A time-dependent perturbation theory is used to obtain the cross sections and rates for the quenching of metastable helium ions in collision with molecules (${\mathrm{H}}_2$, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and C${\mathrm{O}}_2$). The results are compared with the recent experimental data of Prior and Wang.

We propose a variational method for scattering in which the functional is of a fractional form as for the Schwinger variational principle. However, our functional does not involve the Green's function, but the Hamiltonian and the potential function. This method shows features of both the Schwinger-type variational principles and the Kohn-type standard variational principles. As a result, our method can derive distinct advantages from both of these approaches. The resultant $K$ matrix is symmetric and anomaly-free. Some other properties, including a minimum principle, which is useful in the selection of an optimum basis for the expansion of the scattering functions are also discussed.

An $L^2$ approach to our variational method which is based on a functional of fractional form is proposed. As in the $R$-matrix theory, configuration space is divided into two parts. However, unlike the $R$-matrix theory, the associated wave function is always smooth. The resulting $K$ matrix is anomaly-free and symmetric (and hence the $S$ matrix is unitary). Application of this method to an exactly soluble two-channel model problem shows that our new approach gives much better results than the other standard variational principles.

The whole-atom integral incoherent-scattering cross sections have been obtained from the total attenuation cross sections in elements whose atomic number ($Z$) ranges from 1 to 56, at photon energies 279.2, 514, 661.6, and 1115.5 keV. The total attenuation cross sections in elements were derived with the aid of mixture rule from total attenuation cross sections in 26 solid chemical compounds, measured by performing transmission experiments in a good geometry setup. The present values of the whole-atom integral incoherent-scattering cross sections have been compared with the Klein-Nishina cross sections, the self-consistent-field Hartree-Fock values of Hubbell et al., and the available earlier experimental results. Electron binding effects have also been discussed.

High-resolution $L_{2,3}{M}_{2,3}{M}_{2,3}$ and $L_{2,3}{M}_{2,3}{N}_1$ Auger-electron spectra from potassium vapor have been measured using electron-beam excitation. The spectra have been analyzed with the aid of the optically known energy levels of the $3p^{4}4s$ and $3p^5$ final-state configurations. The relative intensities of lines in the $L_{2,3}{M}_{2,3}{M}_{2,3}$ spectra are found to correspond very well to the intensities of the $3p^4$ parent Auger lines calculated in a mixed-coupling scheme. The separation of the $3p^4{}_{}{}^3{}_{}{}^{}P$ parent lines into the $3p^4\left({}_{}{}^3{}_{}{}^{}P\right)4s{}_{}{}^2{}_{}{}^{}P$ and $3p^4\left({}_{}{}^3{}_{}{}^{}P\right)4s{}_{}{}^4{}_{}{}^{}P$ lines yields relative intensities which agree quite well with the statistical weight of these states. For the $2p_{\frac{1}{2}}$ and $2p_{\frac{3}{2}}$ binding energies in atomic potassium 303.6±0.1 and 300.7±0.1 eV, respectively, have been obtained.

Transition rates, angular distributions, and power spectra of stimulated-electromagnetic-shock radiation are calculated by means of relativistic quantum mechanics for a circularly polarized monochromatic plane-wave incident at an arbitrary angle to the direction of the electron beam. Usually the process can be divided into a high-frequency branch which is similar to ordinary Čerenkov radiation and a low-frequency branch which corresponds to high-intensity Compton scattering (HCS). No significant enhancement of Čerenkov radiation is found. The transition rates for the HICS branch, however, can be considerably larger than in vacuum.

In an attempt to resolve the disagreement between previous theoretical calculations of the $2s$ partial photoionization cross section in neon, we have examined in detail the relative contribution from the initial-state configuration interaction and the final-state interchannel interaction. In addition, we have calculated the ratio of the $2s$ to $2p$ partial photoionization cross sections for photon energies ranging from the $2s$ ionization threshold to about 220 eV. The calculated value is compared with the recent experimental measurement.

A highly excited (Rydberg) atom bathed in blackbody radiation is perturbed in two ways. A dynamic Stark shift is induced by the off-resonant components of the blackbody radiation. Additionally, electric-dipole transitions to other atomic energy levels are induced by the resonant components of the blackbody radiation. This depopulation effect shortens the Rydberg-state lifetime, thereby broadening the energy level. Calculations of these two effects in many states of hydrogen, helium, and the alkali-metal atoms Li, Na, K, Rb, and Cs are presented for $T=300\mathrm{}$ K. Contributions from the entire blackbody spectrum and from both discrete and continuous perturbing states are included. The accuracy is considerably greater than that of previous estimates.

We show that positronium level shifts which require the reduced Coulomb Green's function in a particular order are considerably simpler to evaluate in the coordinate representation. This simplification occurs because the coordinate-space-reduced Green's function is not particularly complicated and leads to integrals which are elementary. The technique is illustrated using the example of double transverse-photon exchange. We obtain an analytical confirmation of the numerical result previously obtained by Caswell and Lepage.

The 19.37-eV helium scattering resonance profile has been measured with an instrumental width less than the natural width and much less than that attained in any previously published study. The electron beam was produced by photoionization and scattered from a He beam from a supersonic nozzle. The instrumental width, including residual Doppler effects, was routinely around 5 meV and the current was 5×${10}^{-12\mathrm{}}$ A. The profile was measured at 22°, 90°, and 135° scattering angles. From the 90° and 135° data the $s$- and $p$-wave phase shifts were found to be 1.813±0.017 and 0.309±0.013 radians, respectively. The natural width $\Gamma$ of the resonance was inferred by two methods: nonlinear least-squares fitting, and use of the integral of the differential cross section over the resonance. Both methods yield 11.0±0.5 meV, if it is assumed that there is no instrumental background in the scattered electron signal. Experimental evidence indicates that any such instrumental background must be less than 15% of the total signal, and is probably less than 5%. If an extreme allowance is made for the larger figure, a $\Gamma$ as high as 13 meV could be possible.

X rays of energy beyond the $K$-series limit have been detected during the bombardment of various low-$Z$, solid and gaseous targets by ${\mathrm{C}}^{+}$, ${\mathrm{N}}^{+}$, and ${\mathrm{O}}^{+}$ ions of energy 0.75 to 1.9 MeV. $K\alpha \alpha$ x rays, most likely from the transition $\left(1\mathrm{}{s}^{-2\mathrm{}}2p^{-1\mathrm{}}\right)\to \left(2\mathrm{}{s}^{-1\mathrm{}}2p^{-2\mathrm{}}\right)$, are emitted by both collision partners in gaseous targets. The low-resolution energy measurements are in good agreement with published calculations. The relative yield from the heavier collision partner is larger than simple vacancy-sharing models would indicate, but electron screening may account for the excess. Molecular-orbital (MO) continuum radiation completely obscures the $K\alpha \alpha$ lines from thin solid carbon targets. The exponential shape of the MO spectrum beyond the united-atom limit is in reasonable agreement with collision-broadened spontaneous emission.

We have observed large oscillations in the photoabsorption cross sections of Ba and Na in the presence of an electric field. The two-step laser excitation technique allowed the use of various polarization combinations for studying the oscillations in the vicinity of the zero-field ionization limits. Thus, we could for the first time determine the relative contributions from two entirely different theoretical models: The quasibound $m=0\mathrm{}$ states (strong-field-mixing resonances) on the one hand, and symmetry-induced oscillator-strength cancellations on the other. We found that the model of strong-field-mixing resonances alone is able to account for all our experimentally observed cross-section oscillations.

The isotopes shifts of nine molybdenum lines between the levels $\left(4\mathrm{}{d}^{4}5s^2\right)a{}_{}{}^5{}_{}{}^{}D-\left(4\mathrm{}{d}^{5}5p\right)z{}_{}{}^5{}_{}{}^{}P$ have been studied in a newly developed hollow-cathode discharge tube with Doppler-free intermodulated fluorescence and optogalvanic spectroscopy. A homogeneous linewidth of 25 MHz is observed. The isotope shifts are determined with an accuracy of 2 MHz. This is an improvement of approximately one order of magnitude compared to previous measurements. Our results for the isotope shifts agree with previous results of Doppler-limited measurements within the error limits.

A technique of third-harmonic generation (THG) with nonsynchronous pulses is applied to study the dynamics of resonant wave mixing. A circularly polarized laser pulse is focused into a cell containing ${\mathrm{I}}_2$ vapor to create the coherent dipole moments. An oppositely circularly polarized pulse is then focused into the same region to generate the third harmonic. Since no THG is produced by any individual pulse, correlated THG can be easily measured without using any fast detection scheme. A theory is presented to explain the measured coherent lifetime of approximately 1 ns. The technique of wave mixing with two linearly polarized pulse is applied to study saturation in resonant THG and to measure the homogeneous relaxation rate of the molecular states. This technique is also applied to study the photon echo generating process.

The energies and intensities of the $2{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\to 1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$, and $2{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\to 1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ transitions in He-like sulfur ions, and of the $2{}_{}{}^2{}_{}{}^{}P\to 1{}_{}{}^2{}_{}{}^{}S$ transition in H-like sulfur ions have been studied as a function of the thickness and electron density of the solid through which the ions travel. The thickness dependence of the x-ray intensities was analyzed in terms of a three-component model description of $K$-shell vacancy production and decay. Cross sections for electron excitation or ionization and capture deduced from this analysis were used to establish the energies of the x-ray peaks for complete emission in vacuum (i.e., outside the target). Energy shifts were obtained by comparing the peak energies for emission in thick targets to those for emission in vacuum. The results show that the energy shifts increase approximately linearly with the square root of the valence electron density of the target and are in good agreement with theoretical expectations.

Measurements are reported which show the effect of nonradiative losses at a gas-window interface on the backscattered fluorescence intensity for Na vapor at frequencies in the vicinity of the resonance lines near 589 nm. The Na $3P_{\frac{1}{2},\frac{3}{2}}$ states are excited with a low-intensity single-mode tunable dye laser at high Na densities and the frequency integral of the backscattered fluorescence intensity in the $D1\mathrm{}$ and $D2\mathrm{}$ lines is measured. As the laser is tuned through resonance, the loss of atomic excitation to the window appears as a sharp decrease in the frequency-integrated fluorescence intensity. For example, at 7×${10}^{20}$ atoms ${\mathrm{m}}^{-3\mathrm{}}$ the fluorescence intensity decreases by a factor of 4 in a frequency interval of 4 GHz. Measured absolute fluorescence intensities versus laser frequency are compared with predictions made using the theory of Hummer and Kunasz which includes both radiative and nonradiative transport processes. The agreement between theory and experiment is remarkably good when one considers that the theory contains only one unknown coefficient, i.e., the reflection coefficient for excited atoms at the windows. In our case the excited atoms are assumed to be completely destroyed at the window.

The fast-atomic-beam microwave-optical resonance technique has been used to measure the $8F-8G$, $8F-8H$, $7F-7H$, and $7F-7I$ intervals in helium. The electrostatic fine-structure intervals derived from these measurements and from theoretical values of the magnetic fine structure are $8F-8G$, 3898.525(0.041); $8G-8H$, 931.34(0.44); $7G-7H$, 1359.16(0.11); and $7H-7I$, 402.8(4.7) MHz. Additional theoretical work is needed to understand these intervals beyond the 1% level.

A class of pulse functions is found for which analytic solutions to the problem of two levels coupled by these pulse functions is obtained. The hyperbolic-secant coupling pulse is included in this class of functions leading to the Rosen-Zener solution, but all other pulses belonging to the class function are asymmetric. The asymmetric pulses lead to qualitatively new features in the solutions; in general, it is impossible to have a zero-transition probability with such asymmetric pulses.

We comment on the spectral modification and temporal reshaping of a narrow-band light pulse propagating through an atomic absorber that has a still narrower spectral hole. The regime of propagation narrowing is distinguished from the regime of Beer's law.

Intensity correlations in a two-mode laser oscillating on two coupled transitions have been studied by means of the Fokker-Planck equation. It is shown that they can be expressed in terms of the eigenvalues and eigenfunctions of a one-dimensional Schrödinger-type equation. It is found that near threshold intensity correlations cannot be approximated by a single exponential. For moderately large excitations, however, a single exponential dominates. Approximate analytic expressions for large excitations have been obtained which show that the correlation time increases with increasing excitation.