The bremsstrahlung emitted from a tungsten anode in an x-ray tube has been used for continuous analysis of krypton and xenon absorption spectra between 8 and 0.8 keV (1.5 to 15 Å). Attenuation coefficients were determined every 0.05 Å between 1.5 and 8 Å (in steps of energy varying from 150 to 10 eV) and every 0.1 Å between 8 and 15 Å (20 to 5 eV). Results obtained are compared with previously determined experimental values and with semiempirical and theoretical determinations. Tabulated data of McMaster et al. and calculations of McGuire are shown to be in good agreement with the experimental results, generally within 10%. Multiply excited and ionized states have been observed in krypton, owing to simultaneous interaction of incident radiation with $2p$ and $4p$ (and $4s$) electrons, and a nonhydrogenic behavior of the xenon $3p$-subshell photoionization cross section has been revealed. Krypton and xenon $L$ and xenon $M_{\mathrm{III}}$ absorption jump ratios have been determined. Finally, continuous oscillator strengths of krypton and xenon $L$ shells and the xenon $M$ shell have been evaluated.

A theoretical approach, capable of providing quantitative results for $N$-electron nonrelativistic "nonstationary" states is presented. I treat inner-hole or doubly excited states, observed in various types of experiments, from a conceptually single point of view, as decaying states. First, the relevant important quantities already known, e.g., from Feshbach's theory, are derived and interpreted in a mathematically and physically meaningful way. Then I consider the exact square-integrable $N$-electron function describing the initial localized $N$-electron state and, from straightforward variation-perturbation-theory considerations, I derive a variational minimum principle which permits one to incorporate systematically the important correlation effects without the danger of a "variational collapse." This method requires projection onto known one-electron zeroth-order functions and it thus overcomes the difficulties of the well-known $P$, $Q$ methods which require projection onto exact wave functions. From preliminary $N$-body calculations I find the ${\mathrm{He}}^{-}$${}_{}{}^2{}_{}{}^{}P_{}^0{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}D$ resonances, previously observed experimentally, at about 57.3 and 58.4 eV. In addition, I predict the positions of various autoionizing states: in Li I at about 140.7 eV (a ${}_{}{}^2{}_{}{}^{}P_{}^0{}_{}{}^{}$ state), in C IV at about 306.7 eV (${}_{}{}^2{}_{}{}^{}D$), in N I at about 14.9 eV (${}_{}{}^2{}_{}{}^{}D$), and in F I at about 22.4 eV (${}_{}{}^2{}_{}{}^{}S$) above the ground state. These states, which are just samples of states treatable by this approach, may in principle cause observable structures, e.g., in photon-absorption experiments, in particle-atom scattering experiments, or in beamfoil experiments.

Five-MeV He and Ne ions were used to excite the aluminum $K\alpha$ and $K\beta$ parent and satellite x-ray spectra of A1 metal, oxide, and nitride. Compared to the metal, the $K\alpha$ line and $K\alpha$ satellites from the oxide were at energies a few tenths of an eV higher with helium-ion excitation, similar to observations with electron excitation. With neon bombardment, the $K\alpha$ satellite lines were broader and the energy shifts reduced because of target-atom recoil effects. The chemical shifts in the $K\beta$ spectra vary from negative in the parent band with helium ions to positive shifts as large as 6 eV in the higher-energy $K\beta$ satellites produced by neon ions, and were found to depend on the degree of $L$-shell ionization.

The cross section for the transition $6{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}\to 6{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ in mercury, induced in collisions with ${\mathrm{N}}_2$ molecules, has been determined by the method of delayed coincidences. The Hg ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state was excited by pulses of 2537-Å Hg resonance radiation and the decay of the long-lived 2537-Å afterglow was studied in relation to ${\mathrm{N}}_2$ pressure. The resulting cross section $Q_{12}({}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{})=4.18\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{\AA }}^2$ was found to be good agreement with the prediction of the principle of detailed balancing when compared with the cross section $Q_{21}({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{})$. It was also found that, within the sensitivity of the method, collisions with ${\mathrm{N}}_2$ molecules do not quench ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ or ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ Hg atoms to the ground state.

Electron-impact excitation cross sections for $\mathrm{OI}({}_{}{}^3{}_{}{}^{}P-3s{}_{}{}^3{}_{}{}^{}S_{}^0{}_{}{}^{})$ are calculated in unitarized Born, nonexchange, and close-coupling approximations. The close-coupling cross sections have the same energy dependence as measurements by Stone and Zipf but are lower in magnitude by a factor of 4. Two autodetaching levels of ${\mathrm{O}}^{-}\left[2\mathrm{}{p}^3\right({}_{}{}^4{}_{}{}^{}S_{}^0{}_{}{}^{}\left)3s3p{}_{}{}^{2,4}{}_{}{}^{}P\right]$ are found at 9.67 and 9.94 eV. The doublet state is tentatively identified as a state found experimentally by Edwards at 9.52 eV.

An analysis of electron drift-velocity data in cesium has been conducted in order to determine the electron momentum-transfer cross section. Numerical evaluation of the drift-velocity integral using numerous trial functions for the cross section has revealed the qualitative and semiquantitative nature of the electron momentum-transfer cross section in cesium. The cesium cross section found to be most consistent with the available experimental data exhibits considerable variation with electron energy in the range 0.1-1.0 eV, the region of primary importance in plasma applications.

Calculations have been made on the elastic scattering of low-energy electrons by helium using a variational procedure which takes polarization and correlation effects into account by means of continuum Bethe-Goldstone equations. The convergence of the results is examined using two methods to obtain a complete set of basis functions. Results for the $s$, $p$, $d$, and $f$ waves are presented. The width of the ${}_{}{}^2{}_{}{}^{}S$ closed-channel resonance below the $n=2\mathrm{}$ threshold is found to be 0.015 eV, in comparison with the 0.015-0.020-eV estimates of Andrick and Ehrhardt from experiment and the 0.01-eV estimate of Simpson and Fano.

The four second-order terms in the Born series for the proton-hydrogen electron-transfer problem are analytically reduced from six-dimensional to three-dimensional integrals. No mass approximations are made. This permits an accurate numerical calculation of the total cross section to second order. Numerical results are given from 0.1 to 2.5 MeV. The complete second-order cross section reduces the first-order results by 30% from 1 to 2.5 MeV. The various first- and second-order Born approximations for this problem are discussed.

Low-energy-photoionization cross sections for the elements hydrogen through plutonium were calculated using a nonrelativistic single-particle model. Initial-atom and final-ion wave functions were developed from the Hartree-Fock equations using Slater's free-electron exchange approximation. Core relaxation was included approximately by using experimental binding energies in the Schrödinger equation for the continuum electron. Subshell contributions and total-cross-section calculations for the noble gases are compared with Hartree-Fock values with complete exchange. Total cross sections are compared with experiments for low-, medium-, and high-atomic-number elements.

The projection-operator formalism advanced by Feshbach is used to derive a numerically tractable equation which describes the elastic scattering of electrons from atomic hydrogen under multichannel conditions. By neglecting the potential of interaction in the inverse operator, analytical expressions can be obtained for the Green's function which permit the inclusion of both discrete and continuum target-state contributions to the optical potential. The numerical procedures used to solve the resulting nonlocal integrodifferential equation and to generate differential, total elastic and inelastic cross sections are discussed. Good agreement is found with available experimental data.

The $\frac{K\beta }{K\alpha }$ radiative-transition probabilities have been measured for 26 elements ranging in atomic numbers from ${}_{11}{}^{}{}_{}{}^{}\mathrm{Na}$ to ${}_{45}{}^{}{}_{}{}^{}\mathrm{Rh}$. The samples were in an amorphous state except ${}_{17}{}^{}{}_{}{}^{}\mathrm{Cl}$ and ${}_{35}{}^{}{}_{}{}^{}\mathrm{Br}$, which were in crystal form. The elements ${}_{11}{}^{}{}_{}{}^{}\mathrm{Na}$, ${}_{12}{}^{}{}_{}{}^{}\mathrm{Mg}$, ${}_{19}{}^{}{}_{}{}^{}\mathrm{K}$, and ${}_{20}{}^{}{}_{}{}^{}\mathrm{Ca}$ were studied in both amorphous and crystal forms. The $K$ vacancies were produced by radiation from commercial ${}_{74}{}^{}{}_{}{}^{}\mathrm{W}$ and ${}_{24}{}^{}{}_{}{}^{}\mathrm{Cr}$ x-ray tubes. The corrected measured ratios are compared with the most recent calculations based on a relativistic Hartree-Fock-Slater (RHFS) potential and relativistic screened Coulomb potential. Although the form of the dependence of this ratio on atomic number predicted on the basis of a RHFS potential seems to be correct, the experimental values are consistently higher than the calculated results. Comparison with other recent experimental results is also made.

Many-body perturbation theory is used to calculate the total photodetachment cross section of ${\mathrm{O}}^{-}$ from threshold to 1.1 keV. This nonrelativistic calculation uses the velocity form of the dipole approximation. We include the effects of resonances owing to $2s\to 2p$ and $1s\to 2p$ excitations. Comparison is made with experiment and other theoretical treatments.

Inelastic-collisional effects are incorporated into a quantum-mechanical transport equation (QMTE) that was developed in an earlier paper. The QMTE enables one to follow the quantum-state evolution of moving atoms which are interacting with some external fields while undergoing collisions with perturber atoms. The collisional processes are treated quantum mechanically and then reinterpreted in terms of classical variables so that the QMTE becomes an integrodifferential equation for atomic density-matrix elements containing both well-defined quantum-mechanical collision parameters (i.e., scattering amplitudes) and densitymatrix elements which are functions of classical position and velocity variables. Solutions of the QMTE enable one to derive line-shape formulas, and a discussion will be given of the general features to be expected for spectral profiles, Hanle-effect line shapes, and laser output curves, as well as the manner in which these features differ from those predicted by theories that neglect some quantum-mechanical aspects of the collision events. The inclusion of inelastic-collisional effects does not cover cases in which the frequency spacing of the atomic levels under consideration is comparable to the inverse duration time of a collision; nevertheless, the QMTE to be derived will be applicable to the analysis of a large number of atomic systems.

The variational methods of Kohn and Hulthén are used to calculate the scattering parameters of the positron-hydrogen rearrangement collision. The $R$-matrix elements are computed for positron energies 0-0.33 a. u. with accuracy of (1-10)%. It is also shown that a good approximation to the diagonal elements of the $R$ matrix can be obtained by ignoring the coupling between the channels.

We utilize the analytic atomic independent-particle model (IPM) of Green, Sellin, and Zachor to calculate generalized oscillator strengths (GOS) and total cross sections for excitation and ionization of atomic oxygen. First we average over the experimental energy levels within a multiplet to arrive at single-particle levels. Then we adjust the two parameters of the IPM potential so that it accurately characterizes the ground state and 15 lowest excited states. Using the wave functions so obtained, and assuming the Born approximation and the $\mathrm{LS}$-coupling scheme, we calculate absolute GOS and cross sections for excitation to these levels, and for ionization with incident energies up to 1000 eV and secondary electron energy up to 200 eV. We obtain an analytic representation of the excitation GOS as a function of the momentum transfer. We also obtain an analytic representation of the energy differential cross section for ionization as a function of the energies of the incident and secondary electrons. Comparison is made with available experimental data and other calculations.

Dissociative excitation of molecular hydrogen can proceed via the process ${\mathrm{H}}_2+e\to \mathrm{H}\mathrm{}\left(2s\right)+\mathrm{H}+e$ and yield metastable $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ atoms that have kinetic energies near 0.3 eV ("slow") or near 4 eV ("fast"). The dissociation process has been studied using a pulsed electron gun with an energy resolution of ± 0.3 eV and using a metastable atom detector capable of viewing $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ atoms with an angular resolution of 1° over a range 60°-120° with respect to the electronbeam direction. The measurement of the angular intensity distribution gives information about the final states that are involved in the dissociation process. (i) For slow $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ atoms, the electron energy threshold for production of the least energetic of the slow metastable atoms is 14.6 ±0.3 eV. The excitation function and the angular distribution of the slow $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ atoms suggest that the $B^{\prime }{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$, $e{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$, $D{}_{}{}^1{}_{}{}^{}\Pi _u^{+}{}_{}{}^{}$, and $d{}_{}{}^3{}_{}{}^{}\Pi _u^{+}{}_{}{}^{}$ excited states are involved in the formation of these metastable fragments. (ii) For fast $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ atoms, the electron energy threshold for production of the least energetic of the fast $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ atoms is near 29 eV. The angular distribution data would indicate that these atoms arise from a ${\Pi }_u$ state; the form of the excitation function indicates that the parent state has a multiplicity of 1. The change in energy distribution of the fast $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ atoms, measured as a function of electron-gun voltage, supports the view that the ${}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ state is a previously unreported doubly excited state that has an asymptotic energy of 24.9 eV.

Laser magnetic resonance of the ${\mathrm{O}}_2$ molecule is observed using the 119- and 78-μm lines of the ${\mathrm{H}}_2$ O laser. The relevant transitions for the 119-μm line are $(N=13, J=14, M)\to (N=15, J=14, M^{\prime })$, and those for the 78-μm line are $(N=21, J=22, M)\to (N=23, J=22, M^{\prime })$, where $M^{\prime }=M or M\pm 1$ depending on the polarization. It is found that $g_{\perp }=2.0044\mathrm{}\pm 0.0008$, $g_z=2.0020\mathrm{}\pm 0.0001$, $g_n=0.000125\mathrm{}\pm 0.000008$ give slightly better agreement between theory and experiment than Hendrie and Kusch's values ($g_{\perp }=2.005169\mathrm{}$, $g_z=2.001939\mathrm{}$, $g_n=0.000122\mathrm{}$) and Bauer, Kamper, and Lustig's values ($g_{\perp }=2.004838\mathrm{}$, $g_z=2.002025\mathrm{}$, $g_n=0.000126\mathrm{}$), but the present experimental accuracy is not high enough to exclude these older $g$-factor values. Using the existing microwave data and the known laser frequencies, the zero-field frequencies for the transitions $\mathrm{}(N=J=13\mathrm{})\mathrm{}\to \mathrm{}(N=J=15\mathrm{})\mathrm{}$ and $\mathrm{}(N=J=21\mathrm{})\mathrm{}\to \mathrm{}(N=J=23\mathrm{})\mathrm{}$ are found to be 2496.283±0.30 and 3865.81±0.03 GHz, respectively. Combining these results with the frequency of the $\mathrm{}(N=J=1\mathrm{})\mathrm{}\to \mathrm{}(N=J=3\mathrm{})\mathrm{}$ transition obtained by McKnight and Gordy, we obtain $B_0=43.100518\mathrm{}\pm 0.000020$ GHz, $B_1=-0.14496\mathrm{}\pm 0.00030$ MHz, and $B_2=-0.17\mathrm{}\pm 1.00$ Hz.

A relationship $dS=\frac{\mathrm{dQ}}{T}$ is derived for slow changes in a steady-state system far from equilibrium. Systems consisting of one conservative degree of freedom, coupled to a dissipative nonequilibrium system without energy storage are considered. The entropy $S$ is defined in the conventional statistical mechanical sense by an integral $-k\int \rho \ln \rho \mathrm{dq}$ over the conservative degree of freedom. The fluctuations are assumed to be narrow and the temperature $T$ is the noise temperature, i.e., the temperature characterizing the intensity of the fluctuations in stored energy. $-dQ$ is the energy given up to the reservoir to the extent that it exceeds that predicted for steady-state losses on the basis of the macroscopic equations. Generalizations to the case of two or more degrees of freedom are successful only in special cases. These include the case where one degree of freedom adjusts rapidly compared to the other. It also includes cases where the different degrees of freedom see the same noise temperature.

For the description of an assembly of two-level atoms, atomic coherent states can be defined which have properties analogous to those of the field coherent states. The analogy is not fortuitous, but is shown to be related to the group contraction of exponential operators based on the angular momentum algebra to exponential operators based on the harmonic-oscillator algebra. The derivation of the properties of the atomic coherent states is made easier by the use of a powerful disentangling theorem for exponential angular momentum operators. A complete labeling of the atomic states is developed and many of their properties are studied. In particular it is shown that the atomic coherent states are the quantum analogs of classical dipoles, and that they can be produced by classical fields.

The statistics of the sum of photocounts in partially coherent Gaussian light is investigated. Both the case of detection at $L$ discrete points and the case of an extended surface of detection are considered. The combinatorial-analysis approach is applied to derive the moments and cumulants of the distribution. They all can be expressed in terms of the second-order correlation function. The results are generally valid independent of the ratio of the observation time to the coherence time of light. A comparison between the theoretical moments and the moments computed from experimental distributions as a function of the detector surface is carried out with the help of a pseudothermal source.