Weighted-least-squares fits to the small momentum transfer ($k\le 1$ ${\mathrm{\AA }}^{-1\mathrm{}}$) results of Woods and Cowley have been carried out. We find that the neutron data presently available (i) are not of sufficient accuracy to determine whether or not quadratic terms are present in the dispersion relation and (ii) weakly favor positive dispersion in the absence of the quadratic term.

Approximate numerical calculations are used in order to understand some of the differences in size and shape of secondary structure obtained in calculations of the one-phonon spectral function for solid helium that have been reported in the literature. It is seen that Horner's self-consistent treatment of the bubble diagram significantly increases the size of such structure over that obtained in perturbative calculations such as used by Glyde and co-workers. A computational procedure used by Horner in evaluating the spectral function may also further enhance the appearance of secondary peaks in the tail region. Previous explanations of these secondary peaks are reviewed and criticized. Other calculations of the one-phonon spectral functions for the solid heliums are briefly discussed.

An investigation of the line spacing in the fluorescence spectra of ${\mathrm{I}}_2$ excited with 5145-Å light indicates a decrease with overtone number, in disagreement with previously published results.

It is shown that the multiple scattering of fast charged particles does not depend significantly on the sign of the charge at energies $\gtrsim 1$ MeV, at least for scatterers of low atomic number.

In the Born approximation as the interaction occurs with only one electron, the total cross section for producing a $K$-shell vacancy with a heavy projectile is obtained by requiring the electron to be excited above the Fermi sea. We demonstrate that for an independent-particle model of the atom this result is true to all orders of the Born series. This means the codes currently developed for proton-hydrogen scattering are immediately applicable to $K$-shell ionization.

It is shown that the edge and curvature effects in the asymptotic distribution of the eigenvalues of the Laplace operator ${\nabla }^2$ for a cylindrical domain, studied recently by Baltes, arise from a common origin and can be obtained directly from Fedosov's formula for a polyhedron. Generalization to arbitrary domains (with pure boundary conditions) and to cylindrical domains (with mixed boundary conditions) is presented. The latter results substantiate certain conjectures made previously by one of the authors.

The analysis of electron-helium elastic scattering at small and intermediate angles given in a previous paper is extended to include the case of large-angle scattering. Agreement with absolute large-angle measurements is excellent.

The 40 levels of the ground-state configuration $5f^3\left({}_{}{}^4{}_{}{}^{}I\right)6d7s^2$ of neutral uranium are calculated in intermediate coupling with seven radial parameters. A least-squares fit to 27 observed levels (rms error of 475 ${\mathrm{cm}}^{-1\mathrm{}}$, $\sim$ 3% of the width) results in new values for the radial parameters, predictions for the missing levels and for $g$ factors, and percentage compositions in $L-S$ and $J-j$ couplings.

The only relatively long-lived fundamental particle which may possess an electric quadrupole moment is the ${\Omega }^{-}$ hyperon, since it has spin 3/2. We consider the possibility that ${\Omega }^{-}$ hyperons may be captured into atomic orbits at some future date. If this possibility should be realized (in spite of great technical difficulties), then it may be possible to determine simultaneously the electric quadrupole moment $Q_{\Omega }$ and the magnetic dipole moment ${\mu }_{\Omega }$ of the ${\Omega }^{-}$ hyperon. In the present paper, we have calculated the fine structure of the ${\Omega }^{-}-\mathrm{P}\mathrm{b}$ atom for reasonable values of $Q_{\Omega }$ and ${\mu }_{\Omega }$. The $n=11\mathrm{}$, $l=10\mathrm{}\to n=10\mathrm{}$, $l=9\mathrm{}$ transition has been considered, since there is some indication from an experiment on antiprotonic atoms that the capture of the ${\Omega }^{-}$ by the nucleus will take place from a hydrogenic state with $n$ of the order of 10 for lead, and $l\sim n-1\mathrm{}$. It is shown that for $Q_{\Omega }=2\mathrm{}\times {10}^{-26\mathrm{}}$ ${\mathrm{cm}}^2$, the quadrupole splittings should be resolvable experimentally. The magnetic dipole splittings have also been calculated.

It is shown that a recent quantum-electrodynamic derivation by Chang and Stehle of double-quantum resonance-frequency shifts is equivalent to a previously known semiclassical approximation, and that neither of these methods is adequate to account for the results of Kusch's experiments. A more-exact semiclassical computation is given, which is in reasonable agreement with Kusch's results in the region where these results are meaningful. It is concluded that the assertion of Chang and Stehle that quantum electrodynamics is necessary for such situations is unfounded.

A new method is described to obtain a sequence of wave functions and energy eigenvalues which converge rapidly to the exact bound state of the Schrödinger equation for the exponentially screened Coulomb potential.

Wave functions, which include interelectron coordinates $r_{\mathrm{ij}}$ explicitly, are calculated for the $1s^{ 2}2s^{ 2}{}_{}{}^1{}_{}{}^{}S$ and $1s^{ 2}2s 2p {}_{}{}^1{}_{}{}^{}P$ states of Be I, C III, and O V. These wave functions are used to calculate oscillator strengths, including upper and lower bounds, for the lowest ${}_{}{}^1{}_{}{}^{}S-{}_{}{}^1{}_{}{}^{}P$ transition. Interpolation techniques are used to make a graphical study of the oscillator-strength behavior along the isoelectronic sequence. Comparisons are made with previous experimental and theoretical results. The results of this study are oscillator strengths for the $1s^{ 2}2s^{ 2} {}_{}{}^1{}_{}{}^{}S\to 1s^{ 2}2s 2p {}_{}{}^1{}_{}{}^{}P$ Be isoelectronic sequence with rigorous upper and lower bounds of (7-10)% and probable accuracy ≤ 2%.

Wave functions, which include interelectron coordinates $r_{\mathrm{ij}}$ explicitly, are employed for the $1s^{ 2}2s^{ 2}{}_{}{}^1{}_{}{}^{}S$ and $1s^{ 2}2s 2p {}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ states of Be I, C III, and O V in obtaining lower bounds and Hylleraas variation-perturbation estimates of dipole polarizabilities for the lowest ${}_{}{}^1{}_{}{}^{}S$ states of Be I, C III, and O V. Interpolation techniques are used to make a graphical study of the polarizability behavior along the entire isoelectronic sequence. The results of this study are polarizabilities for the lowest ${}_{}{}^1{}_{}{}^{}S$ state of Be I with probable accuracy ≤ 2%, and the rest of the isoelectronic sequence with probable accuracy of (2-5)%.

Static dipole polarizabilities, accurate to within 5% are presented for the ground states and some valence excited states of the first-row atoms. The polarizabilities are obtained from multiconfigurational self-consistent-field wave functions, which were computed with the perturbing electric field included directly in the Hamiltonian. The use of the multiconfigurational framework allows any state of both degenerate and nondegenerate atoms to be considered, and also allows for the explicit introduction of electron-correlation effects. Detailed discussions of basis-set selection and the effects of electron correlation are presented along with comparisons with experimental and other theoretical polarizability results.

It is shown that, by applying an "accelerated" or "multi-step" ladder-operatorial procedure, one can obtain, easily, a symmetric closed-form expression for the off-diagonal ($n\ne n^{\prime },l\ne l^{\prime }$) hydrogenic $r^k$ matrix elements.

A calculation has been made of the ionization potentials for atoms of arbitrary $Z$ and arbitrary degree of ionization using the Thomas-Fermi model. A modified approach is used to numerically evaluate the binding and ionization energies which depends on an integration scheme that starts at the atomic radius and proceeds inward to the origin. Since exchange energy is not included, the results are not reliable for $\gamma <0.1\mathrm{}$, where $\gamma$ is the fractional deviation of the ion from neutrality. Also the results cannot be used when the ion has only a few electrons left since then the statistical assumption breaks down.

The O-O band of the $B {}_{}{}^2{}_{}{}^{}\Sigma \to X {}_{}{}^2{}_{}{}^{}\Sigma$ transition of lanthanum oxide has been studied using an interference spectrometer HYPEAC and a "dressed-walls" hollow cathode. The accuracy of the measurements allows a detailed study of nuclear hyperfine effects. A theoretical interpretation of experimental results is proposed which takes into account residual fine- and hyperfine-interaction contributions. A satisfactory explanation of the variation with $N$ of the intensities is obtained when introducing intermediate coupling $b_{{\beta }_S}-b_{{\beta }_J}$ effects in the ground state. From the comparison between experimental and theoretical results, the following values of some hyperfine- and fine-structure parameters are deduced, i.e., for the $X {}_{}{}^2{}_{}{}^{}\Sigma$ state ${\gamma }_{SR}=2.57\mathrm{}\pm 0.25$ mK and $b=123.5\mathrm{}\pm 1.8$ mK, and for the $B {}_{}{}^2{}_{}{}^{}\Sigma$ state $b^{\prime }=21.7\mathrm{}\pm 2.0$ mK and $c^{\prime }=-5\pm 12$ mK.

The value of vacuum-polarization amplitude is investigated in the region of positronium bound-state poles, where the naive Feynman-graph expansion fails. The corresponding contribution to positronium-ground-state splitting is explicitly evaluated up to order ${\alpha }^6$. The previously given result for the ${\alpha }^6 \ln {\alpha }^{-1\mathrm{}}$ term coming from fourth-order vacuum-polarization corrections to the one-photon annihilation diagram is confirmed and put on a sounder basis. The ${\alpha }^6$ term is found to receive, besides the obvious contribution from ${\alpha }^2$ vacuum-polarization term, an additional ${\alpha }^6$-contribution which can be considered as generated by an infinite series of terms of higher nominal order in $\alpha$.

The contribution to the $n {}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ ionization energy owing to mixing with the $n {}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state has been computed for the $2 {}_{}{}^3{}_{}{}^{}P$ to $5 {}_{}{}^3{}_{}{}^{}P$ states of the helium isoelectronic sequence up to $Z=10\mathrm{}$. Corrected values for the fine-structure splittings of these levels are listed. The theoretical and experimental values for the $2 {}_{}{}^3{}_{}{}^{}S_{ 1}^{}{}_{}{}^{}-2 {}_{}{}^3{}_{}{}^{}P_{ 1}^{}{}_{}{}^{}$ energy difference are found to be in good agreement provided that the $2 {}_{}{}^1{}_{}{}^{}P_{ 1}^{}{}_{}{}^{}$ mixing correction to the $2 {}_{}{}^3{}_{}{}^{}P_{ 1}^{}{}_{}{}^{}$ level and an estimate of the Lamb-shift correction to the $2 {}_{}{}^3{}_{}{}^{}S_{ 1}^{}{}_{}{}^{}$ energy are included in the calculation.

Ab initio calculations for the multistate ket associated with the pair of molecular states arising from the lowest-lying separated-atom limit are carried out. Comparison with the usual variational approach is made. Computational advantages, including the avoidance of multicenter exchange integrals, are discussed.