This paper presents measurements of the Lyman-$\alpha$ photons emitted when target gases He, Ar, ${\mathrm{O}}_2$, and ${\mathrm{N}}_2$ are bombarded by a beam of ground-state hydrogen atoms. The collisions take place in the presence of an axial electric field and the observed Lyman-$\alpha$ brightness depends on field direction. This observation is interpreted as evidence for excitation of hydrogen atoms to states which are linear superpositions of $2s$ and $2p$. Measurements are presented of a "mixed" cross section ${\sigma }_{\mathrm{sp}}$ which characterizes the degree of coherent excitation. The real part of ${\sigma }_{\mathrm{sp}}$ measures the electric dipole moment created by the collision, while the imaginary part measures the rate at which the moment is changing. It is found that these quantities vary substantially over the energy range 3-30 keV, with maximal values being about as large as permitted theoretically. Coherent excitation should be present to some degree in all inelastic collisions and, when measurable, provides new tests of scattering theory. Some implications are also discussed for precision frequency measurements and searches for weak-interaction effects in atomic physics.

A systematic investigation of $K$-x-ray production for 20-80-MeV Cl ions in collision with thin self-supporting Cu targets has been conducted. Target and projectile characteristic x rays and radiative electron capture (REC) have been measured as a function of target thickness for incident charge states $q<\mathrm{}{Z}_1-2\mathrm{}$. At 80 MeV data were also obtained for $q=Z_1-1\mathrm{}$. Large enhancements in both characteristic x-ray production and REC were observed for $q=Z_1-1\mathrm{}$. Measured x-ray yields were parametrized versus target thickness using the model of Betz et al., and least-squares fits to the data were performed. Target $K$-x-ray production for $q<\mathrm{}{Z}_1-2\mathrm{}$ is described reasonably well by the Coulomb perturbed-stationary-state relativistic plus electron capture relativistic (CPSSR+ECR) theory. For $q=Z_1-1\mathrm{}$ the enhancement in the x-ray yield is predicted quite well by the method of Gray et al. The mean fluorescence yield for the highly stripped Cl ions is determined and found to increase by a factor of about 6 over the range 20-80 MeV, having a value (∼ 0.1) nearly equal to the single $K$-vacancy value at 20 MeV. The radiative lifetime for the projectile ions is found to be ∼ 3 × ${10}^{-14\mathrm{}}$ sec, which is about three times longer than the single-$K$-vacancy radiative lifetime calculated by Scofield. Parametrization of the REC yields versus target thickness is used to normalize the measured REC intensity to the fraction of ions with $K$ vacancies. Resulting REC cross sections are compared with the free-electron theory of Bethe and Salpeter and good agreement is obtained if it is assumed that each of the "loosely" bound electrons in Cu contributes equally to the REC process. By combining the results obtained for the characteristic x rays and REC, the fluorescence yield for $K$-shell capture events may be estimated, giving values in the range (2-4) × ${10}^{-3\mathrm{}}$ for the beam energies studied.

The metastability-exchange cross section between $\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)\mathrm{Kr}$ atoms and $\left({}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)\mathrm{Kr}$ atoms is measured by means of a two-laser saturated-absorption experiment performed on the $\lambda =557\mathrm{}$-nm transition. A study of velocity changes occurring in pure ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}$ and in (${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}$-${}_{}{}^{78}{}_{}{}^{}\mathrm{Kr}$) discharges leads to a value for the cross section $Q=(75\mathrm{}\pm 10)$ ${\mathrm{\AA }}^2$.

The optical potential in principle gives a complete description of the effect of the target continuum on an electron-scattering problem truncated to a discrete set of channels. A momentum-space form for the optical potential has been derived and computed for the continuum in various approximations for the case of hydrogen. The total ionization cross section is excellently reproduced in the weak-coupling approximation above 100 eV by the most detailed model, and is tolerable as low as 50 eV.

Four-body trajectory calculations are presented for collisions of $\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ and $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ atoms with atomic hydrogen. Since none of the ${\mathrm{H}}^{-}$ formations was found to be classically stable, only cross sections for electron loss due to direct and exchange processes are presented. Where comparable ionization cross sections are not available in the Born and classical impulse approximations, fresh calculations have been carried out. The various cross sections are compared among themselves and with available experimental data.

Absolute energies of the $\mathrm{Ar}K$, $\mathrm{Kr}K$, and $\mathrm{Xe}{L}_1$, $L_2$, and $L_3$ levels have been determined from absorption edges measured with synchrotron radiation. The double-crystal x-ray monochromator was calibrated by a method that ties the energy scale directly to the crystal lattice constant and $\mathrm{hc}$. Theoretical model spectra were constructed from ≥ 4 Lorentzians representing the lowest-energy one-electron electric-dipole transitions to bound excited states, and an arc tangent representing transitions to higher bound states and to the continuum. The transition energies were found by minimizing ${\chi }^2$ for the fit of the theoretical spectrum shape to the data. Energy differences from optical spectral series were used to relate the excited-state energies to the vacuum level. Results are compared with earlier measurements and with theory.

The beam-foil spectrum of helium from 2050 to 3600 Å has been acquired at 160-keV incident ion energy using a multiple-scan, computerized system. Eleven doubly-excited-state transitions, including two not previously observed, have been assigned, and the agreement between experimental and theoretical energy levels is excellent. The Stokes parameters as a function of foil-tilt angle have been measured for the two strongest transitions (2578 and 3013 Å) from 0° to 80° in 10° increments and for two weaker transitions (2562 and 2818 Å) at 0°, 20°, 40°, and 60°. The polarization patterns are quite different from those of the helium singlets and include the first measurement of negative $\frac{M}{I}$ (a Stokes parameter) at 0° foil tilt for helium at this energy. The lifetime of the 2578-Å transition has been investigated in detail. The present result, 0.109±0.004 ns, agrees with previous measurements and yields an upper limit to the autoionization width of the $2p3p{}_{}{}^3{}_{}{}^{}D$ levels of 6×${10}^{-6\mathrm{}}$ eV.

Resonance fluorescence due to intense laser fields from a Zeeman degenerate atom being perturbed by collisional interactions is calculated in the impact regime by using the quantum-fluctuation-regression theorem. Various interesting effects are found. For example, the scattered intensity spectrum for a $J=0\mathrm{}$ to $J=1\mathrm{}$ transition for polarization parallel to the laser polarization is essentially an asymmetric triplet, whereas for a perpendicular polarization due to collisions the spectrum is essentially a doublet (whose frequencies do not correspond with any of those of the triplet). Further, the width of the fluorescent component (whose frequency is close to the unperturbed frequency) actually decreases with increasing laser power.

The collision of Na with Xe in the presence of both the rhodamine-110 dye laser and the Nd: glass laser is investigated within a quantum-mechanical close-coupled formalism, utilizing ab initio potential curves and transition dipole matrix elements. Both one- and two-photon processes are investigated; the Na + Xe system is not asymptotically resonant with the radiation fields, so that these processes can only occur in the molecular collision region. The one-photon processes are found to have measurable cross sections at relatively low intensities; even the two-photon process has a significant cross section for field intensities as low as 10 MW/${\mathrm{cm}}^2$.

A configuration-interaction model is used to study line strengths and $\mathrm{gf}$ values for transitions in which level crossing occurs in either the initial or final state. It is shown that the line strength varies continuously for the lowest eigenstate, for example, but not for the eigenstate with a given dominant component. The latter exhibits marked irregularities in the vicinity of a crossover. Some plots for line strengths are presented showing the possible types of irregularities using a model interaction matrix. Computed $\mathrm{gf}$-value trends for $3p$ or $4p{}_{}{}^2{}_{}{}^{}P-(3\mathrm{}{s}^{2}4s,3s3p^2){}_{}{}^2{}_{}{}^{}S$ transitions, as a function of $Z$, illustrate some of these irregularities.

The finite-elements method is used to solve, to the given degree of accuracy, bound states of the H atom and the molecular ion ${\mathrm{H}}_2^{+}$ of hydrogen in a strong magnetic field, ${10}^9$ ${10}^{13}$ gauss, and stronger. In the case of the hydrogen atom, the results are in agreement (within a factor of ∼ ${10}^{-4\mathrm{}}$) with results of the best variational calculations in the area of field changes, while in the case of the molecular hydrogen ion and for the 0${10}^{11}$ gauss field they are far better than all calculations known to date. The opinion presented here is that the finite-elements method used in this paper—i.e., the method of direct solution of the particular problem on a plane—can also be successfully used in many other physics problems which are reduced to partial differential equations on a plane, and when perturbation theory or some other similar method of solution is not applicable.

A generalized method for obtaining individual level population ratios is used to obtain relative intensities of extreme ultraviolet Fe xv emission lines in the range 284-500 Å, which are density dependent for electron densities in the tokamak regime or higher. Four lines in particular are found to attain quite high intensities in the high-density limit. The same calculation provides inelastic contributions to linewidths. The method connects level populations and level widths through total probabilities $t_{\mathrm{ij}}$, related to "taboo" probabilities of Markov chain theory. The $t_{\mathrm{ij}}$ are here evaluated for a real atomic system, being therefore of potential interest to random-walk theorists who have been limited to idealized systems characterized by simplified transition schemes.

Numerical predictions are obtained, within a relativistic multipole central-field approximation calculation, for the radial matrix elements and resulting angular distributions of photoelectrons ejected from inner through outer subshells of uranium and for photoelectron energies from near threshold (1 eV) to 100 keV. Some data are also presented for outer subshells of mercury. We confirm that for inner shells higher-multipole effects persist to low energies, while we find that for outer shells such effects become small. For uranium inner $\mathrm{ns}$ subshells the asymmetry parameter ${\beta }_{\mathrm{ns}}$ differs from its nonrelativistic value 2, but not more than 30% (for $n<\mathrm{}4\mathrm{}$), until the energy becomes quite high (the radial matrix elements for $\mathrm{ns}\to \epsilon p_{\frac{1}{2}}$ and $\mathrm{ns}\to \epsilon p_{\frac{3}{2}}$ transitions for these inner shells are similar). For outer $s$ subshells relativistic spin-orbit splittings cause large deviations from the nonrelativistic predictions which can be understood from the magnitudes, zeros, and splittings of the two radial matrix elements. For U $6p_{\frac{1}{2}}$ and $6p_{\frac{3}{2}}$, ${\beta }_{6p}$ has the same qualitative features found in nonrelativistic calculations for outer $p$ shells of other high-$Z$ elements, but the angular distributions from the two states do differ in detail. Such differences in angular distributions of the photoelectrons from the two $j$ substates of given $l$ become smaller for inner $p$ shells. For outer $d$ and $f$ subshells the asymmetry parameter oscillates with photoelectron energy in a manner similar to that found by Manson in nonrelativistic dipole $d$-subshell calculations, and no qualitatively important relativistic effects have been identified; this is due to the decrease of the fine-structure-splitting interval with increasing angular momentum. For high energies the shapes of the angular distributions from a sequence of states of varying principal quantum number $n$, for fixed angular momentum ($\mathrm{JL}$), tend to merge into a common curve because at high energies the matrix elements are determined at small distances where all radial wave functions of given ($\mathrm{JL}$) have the same shape.

We have measured the absolute cross section for photoionization of the $4D$ and $5S$ excited states of sodium for 1.06 μm radiation. The method of measurement is based on saturation of ionization probability at high intensity of the ionizing radiation. The measured cross sections for ionization of unaligned atoms are 15.2±1.7 Mb for the $4D$ state and 1.49±0.13 Mb for the $5S$ state, both in excellent agreement with calculated values.

Spectra of $K\alpha$ x rays from 64-MeV sulfur ions incident on a wide range of thick elemental targets have been measured with a plane crystal spectrometer. Various features of the spectra were found to be sensitive to the atomic structure of the targets. In particular, the $K\alpha$ satellite and hypersatellite intensity distributions displayed oscillatory variations ∼ 14% as a function of target atomic number. This behavior is satisfactorily accounted for by the systematics of electron-capture cross sections. Considerable line broadening was observed, and the Lorentzian component of the total linewidth was found to increase linearly with the product of the target atomic number and the atomic concentration.

This paper reports the use of oscillatory fields in two spatially separated interaction regions to make a two-quantum radio-frequency measurement of the $3{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ fine-structure interval in atomic hydrogen. The measurement was carried out in zero magnetic field with a fast hydrogen beam. Radio-frequency fields from two separate oscillators were applied in both interaction regions and used to drive the two-quantum transition. The relative phase in the two interaction regions of one of the radio-frequency fields was alternated between 0° and 180° so as to isolate the separated-oscillatory-field interference signal; the frequency of the other radio-frequency field was varied so as to sweep over the resonance. An adaptation of the earlier reported theory was used to calculate the line shape and power dependence of the separated-oscillatory-field interference signal. The measured value for the $3{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ interval is 4013.106(57) MHz. This value agrees satisfactorily with both the previously reported single-radio-frequency-field measurement and the theoretical value for this interval. The value for the $3{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ interval obtained by combining the results from this measurement with the single-field measurements reported earlier is 4013.155(53) MHz.

The natural linewidths $\Gamma$ and component intensity ratios $\frac{K{\alpha }_2}{K{\alpha }_1}$ are determined using Ge(Li) spectroscopy for four $K\alpha$ x-ray doubles in the range $70\le Z\le 82$. The necessary spectrum-fitting techniques employ two different approaches to convolute the intrinsic Lorentzian profiles with the detector resolution function. The forbidden $K{\alpha }_3$ transition is seen in Ge(Li) spectra for the first time. All results agree closely with Scofield's relativistic Hartree-Fock-Slater calculations.

The second-order process, photon-catalyzed unimolecular decomposition (PCUD), is shown to be comparable to and sometimes larger than the first-order single-photon stimulated decomposition (SPSD) when the intermediate molecular transition is coherently saturated. Thus PCUD is a dominant, identifiable process even in the large class of molecular bound states with nearby continuum allowing SPSD, e.g., the halogen diatoms in the $B{0}^{+}u$ states. It may also be important in the multiphoton dissociation or ionization of molecules.

The incomplete spectrum of finite complex-scaled Hamiltonian matrices $H_{\eta }$ is studied. It is pointed out that the occurrence of an incomplete spectrum of complex-scaled Hamiltonians in the finite-element approximation is neither accidental nor rare, and the existence of a defective eigenvector (orthogonal to itself) of $H_{\eta }$ can be associated with a complex-stationary point which represents the resonance state. A physical interpretation of the incomplete spectrum (the eigenvalues of a defective Hamiltonian matrix) is given, supported by numerical results for $e^{-}$-${\mathrm{He}}^{+}$ scattering worked out as an example. The numerical procedure suggested here for the purpose of identifying the resonance state with the eigenvalue associated with the defective eigenvector of $H_{\eta }$, may prove to be not very practical. This is so as long as only relatively small basis sets are used. However, in the finite-element approximation, this procedure does yield a better understanding of the behavior of the resonance solution.

The double Auger rate of Li $2s^{2}2p$ in which two electrons are emitted simultaneously was calculated using many-body perturbation theory with $\mathrm{LS}$-coupled intermediate states. The final states considered were $kskp\left({}_{}{}^1{}_{}{}^{}P\right)1s$, $kskp\left({}_{}{}^3{}_{}{}^{}P\right)1s$, $kpkd\left({}_{}{}^1{}_{}{}^{}P\right)1s$, and $kpkd\left({}_{}{}^3{}_{}{}^{}P\right)1s$. The ratio of the double Auger rate to the single rate is found to be 0.0728, or approximately 6.8% of the total $2s^{2}2p$ Auger rate.