The author points out that previous measurements of the fine and hyperfine structure of ${}_{}{}^{6,7}{}_{}{}^{}\mathrm{Li}$ii by Bacis and Berry are in agreement with theory, in contradiction to the criticism of Fan et al.

An analysis is made of the theory of Van der Waals interaction between atoms by means of linear-response theory. It is shown that the spread of the atomic wave functions leads to removal of divergences at close distances in the interaction in a natural way, while asymptotic large-distance behavior remains unchanged, being of the London form.

The author discusses a recent paper by Fortner and Garcia in which these workers analyze thick-target x-ray yields and spectra and derive populations of projectile inner- and outer-shell vacancies, and concludes that some effects which were not considered should be taken into account in any such analysis. These include the generation of target x rays by recoiling target atoms, vacancy sharing, collisional quenching and the effect of differences in the wave functions of outer-shell electrons, x-ray energies, and transition rates in solids as compared with gases.

The assumptions used in a previous study on the analysis of characteristic x rays emitted by a projectile while traversing a solid are reexamined. New information, in addition to accompanying comments by another author, is considered. While more work is needed on the subject, it is concluded that these new studies support the potential use of characteristic x rays as diagnostic tools for the study of ions traveling through solids.

An improvement upon Salpeter and Van Horn's relaxed-lattice model is made by taking into account the quadratic screening potential near zero separation. Implications of a recent experiment on dense plasmas are found to support the lattice model.

Energy curves have been calculated for low-lying states on ${\mathrm{Sn}}_2$ and ${\mathrm{Pb}}_2$ by means of the density-functional formalism. Remarkably similar results can be obtained by representing the core by a simple local pseudopotential. With these and our earlier results for ${\mathrm{C}}_2$-${\mathrm{Ge}}_2$, trends in this series are discussed, with particular reference to the tails of the atomic $s$- and $p$-valence functions. An immediate consequence is an understanding of the special nature of the C-C bond.

The importance of the interaction between $4s4d{}_{}{}^1{}_{}{}^{}D$ and $4p^2{}_{}{}^1{}_{}{}^{}D$ is studied in the Zn I isoelectronic sequence from Zn I to W XLV. Multiconfiguration Hartree-Fock calculations have been carried out for the two lowest ${}_{}{}^1{}_{}{}^{}D$ terms in this sequence and used to calculate $\mathrm{gf}$ values for the ${}_{}{}^1{}_{}{}^{}P-{}_{}{}^1{}_{}{}^{}D$ transitions. For the heavier elements relativistic effects are important and intermediate-coupling calculations of the $\mathrm{gf}$ values using multiconfiguration Dirac-Hartree-Fock transition energies have been carried out. Final $\mathrm{gf}$ values take into account relativistic effects in an approximate way, as well as core-polarization effects. The latter are found to be as important for the ${}_{}{}^1{}_{}{}^{}P-{}_{}{}^1{}_{}{}^{}D$ transitions as for the ${}_{}{}^1{}_{}{}^{}S-{}_{}{}^1{}_{}{}^{}P$ resonance transition even for high-ionization stages. The $\mathrm{gf}$ values for transitions from the lowest ${}_{}{}^1{}_{}{}^{}D$ terms were found to be small due to destructive interference. Little experimental data exist with which the present results can be compared. Furthermore, it is shown that much of the earlier experimental material concerning the ${}_{}{}^1{}_{}{}^{}D$ terms are in error. Comparison with a few very recent experimental investigations shows good agreement, however, and the present results point to the need for further experimental studies of this sequence, even towards the neutral end.

An improved method for calculating magnetic fine structures in helium Rydberg states is developed and the results are compared with previous calculations and with existing precise experimental determinations. Agreement with experiment is markedly improved in $D$ manifolds, but systematic anomalies in $F$ and $G$ manifolds remain unexplained. Relativistic and mass-polarization contributions to electric fine structure are evaluated and found to be significant at the same order as recently calculated radiative corrections. Agreement with experimental determinations is no better than about 1%.

Five-state close-coupling equations for electron-helium scattering are solved in the energy region from 30 to 100 eV. Integral and differential cross sections for excitation of the ground state to the $n=2\mathrm{}$ states $2{}_{}{}^3{}_{}{}^{}S$, $2{}_{}{}^1{}_{}{}^{}S$, $2{}_{}{}^3{}_{}{}^{}P_{}^0{}_{}{}^{}$, and $2{}_{}{}^1{}_{}{}^{}P_{}^0{}_{}{}^{}$ are presented. Calculated shapes of differential cross sections versus angle for various energies are in fair agreement with measurements, but the magnitudes of the cross sections are overestimated. Allowance for coupling between $2{}_{}{}^3{}_{}{}^{}S$ and $2{}_{}{}^3{}_{}{}^{}P_{}^0{}_{}{}^{}$ brings calculated differential cross sections into good quantitative agreement with experiment.

Sternheimer shielding functions $\gamma \mathrm{}\left(r\right)\mathrm{}$ are derived by means of Sternheimer's procedure for a series of elements (Li, Na, K, Rb, F, Cl, Br, I, Cu, Fe, Ag, and Pr) with varying electronic configurations, with and without valence electrons, which are generally included in molecular-orbital calculations with a limited basis set. Direct and exchange contributions to $R=\frac{〈\gamma \mathrm{}\left(r\right)\mathrm{}{r}^{-3\mathrm{}}〉}{〈r^{-3\mathrm{}}〉}$ are presented, and the various contributions to $\gamma \mathrm{}\left(r\right)\mathrm{}$ due to angular and radial excitations are discussed. The discrepancy in $R$ values for halides compared to Sternheimer's values is due mainly to an exchange contribution to $R$ which has been omitted by Sternheimer. Self-consistent calculations of $\gamma \mathrm{}\left(r\right)\mathrm{}$ have been performed with and without $X\alpha$ exchange interaction. The general tendency of self-consistent ${\gamma }_{\infty } [={\lim }_{r\to \infty }\gamma \mathrm{}(r\left)\right]$ results is that direct Coulomb interaction leads to ${\gamma }_{\infty }$ values more positive than those derived from Sternheimer's procedure (noniterative and excluding exchange interaction), while exchange interaction partly balances this effect. The overall effect in the case of iron is that Sternheimer's value is nearly identical to our self-consistent ${\gamma }_{\infty }$ value including exchange contributions. Self-consistency was obtained only for neutral atoms and positive ions. However, no such self-consistency was obtained for negative ions. Thus the $X_{\alpha }$ approximation is not very appropriate for the present purpose of calculating $\gamma \mathrm{}\left(r\right)\mathrm{}$ for elements with varying electronic configurations.

The authors tested several approximations commonly used in molecular energy calculations by applying them to the six-site half-filled Hubbard model and comparing the results with the exact solution. Three main conclusions follow from this study: (i) for $\frac{\beta }{U}$ in the range of interest for molecules, perturbations to the molecular-orbital ground state produce better results than the other more elaborate methods tested; (ii) Nesbet's pair theory is only slightly worse in this range but has the advantage of working well for all values of the parameters, and (iii) perturbative corrections to the unrestricted Hartree-Fock ground state give very poor results when this state has lower symmetry than the Hamiltonian.

Gauge transformations on the wave function are formulated in second quantization, and it is shown that the Schrödinger equation in second quantization is form invariant under local gauge transformations. Hartree-Fock theory is examined in the second-quantization formalism and shown to be gauge invariant in spite of being nonlocal, contrary to recent reports. Rowe's equation-of-motion method, of which the random-phase approximation is a special case, is also shown to be gauge invariant. The length and velocity forms of the dipole oscillatory strengths are shown to be equal in Rowe's theory under certain conditions, which the random-phase approximation satisfies.

We present the details of our calculation of radiative corrections affecting the two-photon virtual-annihilation contributions to the positronium hyperfine splitting in order $m{\alpha }^6\left({\alpha }^4{R}_{\infty }\right)$. Our result, which is obtained in analytic form, is $\Delta E_{2\gamma }^A\left({\alpha }^4{R}_{\infty }\right)=-13.13\mathrm{}$ MHz. We point out the gauge invariance of the result and demonstrate the cancellation of potential infrared contributions which appear at intermediate stages of the calculation.

The density equation proposed by Nakatsuji assumes a matrix form when a basis set is introduced. The matrix equation is shown to have highly degenerate solutions for almost any value of the energy, and thus to provide little useful information in the absence of $N$-representability constraints. The imposition of such constraints is also considered, and approximate constraints are predicted to be of little value.

Cu $K$ x-ray production cross sections for 1.7-MeV/amu C, N, O, and F ions were determined in the limit of vanishingly thin solid Cu targets. These data were used in a systematic study of the $Z_1$ dependence of Cu $K$ x-ray production for projectiles from H to Cl at 1.7 MeV/amu. Studies of the energy dependence of Cu $K$ x-ray production for F ions at 1.7, 2.0, 2.2, and 2.5 MeV/amu were also made for incident projectiles with 0, 1, and 2 initial $K$-shell vacancies. These data require the inclusion of electron transfer from the target $K$ shell to the projectile in addition to direct ionization of the target in order to explain the charge-state and $Z_1$ dependences of the x-ray-production cross sections.

The "molecule" positronium hydride (PsH), consisting of one atom each of positronium and hydrogen, has one well-known particle-stable state of total energy $E=-1.575\mathrm{}$ Ry. In addition, for each $L$ it must have an infinite Rydberg series of excited states whose principal configuration is ($e^{+}{\mathrm{H}}^{-}$), converging to a limit at $E=-1.0555\mathrm{}$ Ry, the energy of ${\mathrm{H}}^{-}$. All of these excited states are energetically able to dissociate into ground-state Ps + H, and the higher-lying states can also decay with emission of excited Ps and ground-state H. These Rydberg states should appear as resonances in Ps + H scattering. In this paper I compute the lowest $S$-wave resonance parameters, using an optical-potential formalism based on the ($e^{+}{\mathrm{H}}^{-}$) configuration. The results are in rough agreement with those previously obtained using Kohn variational or complex-rotation techniques with highly correlated trial functions. The physical description of the PsH excited states is thus clarified.

We present results of various model calculations for the density-matrix elements of hydrogen excited by electron impact. These density-matrix elements are discussed in terms of expectation values of physically understandable observable multipole moment operators and their time derivatives, thereby enabling us to isolate and understand central features of the collision dynamics hidden in the off-diagonal density-matrix elements. The strengths and weaknesses of these various scattering models, including plane-wave Born, distorted-wave Born, Glauber, classical trajectory, quasiclassical close-coupling, and close-coupling approximations are pointed out. The effects of angular momentum barriers, the impulsive nature of excitation, the mixing and splitting of degenerate energy eigenstates of the final state manifold, and the various ranges and times of the interactions occurring durng the collision are described. We observe that perturbative scattering models are inappropriate to describe certain of these multipole, even at very high energies. Experiments which determine these multipole-moment parameters are discussed.

Cross sections for charge transfer and impact ionization in ${\mathrm{O}}^{8+}$ + H collisions have been calculated in the range of collision velocities (0.1-10) × ${10}^8$ cm/sec. At the lower velocities, up to 1.2 × ${10}^8$ cm/sec, charge-transfer cross sections were determined by means of the perturbed-stationary-state method in the impact-parameter approximation with a selective basis set of adiabatic one-electron two-center orbitals. The charge-transfer cross section increases monotonically in this region, attaining a value of 8 × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ at 1.2 × ${10}^8$ cm/sec. Rotational coupling was found to be an important mechanism which contributes significantly to the large cross sections in the molecular regime. Thus the present results are at least a factor of 2 larger than previous Landau-Zener calculations. Above 2.2 × ${10}^8$ cm/sec, a classical-trajectory Monte Carlo approach was used to compute both charge-transfer and ionization cross sections. At velocities above 5 × ${10}^8$ cm/sec, ionization becomes the dominant electron-removal process.

The $L$-subshell ionization cross sections for tungsten have been measured for incident electron beams of low energies. The electron energy was in the range of $1<\mathrm{}\frac{E}{I_{L_i}}\le 4$. The values of the three $L$-subshell cross sections ${\sigma }_{L_1}$, ${\sigma }_{L_2}$, and ${\sigma }_{L_3}$ were deduced from the thick-target yields of $L{\beta }_3$, $L{\beta }_1$, and $L{\alpha }_1$ x rays of tungsten. A differential method was employed in the deduction procedures. The x-ray spectra were obtained by an improved version of a single-crystal, high-angle goniometer. The shape of the energy dependence of the measured cross sections deviates from the predictions given by McGuire's scaling result as well as Gryzinski's classical scaling result.