The three leading strongly coupled plasma approximation schemes are compared: Their implications as to the three-particle correlation function and the quadratic polarizability are established.

The work of Gau and Macek on large-angle inelastic electron-hydrogen scattering in the unrestricted Glauber approximation is extended to electron-helium scattering. "Unrestricted" in this context means that we do not make the additional approximation of purely transverse linear-momentum transfer. Once again, we find at large angles for $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\to 2{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ collision-induced transitions the electron-nucleus interaction dominates and has a $q^{-4\mathrm{}}$ behavior in the differential cross section. Further, we calculate the orientation parameter $O_{1-}^{\mathrm{col}}$.

An analytic expression is derived for the energy spectrum of hydrogenlike atoms in an intense radiation field, which is valid up to intensities for which $R_0\ll \mathrm{a}$ Bohr radius, where $R_0$ is the amplitude of the classical displacement of a free electron in the radiation field.

A $Z$-expansion procedure is used to obtain eigenvalues and eigenfunctions for the $1s^{2}2s^2{}_{}{}^1{}_{}{}^{}S$, $1s^{2}2p^2{}_{}{}^1{}_{}{}^{}S$, and $1s^{2}2s2p{}_{}{}^1{}_{}{}^{}P$ states of the beryllium isoelectronic sequence. The degeneracy effects associated with the $1s^{2}2s^2{}_{}{}^1{}_{}{}^{}S$ and the $1s^{2}2p^2{}_{}{}^1{}_{}{}^{}S$ states are included to every order in the perturbative procedure. $Z$ expansions of the dipole length and dipole velocity forms of the oscillator strength for the $1s^{2}2s^2{}_{}{}^1{}_{}{}^{}S-1\mathrm{}{s}^{2}2s2p {}_{}{}^1{}_{}{}^{}P$ and $1s^{2}2s2p{}_{}{}^1{}_{}{}^{}P-1\mathrm{}{s}^{2}2p^2{}_{}{}^1{}_{}{}^{}S$ transitions are compared with the results of calculations using individual values of the nuclear charge $Z$.

The hyperfine structure of the second-excited $D$ states of ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$, ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$, and ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$ has been measured by the method of cascade-radio-frequency spectroscopy and cascade-level crossing. The sign of the magnetic-dipole coupling constant $A$ is determined by the method of cascade-decoupling and cascade-radio-frequency spectroscopy with narrow-band excitation. Lifetimes $\tau$ of some of these states are measured by the cascade-Hanle effect. We find that for ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$, $A\left(5\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\right)=14.43\mathrm{}\pm 0.23$ MHz, $A\left(5\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}\right)=-7.44\mathrm{}\pm 0.10$ MHz, $\tau \left(5\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\right)=205\mathrm{}\pm 40$ nsec; for ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$, $A\left(5\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\right)=4.18\mathrm{}\pm 0.20$ MHz, $A\left(5\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}\right)=-2.12\mathrm{}\pm 0.20$ MHz; for ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$, $A\left(6\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\right)=16.30\mathrm{}\pm 0.15$ MHz, $A\left(6\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}\right)=-3.6\mathrm{}\pm 1.0$ MHz, $\tau \left(6\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\right)=57\mathrm{}\pm 15$ nsec.

Electron-positron vacuum polarization potentials, accurate to all orders $n$ in ${\left(Z\alpha \right)}^n$, are calculated using realistic nuclear charge distributions for selected nuclei with $26\le Z\le 114$, and for the quasimolecule U-U. We give further details of the numerical methods used in calculations previously reported, and of the improvements which have led to the present increased accuracy. The vacuum polarization potentials are employed to determine muonic energy-level shifts [order ${\left(Z \alpha \right)}^{n\ge 1}\alpha$] for most relevant states with $l\le 6$. For the shifts of order ${\left(Z \alpha \right)}^{n\ge 3}\alpha$, interpolation procedures for all values of $Z<\mathrm{}137\mathrm{}$ and for other exotic particles are noted. Although the effect of finite nuclear size is small for high-lying states (∼10% reduction of the ${\left(Z \alpha \right)}^{n\ge 3}\alpha$ terms in heavy atoms), it yields a reduction by a factor ≳ 2 for low-lying states. In the case of the quasimolecule U-U, we find that the total vacuum polarization is a minor correction to the dominant Coulomb interaction, with the first-order (Uehling) contribution remaining much larger than the higher-order terms. We also present further details of a previous calculation of order ${\left(Z \alpha \right)}^2{\alpha }^2$ in muonic lead.

The method of $K$ harmonics, which has been successfully used to find some of the basic characteristics of a nucleus, is applied to determine the ground-state energy of the positronium negative ion, $e^{-}{e}^{+}{e}^{-}$. Retaining $K$ harmonics up to $K=2\mathrm{}$ in the expansion for the wave function, the ground-state energy comes out as -0.256 (in a.u.). The energy value improves to -0.259 when the $K$ harmonics up to $K=4\mathrm{}$ are included.

A recently developed variational formalism for the determination of the reduced single-particle density matrix, correct to second order, is applied to the ground state of the helium isoelectronic sequence. For a Slater-determinant-type trial wave function the method requires the initial determination of either the charge density or equivalently its cosine Fourier transform for spherically symmetric systems. The trial wave function employed is a one-parameter Hartree product of hydrogenic functions and use is made of the highly accurate analytic expressions derived elsewhere for the Fourier transform of the charge density for the helium sequence. Analytic expressions for the single-particle density matrix are obtained and the internal self-consistency of the technique with regard to the Kato cusp condition is discussed. These ex pressions are then employed to obtain closed form analytic expressions for the momentum density valid for the entire isoelectronic sequence. These results are subsequently employed to obtain expressions for the expectation values of the operators $p^4$, $p^2$, $\mathrm{}\left|p\right|\mathrm{}$, and ${\mathrm{}\left|p\right|\mathrm{}}^{-1\mathrm{}}$ and the Compton profile in the impulse approximation. Analytic Hartree-Fock calculations for these properties are also performed, and the results of the variational calculation are compared with these results and those of many-parameter correlated wave-function calculations wherever possible. It is observed that the results of the single-parameter variational calculation for helium are highly accurate and improve further for each heavier element of the isoelectronic sequence.

The diffusion coefficient for thermal electrons in neon has been measured by the direct sampling technique of Cavalleri. The result is compared with recent experimental determinations, which show a large scatter by comparison with similar data in other gases, and with values calculated using theoretically derived cross sections. There is satisfactory agreement with the value calculated using a cross section that has been derived from drift-velocity data through a direct application of modified effective-range theory. An analysis of the effects of Penning ionization on the measurement has been made from which the lifetime of the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ neon metastable has been estimated.

A tractable form of the Faddeev equations as used by Chaudhuri et al. has been applied to the proton-hydrogen collision problem, retaining $1s$ and $2s$ states of the hydrogen atom in the expansion. To judge the effect of the proton interaction on the capture cross sections, calculations have been carried out with and without the inclusion of this interaction. The results for the $1s-2s$ capture and excitation cross sections are presented together with the elastic and ground-state capture cross sections. The present results have been compared with experimental findings and other theoretical results.

Numerical solutions of close-coupling equations from the Dirac Hamiltonian, without including the correlation and Lagrangian multiplier terms, are obtained by the method of outward and inward integrations, analogous to the one used in the nonrelativistic calculation. As an illustrative example, we present the results of electron-cesium scattering for $J=0\mathrm{}$.

The vibrational-rotational excitations of the ${\mathrm{}\left(\mathrm{HeH}\right)\mathrm{}}^{+}$ molecular ion by collisions with positrons have been studied by using a semiclassical first-order time-dependent perturbation theory based on the theory of Coulomb excitations of nuclei. The energy of the impinging positrons has been confined to a range for which the trajectories are nonpenetrating. Calculations have been performed for the vibrational excitations 0 → 1 and 0 → 2, accompanied by various rotational excitations. The results show the comparatively large contributions of the dipole term in the multipole expansion of the interaction potential to the vibrational excitation of the ${\mathrm{}\left(\mathrm{HeH}\right)\mathrm{}}^{+}$ ion.

The elastic scattering of electrons by lithium atoms is considered in the Glauber approximation using Franco's method for reducing the (3Z + 2)-dimensional integral occurring in the amplitude for the scattering of charged particles by a $Z$-electron atom. It is found that the involvement of the inner electrons (those in the $1s$ state) causes very little change over the frozen-core Glauber calculations.

The single-electron capture cross section ${\sigma }_{10}$ for ${\mathrm{He}}^{+}$ ions on magnesium and lead vapors has been measured in the energy range 9-40 keV. The results are not in agreement with the conventional near-adiabatic criterion of Massey regarding the energy at which the cross sections ${\sigma }_{10}$ are maxima. This is thought to be due to pseudocrossing of potential-energy curves. Cross sections for Mg are found to be larger than for Pb in spite of the fact that both targets have very similar ionization potentials for their outer electrons.

Low-energy rotational-excitation cross sections have been calculated from model-potential surfaces constructed to represent the interaction of atomic helium with hydrogen fluoride (HF). Quantum-mechanical solutions of the coupled equations were obtained including as many rotational states (open and closed) as needed for convergence. The behavior of the cross sections as a function of energy and the sensitivity to various model-potential surfaces are discussed.

The reduction method developed previously for many-particle scattering is applied here to derive new sets of coupled equations for electron scattering from atomic targets at low energies, fully taking into account the exchange effect and target distortions. The reduced matrix equations have simpler structure than the Faddeev-Watson equations, with the iteration kernels connected only in those channels which are explicitly taken into account. Scatterings by atomic hydrogen, helium, and lithium targets are considered, and the resulting formalism is compared with the earlier work of Faddeev and others. Various approximation procedures are described, and their applicability is tested on the electron-hydrogen scattering system.

The charge-exchange amplitude for the proton-hydrogen collision in the energy range 25-800 keV is calculated in the distorted-coupling Born approximation. The analysis is based on a reduced form of coupled equations of the Faddeev-Watson type, which was derived previously for the general manyparticle scattering. The effective distortion potentials which appear in these equations are determined by minimization of the coupling between the elastic and inelastic excitation channels. The result provides a mathematical basis with which various previous calculations can be compared. The present study strongly supports the applicability and effectiveness of the reduced-matrix equations in treating the rearrangement processes.

Quantum close-coupled calculations are performed for a model two-state curve-crossing problem that was previously treated by a semiclassical analysis. Excellent agreement in the differential cross sections is obtained. The interference structure on the elastic cross sections can be physically interpreted by using only the classical deflection functions of the adiabatic and diabatic potential curves and the interferences between them.

The Van der Waals potentials between heavy alkali-metal atoms (Cs, Rb, K) and gold surfaces have been investigated by the atomic-beam-deflection technique. The result is consistent with a potential of the form $V\left(R\right)=-\frac{k}{R^3}$. The observed interaction constant $k$ is 7.0 ± 0.29 ${\mathrm{D}}^2$, 6.04 ± 0.30 ${\mathrm{D}}^2$, and 5.10 ± 0.62 ${\mathrm{D}}^2$ for Cs, Rb, and K, respectively. These values are smaller than the predictions based on all available theories. At best there is agreement within 60% for estimates based on the macroscopic continuum theory of Lifshitz. Other models disagree with measurements by factors of three (200% difference) or more.

Angular bremsstrahlung cross sections are computed with a point-Coulomb potential. In this calculation, the Dirac equation is expanded in partial waves, the radial functions are the classical ones, and the amplitude is given in an analytical form. We give some curves for the energy range 50 keV-2.5 MeV and for the case $\frac{k}{T}\ge 0.8$, where screening effects are small ($T$ is the kinetic energy of the incident electron, and $k$ refers to the emitted photon). In particular, we consider the tip region of the bremsstrahlung spectrum at 1.84 MeV according to the experiment of Starek, Aiginger, and Unfried. The discrepancy between experimental and theoretical results is very large for low $Z$.