutral component of the scattered beam were obtained by time-of-flight techniques. With a third, energy spectra of electrons ejected by autoionization decays were obtained in the impact energy range 0.5-12 keV. Finally, in a fourth experiment, cross sections were obtained for some important Neii transitions excited by collisions in the energy range 0.2-10 keV. The results of these four experiments are combined with results from previous investigations to give detailed information on the relative role of the various one- and two-electron excitation processes. The interpretation of the experimental findings is carried out within the quasimolecular framework and is based on the results of ab initio calculations for a variety of potential-energy curves of the ${\mathrm{}(\mathrm{N}\mathrm{a}-\mathrm{N}\mathrm{e})\mathrm{}}^{+}$ quasimolecule. It is shown that the observed processes are induced by a succession of independent transition mechanisms, namely, (i) primary single and double excitation of $\mathrm{Ne}2p$ electrons at curve crossings of the $4f\sigma$ molecular orbital with empty $\sigma$ orbitals, (ii) $\sigma \to \pi$ population transfer via rotational coupling, (iii) core rearrangement processes ($L$-vacancy sharing), and finally (iv) outer-electron (Rydberg) sharing. The estimation of the importance of the different mechanisms is made using simple models (Landau-Zener, Demkov-Meyerhof) and extrapolations of previous theoretical and experimental results on the isoelectronic Ne-Ne system. Special attention has been focused on the production of $\mathrm{Ne}\left(2\mathrm{}{p}^{5}3p\right)$ triplet states, where it is demonstrated that simultaneous excitation of both target and projectile can well account for the Ne triplet excitation without invoking a breakdown of the Wigner spin-conservation rule.

The quantum-defect-theory (QDT) treatment of an electron in the Coulomb field surrounding an ionic core is recast in a form largely independent of field characteristics and thus applicable, e.g., to square wells or to the Morse fields of diatomic molecules. The reformulation parallels Seaton's classification of alternative Coulomb-field wave functions, and makes it applicable to other fields. Wronskians of alternative pairs of base functions have an important role in the theory. For electron energies $\epsilon <0\mathrm{}$ in a Coulomb field these Wronskians reduce to trigonometric functions of $\nu ={(-2\mathrm{}\epsilon )}^{-\frac{1}{2}}$, familiar in the QDT; other fields lead to trigonometric functions of different arguments. Quantum defects are generalized to eigenvalues of a reaction matrix, as in Seaton's work, but this matrix can now be calculated even below threshold energies with the introduction of a "smooth" Green's function appropriate to QDT applications.

A three-state, two-center atomic expansion method is used to investigate double-electron capture from the $K$ shell of multielectron atoms to the $K$ shell of projectiles in the energy region where the projectile velocity is nearly equal to the orbital velocity of the target $K$-shell electron. By adopting an independent-electron approximation, the Coulomb interaction between the two electrons is replaced by monopole terms with a screening charge. The validity of this approximation is checked by comparing the cross sections for double capture in $p$-He and ${\mathrm{He}}^{++}$-He collisions obtained from this method with other theoretical calculations and experiments. Double-electron-capture cross sections from the $K$ shell of Ne atoms by ${\mathrm{F}}^{9+}$, ${\mathrm{O}}^{8+}$, and ${\mathrm{N}}^{7+}$ ions are then calculated; the results are shown to compare well with the neon Auger hypersatellite intensities measured by Woods et al.