A discussion is given of the requirements for observing strong level-crossing signals in stepwise fluorescence, where the state under investigation is optically excited via an intermediate state, the atom absorbing in the process two photons of different wavelengths. Data obtained using this technique are presented for fine-structure crossings in the $3^{2}D$ term of Li.

Measurements of the differential cross section for the elastic scattering of low-energy electrons by ${\mathrm{O}}_2$ at 50° exhibit structure resulting from the compound state $\mathrm{O}_2^{}{}_{}{}^{-}$. From these observations we calculate the spectroscopic constants of the ground state ${}_{}{}^2{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ of $\mathrm{O}_2^{}{}_{}{}^{-}$, and we find the values ${\omega }_e\left(\mathrm{O}_2^{}{}_{}{}^{-}\right)=1089\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $r_e\left(\mathrm{O}_2^{}{}_{}{}^{-}\right)=1.377\mathrm{}$ Å. A portion of the potential-energy curve of the $\mathrm{O}_2^{}{}_{}{}^{-}\left({}_{}{}^2{}_{}{}^{}\Pi _g^{}{}_{}{}^{}\right)$ is plotted using the Morse-function representation and our calculated values of the spectroscopic constants.

An effective-range analysis is used to predict properties of the ${\pi }^{-}-{}_{}{}^4{}_{}{}^{}\mathrm{He}$ atom. The method produces precise predictions; however, our predictions are broadened because of systematic differences between phase shifts from the various scattering experiments. The bounds obtained for the $1s$ and $2p$ level shifts (due to the strong interaction) are 90 to 160 eV (toward less binding) and (-2.4 to -4.0) × ${10}^{-3\mathrm{}}$ eV, respectively. The bounds obtained for the nuclear capture rates from the $1s$ and $2p$ states are (0.12 to 1.8) × ${10}^{17}$ ${\sec }^{-1\mathrm{}}$ and (0.46 to 4.0) × ${10}^{12}$ ${\sec }^{-1\mathrm{}}$, respectively. The results are consistent with mesonic x-ray measurements.

Comparisons of theoretical electron-bremsstrahlung cross sections for Al and Au from the work of Brysk, Zerby, and Penny are made with new experimental values at incident-electron energies of 0.05 and 0.20 MeV. Photon energies of 10, 20, 30, and 40 keV are considered in the angular region from 10 to 120 deg at 0.050-MeV incident-electron energy. Photon energies of 46, 76, 106, 166, and 196 keV for Al and 80, 120, and 160 keV for Au are considered at 0.20-MeV incident-electron energy. Agreement between experiment and theory is within experimental error except at small angles and low photon energy.

The fractional hyperfine pressure shift (known as HPS in the literature) of paramagnetic atoms in an atmosphere of noble-gas atoms has been found to be computable quite adequately from recently evaluated extended-basis-set self-consistent-field molecular-orbital wave functions. The actual computation was carried out for lithium and sodium atoms in a helium buffer gas. Computed values of 78.87 × ${10}^{-9\mathrm{}}$/mm Hg versus the experimental value of 77.7 × ${10}^{-9\mathrm{}}$/mm Hg for LiHe and 78.11 versus 73.0 × ${10}^{-9\mathrm{}}$/mm Hg for NaHe were obtained.

Intensity beats in the emission of $\mathrm{L}{\mathrm{y}}_{\alpha }$ from beam-foil excited hydrogen in various static electromagnetic field configurations have been studied. The observed beat frequencies agree with the calculated values, which are independent of the field directions. The beat amplitudes, however, show significant dependence on the field directions relative to the beam. The theory for emission of light from the decay of coherently excited states is applied in the sudden perturbation limit. Agreement with experiment can only be obtained under the assumption that the foil excitation generates initial coherent wave functions ${\Psi }_{\mathrm{I},\mathrm{I}\mathrm{I}}=\alpha |p,\frac{1}{2},\pm \frac{1}{2}〉+\beta |s,\frac{1}{2},\mp \frac{1}{2}〉$, where $|l,j,m_j〉$ notation and the beam as quantization axis are used. The ratio $\frac{\alpha }{\beta }$ is then determined, which gives the ratio of the excitation cross section of the $p$ to that of the $s$ states as $\frac{{\sigma }_p}{{\sigma }_s}>~4\pm 1$ at a beam energy of 200 (keV) per atom.

Starting from the equations of motion expressed as ground-state expectation values, we have derived a higher-order random-phase approximation (RPA) for excitation frequencies of low-lying states. The matrix elements in the expectation value are obtained up to terms linear in the ground-state correlation coefficients. We represent the ground state as $e^U|\mathrm{HF}〉$, where $U$ is a linear combination of two particle-hole operators, and $|\mathrm{HF}〉$ is the Hartree-Fock ground state. We then retain terms only up to those linear in the correlation coefficients in the equation determining the ground state. This equation and that for the excitation energy are then solved self-consistently. We do not make the quasiboson approximation in this procedure, and explicitly discuss the overcounting characteristics of this approximation. The resulting equations have the same form as those of the RPA, but this higher RPA removes many deficiencies of the RPA.

The pair functions which determine the exact first-order wave function for the ground state of the three-electron atom have been found with the matrix finite-difference method. The second- and third-order energies for the $\mathrm{}\left(1s1s\right)\mathrm{}{}_{}{}^1{}_{}{}^{}S$, $\mathrm{}\left(1s2s\right)\mathrm{}{}_{}{}^3{}_{}{}^{}S$, and $\mathrm{}\left(1s2s\right)\mathrm{}{}_{}{}^1{}_{}{}^{}S$ states of the two-electron atom are presented along with contour and perspective plots of the pair functions.

A method is presented for the quantum-mechanical problem of one particle moving in the field of two identical fixed centers. An equation for the problem is derived in both position and momentum space as a special limiting case of our general method for the three-body problem. When applied to the $\mathrm{H}_2^{}{}_{}{}^{+}$ problem, using the Coulomb-Sturmian set as an expansion basis, the method gives an infinite secular equation for the energy eigenvalues which can be solved exactly in the limits as the internuclear distance goes to zero and to infinity. Numerical results are also reported for the energy as a function of internuclear distance for the $1{\sigma }_g$, $1{\sigma }_u$, $2{\sigma }_g$, and $2{\sigma }_u$ states of $\mathrm{H}_2^{}{}_{}{}^{+}$.

The mean lives of six $3p$ levels of singly ionized neon have been measured using the ionic beam method with a gas target. Relative line intensities in two of the strongest multiplets have also been measured. It was found that the levels were populated according to the weight $2J+1$, where $J$ is the quantum number for the total electronic angular momentum. The levels and the measured lifetimes in nanoseconds are $3p{}_{}{}^4{}_{}{}^{}D_{\frac{7}{2}}^{\circ }{}_{}{}^{}(7.8\mathrm{}\pm 0.5)$, ${}_{}{}^4{}_{}{}^{}D_{\frac{5}{2}}^{\circ }{}_{}{}^{}(7.6\mathrm{}\pm 0.1)$, ${}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^{\circ }{}_{}{}^{}(10.1\mathrm{}\pm 0.4)$, ${}_{}{}^4{}_{}{}^{}P_{\frac{3}{2}}^{\circ }{}_{}{}^{}(10.6\mathrm{}\pm 0.4)$, ${}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{\circ }{}_{}{}^{}(8.43\mathrm{}\pm 0.07)$, and $3p^{\prime }{}_{}{}^2{}_{}{}^{}F_{\frac{7}{2}}^{\circ }{}_{}{}^{}(8.5\mathrm{}\pm 0.3)$. The indicated uncertainties are the standard deviations from the means; however, an additional uncertainty of approximately 10% should be added to each value in order to account for possible systematic errors. The reported lifetimes were obtained by fitting appropriate line intensities with the sum of two exponentials and a constant. Such fits adequately described the decay of the level populations of the fast ${\mathrm{Ne}}^{+}$ ions downstream from the exit aperture of the differentially pumped collision cell.

Two approaches to the analysis of level crossing are presented. A theoretical approach utilizes values of the hyperfine coupling constants to predict the entire level structure of a system, including all level-crossing data of interest. A second approach suggests a procedure for determining hyperfine parameters with reasonable accuracy, based on three or four measured quantities. Results of this procedure in 2 ${}_{}{}^2{}_{}{}^{}P$ lithium give the contact, dipole, and orbital hyperfine coupling constants as -9.806 ± 0.117, -1.909 ± 0.034, and 8.638 ± 0.39 MHz, respectively. This work reemphasizes the fact that an accurate determination of magnetic hfs requires three parameters to fully define the three independent magnetic hyperfine interactions.

The theory of the spin polarization of photoelectrons and of its correlation with angle of ejection is extended by the derivation of a cross section for photoionization of a ${\mathrm{}\left(\mathrm{ns}\right)\mathrm{}}^2{}_{}{}^1{}_{}{}^{}S$ atom. The effect of an isolated resonance in the absorption continuum is treated by Fano's theory of configuration interaction. The connection between photoionization and electron scattering leads to the use of complex ingoing-wave eigenfunctions and to an expression of the photoionization cross section in terms of ${\hat{S}}^{\frac{1}{2}}$, the square root of the scattering matrix. The spin polarization is influenced by the exclusion principle and by the action of the spin-orbit forces in the discrete and continuum states. Configuration interaction between discrete and continuum is shown to be the dominant polarization mechanism near an autoionization line and can yield a high degree of polarization. The mean polarization vector has components in and out of the plane of photoemission, and its direction varies rapidly as the light frequency varies across a resonance. Two intensity vectors are introduced, derivable, respectively, from the experimental total and differential cross sections for photoionization. The rotation matrix connecting the two intensity vectors is expressed in terms of the interaction parameters which determine ${\hat{S}}^{\frac{1}{2}}$.

The singlet-stability conditions of the symmetry-adapted Hartree-Fock (HF) ground state of cyclic polyenes (linear metal with Born-Kármán cyclic boundary conditions) are studied, using the Pariser-Parr-Pople Hamiltonian and three different parametrization schemes. It is shown that the HF ground states are singlet-unstable for large enough cycles, so that the diamagnetic (pure singlet) symmetry-nonadapted HF solutions (broken-symmetry HF solutions), having lower energy than the symmetry-adapted HF solutions, must exist. In fact a number of broken-symmetry diamagnetic HF solutions, displaying the charge density waves (CDW's), exist for large enough cyclic polyenes. The most important ones, corresponding to the maximum quasi-momentum transfer and having lowest energy, are studied. The HF equations for these symmetry-nonadapted solutions are given in the BCS-Bogoliubov form, and their solutions are found numerically for cycles containing up to 170 atomic sites. It is shown that these new HF solutions display different types of CDW's, which may be conveniently classified as diagonal and off-diagonal CDW's. Finally, it is shown that the diagonal CDW HF solutions not only have generally higher energy than the off-diagonal HF solutions, but are, moreover, singlet-unstable, while the off-diagonal CDW solutions are singlet-stable. The implications of the existence of singlet instabilities for the occurrence of the energy-gap and bond-length alternation (sublattice formation), as well as for the applicability of some many-body techniques to these systems, are briefly discussed.

Corrections are made to a previous computation of the binding energies of some highly excited states of the $\alpha {\pi }^{-}{e}^{-}$ and $\alpha K^{-}{e}^{-}$ atoms. The corrections take into account the effects of two approximations that were made in the original calculation. These approximations are (i) the use of the Born-Oppenheimer approximation in describing the radial motion of the meson with respect to the $\alpha$ particle and (ii) the use of a variational wave function to describe the motion of the electron. The corrections are found to be too small to have any significant effect on existing estimates of Auger rates for circular orbits. In each instance that is considered, the total correction to the energy difference between a circular and an almost circular orbit with the same principal quantum number is found to be only a few percent at most.

Linked-cluster many-body perturbation theory is applied to study the stability of the ground state of the ${\mathrm{H}}^{-}$ ion. A diagrammatic approach is made to analyze the role of various polarization effects. A complete set of states obtained in the $V^{N-1\mathrm{}}$ potential is used to evaluate the diagrams. The total energy of ${\mathrm{H}}^{-}$ is calculated to be -0.027 66 a.u., leading to the binding energy 0.527 66 a.u., in good agreement with the most accurate value, 0.027 75 a.u., due to Pekeris. The result of our investigation shows conclusively the crucial importance of monopole and dipole polarization effects for the stability of this ion in particular and negative ions in general. A comparison with the results from earlier work is also made.

The fourth-order radiative correction to the slope at $q^2=0\mathrm{}$ of the Dirac form factor of the free-electron vertex is calculated using computer techniques. The result $\frac{m^2\partial F_1^{}{}_{}{}^{\mathrm{}\left(4\right)\mathrm{}}\mathrm{}\left(0\right)\mathrm{}}{\partial q^2}={\left(\frac{\alpha }{\pi }\right)}^2(0.48\mathrm{}\pm 0.07)$ disagrees with previous calculations and implies a new theoretical value for the order ${\alpha }^2{\left(Z\alpha \right)}^{4}m{c}^2$ contribution to the Lamb shift. The new values for the $2S_{\frac{1}{2}}-2\mathrm{}{P}_{\frac{1}{2}}$ separation in H and D are increased by 0.35±0.07 MHz and are in good agreement with the results of recent experiments.

Excitation cross sections for the fourth positive band system in carbon monoxide have been determined from studies of the energy-loss spectra of 20-120-keV protons incident on gaseous CO targets. The energy-loss spectra had an energy resolution of about 2 eV. Prominent peaks in the spectra were observed at 8.5 and 13.8 eV. The first peak is believed to be due to excitation of the fourth positive band system of $\mathrm{CO} (X{}_{}{}^1{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}\to A{}_{}{}^1{}_{}{}^{}\Pi$, while the 13.8-eV peak covers a number of possible states, including the $B{}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ and the $C{}_{}{}^1{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ states. Changes in the slope of the ionization continuum were noted at 16.5 eV, corresponding to the $A{}_{}{}^2{}_{}{}^{}\Pi _i^{}{}_{}{}^{}$ state of C${\mathrm{O}}^{+}$, and at 20.5 eV, corresponding to the $B{}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ state of C${\mathrm{O}}^{+}$. Absolute excitation cross sections for the fourth positive band system of CO are presented, as well as the total inelastic cross sections and the total ionization cross sections for 20-120-keV protons incident on CO.

Spectral data obtained with a magnetic spectrometer are presented for inelastic electron scattering from thin targets of carbon, copper, and gold at incident electron energies of 0.1, 0.2, 0.4, and 3.0 MeV, for scattering angles between 20° and 120°. For angles less than 90°, each spectrum consists of (a) a Møller line which has a half-width that increases with atomic number and which yields an experimental cross section that agrees within experimental error with the theoretical Møller cross section, and (b) a low-energy continuum which rises steeply at energies less than 40 keV. For angles greater than 90°, the Møller line which is kinematically forbidden vanishes, but the steeply rising continuum remains. This continuum may arise from single electron-atom scattering and from multiple scattering in the target. The latter process depends on target thickness. The experimental results for this low-energy continuum tend to confirm that the multiple-scattering effects as calculated by Ford and Mullin dominate the single-scattering process as calculated by Weber, Deck, and Mullin, and by Kolbenstvedt and Cooper even for an 11-μg/${\mathrm{cm}}^2$ carbon target which was the most favorable case for studying the single-scattering process. Because of multiple scattering, accurate experimental data for the low-energy continuum produced by single electron-atom inelastic scattering can best be obtained with gas targets.

A pseudopotential formalism is used to calculate the cross section for photoionization of sodium, lithium, and potassium for ejected electron energies from threshold to about 15 eV. Both the dipole length and dipole velocity matrix forms are computed. For sodium, the dipole length results are in good agreement with experiment away from the lowest threshold. The dipole velocity results for sodium, on the other hand, severely underestimate the cross section except very near threshold. For lithium, the dipole length and velocity results are less than the experimental results but agree well with other theoretical results. For potassium, the cross section exhibits the general shape of experimental curves.

The usual conclusions concerning the energy dependence of high-energy atomic charge transfer are shown to depend critically upon the short-range singularity of the Coulomb potential. The problem is reexamined for the case of smooth potentials. All the previous conclusions concerning the high-energy dependence of the various approximations are changed.