An expression for the wave-vector and frequency-dependent orbital susceptibility (${\chi }^{\mathrm{orb}}$) of an interacting electron gas is derived using the "moment-conserving" method. In the static long-wavelength limit, ${\chi }^{\mathrm{orb}}$ is computed and compared with the corresponding "random-phase approximation" (RPA) result reported recently by one of us. The corresponding spin susceptibilities (${\chi }^{\mathrm{sp}}$) computed in the moment-conserving method and RPA agree. Since the moment-conserving method gives positive structure factor up to ${\mathcal{r}}_s\stackrel{\sim }{<}3$, it may be concluded that the results of the calculations based on the variational solutions of the vertex equations are valid up to ${\mathcal{r}}_s\stackrel{\sim }{<}3$.

Standard variational methods are shown to contain the information necessary to construct the Jost function, a quantity which was previously shown to yield readily to interpolation. This allows narrow resonances to be found and characterized without extensive explicit computations.

Excitation of hydrogen atoms from the ground state to $2s$, $2p$, $3s$, $3p$, and $3d$ states in passing through alkali-metal atoms has been studied using the Born approximation. The form-factor description of the target and the generalized-oscillator-strength representation of the projectile has been used.

$1S-2P$ multiphoton transition amplitudes are calculated for hydrogen atoms in the presence of an intense electromagnetic field. Nonlinear behavior of the transition amplitudes appears as in the case of $1S-2S$ transitions considered earlier.

A method for calculating static dipole polarizabilities of atoms within a multiconfigurational self-consistent-field (SCF) framework is presented. The method involves the direct solution of the multiconfigurational SCF equations of an atom in the presence of a perturbing field which is simulated by a charged particle. The use of a multiconfigurational framework allows this technique to be applied straightforwardly to any given state of both degenerate and nondegenerate atoms, and also allows the explicit introduction of correlation effects. Sample calculations are reported for the static dipole polarizabilities of the carbon atom in its ${}_{}{}^1{}_{}{}^{}S$, ${}_{}{}^1{}_{}{}^{}D$, and ${}_{}{}^3{}_{}{}^{}P$ states with partial inclusion of correlation. The results are compared with those obtained from many-body perturbation theory, and other techniques. In addition, a prescription for specifying a sufficiently flexible set of polarization basis functions is described.

The contributions from the three spin-dependent Breit operators in second-order perturbation theory are calculated when the symmetries of the intermediate states are odd ${}_{}{}^1{}_{}{}^{}P$ or ${}_{}{}^3{}_{}{}^{}D$. Standard Hylleraas expansions with up to 165 terms are used for the perturbations of the wave functions. The large interval of the fine structure of the $2{}_{}{}^3{}_{}{}^{}P$ level in helium is increased by 2.17(2)×${10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ by ${}_{}{}^1{}_{}{}^{}P$, and by 0.0089(6)×${10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ by ${}_{}{}^3{}_{}{}^{}D$. Two methods for handling angular integration over $D$ tensors are described.

The Zr $L$ x-ray emission spectrum, obtained by means of photoelectron spectrometry, is interpreted in terms of the initial distribution of single and multiple vacancies, and radiative, Auger, and Coster-Kronig processes. The model calculation reproduces satisfactorily the salient features, such as relative intensities of satellites and emission branches from $L_1$, $L_2$, and $L_3$ subshells. Subshell-vacancy distribution produced by 9-keV electrons is found to be $L_1:L_2:L_3\approx 0.9:1:2$. Satellites are categorized according to calculated energy differences between diagram and satellite lines, and one class of satellites is found to coincide with diagram lines. Theoretical total rates of Auger transitions are corroborated by measured linewidths, but rates of Coster-Kronig transitions are too high by a factor of about 2. Finally, x-ray transition rates of the $K$ and $L$ series of Zr are calculated in a central-potential model using relativistic Hartree-Slater wave functions. Values agree excellently with Scofield's values. Theoretical and experimental branching ratios of x rays from $L_1$, $L_2$, and $L_3$ subshells are in satisfactory accord.

In many of the usual methods of calculating scattering amplitudes, a basis set is chosen in which to expand the wave function, and then the coefficients are optimized. We ask here, how does one, in addition, optimize the basis set. A natural outgrowth of the formalism is the concept of an "average inelastic channel" which could, under certain circumstances, be interpreted as a collective mode of excitation of the target.

Ten lines in the range $3880\leqq \lambda \leqq 5666$ Å in the beam-foil spectrum of iron have been identified with specific hydrogenic transitions in Fe iv-viii. The same transitions were observed from Ni and Ar beams. Deviations from the hydrogenic wavelengths are shown to be consistent with that expected from core polarization. The absence of these lines in astrophysical sources is discussed. A wavelength table is presented for identification of hydrogenic transitions to be expected in beam-foil spectra.

Ensemble averages are used to define energy functionals for open-shell atoms. Orbital equations and effective potentials for a Hartree-Fock procedure are derived and compared to the hyper-Hartree-Fock method. Total energies and orbitals have been calculated for the atoms Cr, Fe, Co, and Ni. Effective interaction parameters for valence-shell electrons are defined and evaluated.

The anisotropies $\gamma ={\alpha }_{\parallel }-{\alpha }_{\perp }$ of the static electric polarizabilities of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ were measured in a molecular-beam magnetic-resonance experiment. The quadratic Stark shifts of the separated-oscillatory-field resonances in the ground electronic and vibrational and $J=1\mathrm{}$ rotational states were measured in parallel electric and magnetic fields. The results are $\gamma \left({\mathrm{H}}_2\right)=0.3016\mathrm{}\pm .0005$ ${\mathrm{\AA }}^3$ and $\gamma \left({\mathrm{D}}_2\right)=0.2917\mathrm{}\pm .0004$ ${\mathrm{\AA }}^3$, which agree very closely with theory. A previously measured combination of the spin-rotation and quadrupole-interaction constants of ${\mathrm{D}}_2$ was independently remeasured, and the dependence upon orientation of the nuclear magnetic shielding of ${\mathrm{D}}_2$ was found to be ${\sigma }_{\pm 1}-{\sigma }_0=-11\mathrm{}\pm 9$ ppm. An efficient electron-bombardment detector was constructed for this experiment.

Vibration-rotation interactions in the motion of tetrahedral molecules, which are conventionally nonpolar in their ground vibrational and electronic states, permit pure rotational transitions. These transitions, which are electric dipole in nature, occur at microwave frequencies for the following changes in rotational quantum numbers: $\Delta J=0\mathrm{}$ and $\Delta K=\pm 2$. General expressions for spectral line positions and absolute intensities are calculated for $J=0-20\mathrm{}$. The effects of tetrahedral fine-structure splittings and nuclear-spin statistical weights have been included. Detailed results are established for methane, the prototype of molecules with tetrahedral symmetry. Possible competing transitions are discussed.

The application of Delves's variational principle for the calculation of the expectation value of single-particle operators $W$ is investigated in the Hartree approximation. In this approximation the auxiliary function is taken to be of the form ${\psi }_{1T}={\Sigma }_i{f}_i\left({\overrightarrow{\mathrm{r}}}_i\right){\psi }_{0T}$, where ${\psi }_{0T}$ is the trial ground-state wave function. For a given ${\psi }_{0T}$, a set of coupled integrodifferential equations satisfied by the $f_i\left({\overrightarrow{\mathrm{r}}}_i\right)$ is derived by minimizing an auxiliary functional containing ${\psi }_{0T}$, ${\psi }_{1T}$, $W$, and the Hamiltonian of the system. The resulting equations are uncoupled in two different approximations each valid for one- and two-particle systems and are compared to those employed by others and to those previously suggested by us on the basis of certain self-consistency considerations. The uncoupled equations are solved exactly for single-particle operators that depend on the radial distance only. The utility of the technique is demonstrated by showing that for a model hydrogen-atom problem it leads to highly accurate results for the electron density at the origin and the Fourier transform of the electron density even when the calculation of these quantities employing ${\psi }_{0T}$ alone is substantially in error. The results of applying the technique to the helium atom for the calculation of $〈{\mathcal{r}}^n〉$, $n=-2, -1, 1, 2$, and the electron density at the origin employing an energy-minimized product of hydrogenic wave functions for ${\psi }_{0T}$ are reviewed and compared with those of Pekeris and found to have an accuracy equivalent to a numerical Hartree-Fock calculation. Finally, the decoupling approximations are extended to systems containing more than two particles.