Various manifestations of coherent mixtures of even- and odd-parity eigenstates of collision-excited atomic hydrogen in external electric fields are discussed on general grounds. We show that when even-and odd-parity states are coherently excited, application of an electric field perpendicular to the velocity axis induces orientation in the originally unoriented atoms. Circular polarization of the decay radiation is an observable consequence of the orientation.

The cross sections for the $1s-2s$ and $1s-2p$ transitions in atomic hydrogen have been calculated for electron impact energies in the range 12-20 eV using a pseudostate expansion.

The uncertainty-principle implications of the recent study of Williams, Rousseau, and Dworetsky are considered. The incompatible requirements of excitation pulse duration and bandwidth rule out a test of their proposed relation between excitation frequency and scattering time in the transition from resonance fluorescence to Raman scattering.

Measurements of millimeter-wave fine-structure transitions and the $n\left(J\right)=0\mathrm{}\left(1\right)\mathrm{}\to 2\left(1\right)\mathrm{}$ rotational transition of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ have been made with high precision. From analysis of the results the following molecular constants of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ were obtained: $B_0=40\mathrm{}707.408\left(10\right)\mathrm{}$ MHz, $B_1=-0.129\mathrm{}$ MHz, ${\lambda }_0=59\mathrm{}499.097\left(43\right)\mathrm{}$ MHz, ${\lambda }_1=0.053\mathrm{}12\left(80\right)\mathrm{}$ MHz, ${\mu }_0=-238.488\mathrm{}\left(7\right)\mathrm{}$ MHz, ${\mu }_1=-0.000\mathrm{}619\left(116\right)\mathrm{}$ MHz, $B_e=40\mathrm{}931.7\left(6.9\right)\mathrm{}$ MHz, $r_0=1.210\mathrm{}751\left(16\right)\mathrm{}$ Å, and $r_e=1.207\mathrm{}429\left(103\right)\mathrm{}$ Å. The equilibrium values were obtained with the aid of vibration-rotation interaction constants from optical spectroscopy.

Long-range interaction studies of the system ${\mathrm{He}}_2\left({}_{}{}^3{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}\right)$ based on the multiconfiguration self-consistent-field formalism are reported. In this formalism the long-range contribution to the hyperfine pressure shift of metastable $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ in buffer gas of ground-state He is discussed. It is found by actual computation to be an order of magnitude smaller than that predicted by the many-body perturbation theoretic approach. Possible explanations of the discrepancy are discussed.

The spectral dependence of the forward coherent bremsstrahlung produced by beams of 28-MeV positrons and electrons incident upon a 5-μm thick single crystal of silicon was measured with a NaI photon spectrometer. Effects of channeling and perhaps of the nonvalidity of the first Born approximation were observed for beam directions near the $〈111〉$ axis of the crystal. A coherent peak near 0.5 MeV for both electrons and positrons was observed for a compound-interference direction, in agreement with first-order theoretical calculations.

A $\frac{1}{Z}$-perturbation-expansion method is used to calculate the eigenvalues and eigenfunctions for the ${\mathrm{}\left(1s\right)\mathrm{}}^{2}3s{}_{}{}^2{}_{}{}^{}S$, ${\mathrm{}\left(1s\right)\mathrm{}}^{2}3p{}_{}{}^2{}_{}{}^{}P$, and ${\mathrm{}\left(1s\right)\mathrm{}}^{2}3d{}_{}{}^2{}_{}{}^{}D$ states of the lithium isoelectronic sequence. The eigenfunctions are used, together with those of the $2{}_{}{}^2{}_{}{}^{}S$ and $2{}_{}{}^2{}_{}{}^{}P$ states, to determine the dipole-length and dipole-velocity forms of the oscillator strengths for the $2p-3s$, $3s-3p$, $2s-3p$, $3p-3d$, and $2p-3d$ transitions. The results are compared with those obtained from Hartree-Fock calculations for individual values of the nuclear charge. The calculations include members of the lithium series for which accurate eigenenergies or oscillator strengths are not well known.

A $\frac{1}{Z}$-expansion method is used to calculate the eigenvalues and eigenfunctions for the $\mathrm{}\left(1s2s2p\right)\mathrm{}{}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^o{}_{}{}^{}$ state of the lithium isoelectronic sequence. The magnetic quadrupole ($M2\mathrm{}$) decay rates for the $\mathrm{}\left(1s2s2p\right)\mathrm{}{}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^o{}_{}{}^{}-{\mathrm{}\left(1s\right)\mathrm{}}^{2}2s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^e{}_{}{}^{}$ transition are computed for the series from Li i through Ar xvi. It is explicitly demonstrated that, for high values of nuclear charge, the magnetic quadrupole decay channel becomes comparable to that of autoionization in determining the lifetime of the metastable state.

The method of singlet-triplet level anticrossing has been extended to the $n=6\mathrm{}{}_{}{}^{1,3}{}_{}{}^{}D$ levels of He. Measurement of this anticrossing gives a highly accurate determination of the zero-field singlet-triplet separation and a less accurate determination of the antisymmetric part of the spin-orbit coupling perturbation between the $n=6\mathrm{}{}_{}{}^{1,3}{}_{}{}^{}D$ states. The zero-field separation for $n=6\mathrm{}$, although considerably more accurate, is in essential agreement with previous optical results, confirming the accuracy of the intercombination line measurements. The singlettriplet intervals calculated by many-body perturbation theory are also found to be in very good agreement with the experimental results.

The effective-operator form of many-body theory is reviewed and applied to the calculation of the hyperfine structure. Numerical results are given for the $2p$, $3p$, and $4p$ excited states of Li and the $3p$ state of Na. This is the first complete calculation of the hyperfine structure using an effective-operator form of perturbation theory. As in the Brueckner-Goldstone form of many-body theory, the various terms in the perturbation expansion are represented by Feynman diagrams which correspond to basic physical processes. The angular part of the perturbation diagrams are evaluated by taking advantage of the formal analogy between the Feynman diagrams and the angular-momentum diagrams, introduced by Jucys et al. The radial part of the diagrams is calculated by solving one- and two-particle equations for the particular linear combination of excited states that contribute to the Feynman diagrams. In this way all second- and third-order effects are accurately evaluated without explicitly constructing the excited orbitals. For the $2p$ state of Li our results are in agreement with the calculations of Nesbet and of Hameed and Foley. However, our quadrupole calculation disagrees with the work of Das and co-workers. The many-body results for Li and Na are compared with semiempirical methods for evaluating the quadrupole moment from the hyperfine interaction and a new quadrupole moment of ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ is given.

The Ne I resonance transitions were measured with sufficient precision to extend the spectroscopy of the Ne I isoelectronic sequence to $Z=40\mathrm{}$. Ab initio atomic-structure calculations and isoelectronic extrapolations are in agreement with the measured values. Atomic-structure calculations were used to interpret the Na- and Mg-like satellite lines in the $2p-3s$ and $2p-3d$ regions in Se and Zr. The interpretation of the $L$-series satellites may prove important for future plasma diagnostics.

We present rough variational upper-bound estimates of some low-lying bound-state energy levels of two-electron systems, including ${\mathrm{H}}^{-}$, He, and ${\mathrm{Li}}^{+}$, in magnetic fields $B$ above ${10}^{10}$ G, a regime that is relevant to recent astrophysical studies of pulsars. The simple trial wave functions that we use in the Rayleigh-Ritz calculations consist of single antisymmetrized products of single-particle orbitals which are predominantly magnetic in their spatial character. Most importantly, our results indicate that in the regime ${10}^{10}\lesssim B\lesssim {10}^{13}$ G the ${\mathrm{H}}^{-}$ ion has at least one singlet and one triplet bound state; at 2 × ${10}^{12}$ G, e.g., the ionization energy of the triplet ground state of ${\mathrm{H}}^{-}$ is greater than 12 eV. (The number of bound states of ${\mathrm{H}}^{-}$ in this regime of $B$ may be much greater; moreover, the number of levels and their depths is expected to increase monotonically with $B$.) These results appear to contradict a recent indication that there might not be any bound states of ${\mathrm{H}}^{-}$ above ${10}^{10}$ G. For $B\to \infty$ we also present the approximate leading asymptotic terms for the total (nonrelativistic) energies and corresponding ionization energies of some low-lying states of two-electron systems with nuclear charge $Z\ge 2$.

Nonadditive three-body interaction energies are calculated for ${\mathrm{He}}_3$, ${\mathrm{Ne}}_3$, ${\mathrm{Ar}}_3$, and ${\mathrm{Kr}}_3$. The electron density of the total system of three atoms is assumed to be equal to the sum of the three separate atomic electron densities, and the energy is evaluated from this assumed density using an electron-gas energy formula in terms of local electron density. The results show that the three-body contributions to the interaction energy for these systems is very small, usually less than a few percent of the sum of the pair forces, over a large range of internuclear separations.

The failure of the preceding paper to describe the nonadditive three-body forces at large internuclear separations is remedied by using a model developed earlier for the pair interactions by the present author and Gordon. The model includes descriptions of both the long-range forces, which are based on a harmonic-oscillator model for atoms, and the short-range forces with their effect on the long-range forces. The results give predictions of the nonadditive three-body forces for the entire portion of the physically interesting region of the potential surfaces. We find that the nonadditive contributions are a few percent or less of the total interaction over most ranges of internuclear separation.

A Heisenberg-picture treatment of spontaneous emission is given, and the origin of radiative line shifts and widths is discussed. It is shown that radiation reaction and vacuum fluctuations provide complementary conceptual bases for the interpretation of these radiative corrections. Alternative approaches are discussed, including the use of a random classical field to simulate the effects of the quantum-electrodynamical radiation field.

Differential elastic cross sections for the scattering of electrons by hydrogen molecules are calculated for incident momenta ≤0.7 a.u. Calculations are performed using a Gaussian basis-set expansion technique developed previously by the authors for use with nonspherical potentials. With the static-exchange model, cross sections are computed in the body-fixed frame and then averaged over molecular orientations. Our results agree well with those of previous workers. The method is economical and has wide applicability to the electron-molecule scattering problem.

Values of the gas density profile correction factor $\alpha$ are calculated for a series of cylindrical beam-scattering chambers with identical thin circular apertures.

We have observed the collision-induced scattering from compressed C${\mathrm{F}}_4$ up to 70 atm and from C${\mathrm{F}}_4$-He mixtures at concentrations of 27%, 47%, and 48% C${\mathrm{F}}_4$, up to a total pressure of 155 atm. To describe the intensity distribution for pure C${\mathrm{F}}_4$, a single exponential function, $I=C$ $\exp (-\frac{\omega }{{\omega }_0})$, was fitted in the frequency range 5-20 ${\mathrm{cm}}^{-1\mathrm{}}$; the density dependence of ${\omega }_0$ follows the scaling law derived by Fleury for rare-gas spectra. An expression involving the sum of two exponentials was fitted over a broader frequency range 5-45 ${\mathrm{cm}}^{-1\mathrm{}}$. It is argued that the expected intensity due to the second-order dipole-induced dipole interaction or to octupole effects is too small to account for the high-frequency tail. The shape of this tail indicates that it may arise from close encounters in which the collision time is determined principally by the intermolecular potential. The values of ${\omega }_0$ determined from the spectra of the mixtures do not differ significantly from those obtained from pure C${\mathrm{F}}_4$. As the total pressure of the mixtures was varied, there were no sudden changes in the scattering analogous to the sharp increase of dielectric loss observed in the microwave absorption spectra and associated with the formation of dimers. In summary, the characteristics of the scattering closely resemble that from the rare gases.

Absolute cross sections for the emission of the 3914-Å radiation of the ${\mathrm{N}}_2^{+}$ first negative system have been measured for protons incident on a gaseous nitrogen target. The energy range covered was 12-100 keV. The energy dependence of the data presented is somewhat different from most previously published data. A possible energy-dependent source of error that may have occurred in previous measurements is discussed. In the present experiment this error should have been minimized by the use of a calorimeter rather than a Faraday cup to measure incident-beam current.

Cross sections for the $7P_{\frac{1}{2}}\to 6D_{\frac{3}{2}}$ and $7P_{\frac{3}{2}}\to 6D_{\frac{3}{2}}$ transitions, induced at thermal energies by cesium-rare-gas collisions, have been measured over the temperature range from 420 to 615 K. The values of the cross sections are found to be surprisingly high when considering only the energy defect of the levels involved. Moreover, the cross sections for Cs-He collisions exhibit very different behavior than those corresponding to heavier rare gases. A discussion with the aid of theoretical adiabatic potential curves explains the main features of the experimental results. Theoretical calculations of the cross sections have been carried out for some cases, and give results in satisfactory agreement with the experimental values.