The uranium $M$ x-ray spectrum from a thick metallic target excited by 12-keV electrons was measured by the PAX (photoelectron spectrometry for the analysis of x rays) technique. Energies of the strongest lines were obtained with an accuracy of 0.1 eV using Ag $L{\beta }_1$ and Ag $L{\alpha }_1$ as standards. Widths of the uranium lines were obtained by deconvoluting the measured Voigt profiles, and the experimental values were found to agree satisfactorily with McGuire's Hartree-Slater predictions. Natural widths of 4.0(3) and 3.8(3) eV were derived for the $M_4$ and $M_5$ levels, respectively, and the energies of the $M_4$, $M_5$, $N_2$, and $N_3$ levels in uranium metal were determined. Relative intensities of the $M$ lines were measured, and branching ratios were found to be in fair agreement with relativistic Hartree-Slater predictions. The satellite structures of the $M{\alpha }_1$ and $M\beta$ lines were interpreted in terms of the pertinent multiple-hole configurations. Finally, an approximate analytic expression for the Voigt half-width and its graphical representation are given.

We have used two-photon absorption from counterpropagating laser beams of different frequencies to measure Stark shifts and splittings of the $6{}_{}{}^2{}_{}{}^{}S$, $7{}_{}{}^2{}_{}{}^{}S$, $8{}_{}{}^2{}_{}{}^{}S$, $5{}_{}{}^2{}_{}{}^{}D$, and $6{}_{}{}^2{}_{}{}^{}D$ states in sodium. Beams from a fixed-frequency, single-mode ${\mathrm{Ar}}^{+}$ laser and a tunable, single-frequency cw dye laser were focussed into a coarse sodium atomic beam and the fluorescence was monitored. The collimation of the atomic beam reduced the residual Doppler width inherent in using two different frequencies. Using the two lasers allowed two-photon transitions to be observed at frequencies unattainable with the dye laser alone, and enhanced the transition rates due to the near resonance of the dye laser with the strong Na $3{}_{}{}^2{}_{}{}^{}S\to 3{}_{}{}^2{}_{}{}^{}P$ transition. Our experimental results for the scalar and tensor polarizabilities, ${\alpha }_0$ and ${\alpha }_2$, agree with calculations in the Bates and Damgaard Coulomb approximation within 2% for ${\alpha }_0$ and 9% for ${\alpha }_2$. As a by-product the hyperfine-interaction constants $a$ for the $S$ states and the fine-structure intervals $\delta \nu =\frac{(E_{\frac{3}{2}}-E_{\frac{5}{2}})}{h}$ for the $D$ states were obtained.

The collision-induced fundamental infrared absorption band of ${\mathrm{H}}_2$ in the pure gas at 77, 196, and 298 K was recorded for a number of gas densities up to 60 amagat. An analysis of the absorption profiles was performed by assuming appropriate line shapes, and the characteristic half-width parameters ${\delta }_d$ and ${\delta }_c$ of the short-range overlap-induced transitions and ${\delta }_q$ (and ${{\delta }_q}^{\prime }$) of the long-range quadrupole-induced transitions were determined. From this analysis the contributions to the intensity of the band from the overlap and quadrupolar interactions were separated. For the ${\mathrm{H}}_2$-${\mathrm{H}}_2$ molecular pairs, the overlap parameters, $\lambda$ and $\rho$, which give, respectively, the magnitude and range of the overlap dipole moment, and $\mu \left(\sigma \right)$, the overlap-induced dipole moment at the Lennard-Jones intermolecular diameter $\sigma$, were determined by obtaining the best fit of the calculated overlap parts of the binary absorption coefficients as a function of temperature to the experimental values. The values of the overlap parameters obtained are $\lambda =4.53\mathrm{}\times {10}^{-3\mathrm{}}$, $\rho =0.23\mathrm{}$ Å, and $\mu \left(\sigma \right)=2.5\mathrm{}\times {10}^{-2\mathrm{}}e{a}_0$.

The $N_{6,7}{O}_{4,5}{O}_{4,5}$ Auger electron spectrum from mercury vapor has been measured using electron-impact excitation. The experimental spectrum has been decomposed into its components, and the relative energies and intensities have been compared with the theoretically calculated relative energies and intensities. The calculations have been done in the mixed-coupling scheme. Applying $\mathrm{jj}$ coupling to the initial state and intermediate coupling to the final states gives good agreement between the calculated and experimental results for both energy and intensity. The measured width of the Auger lines is greater than would be expected on theoretical grounds.

Correlated two-electron transitions into the doubly ionized $K$ shell have been observed in Al-Al, O-Ca, Ca-Ca, Fe-Fe, Fe-Ni, Ni-Fe, and Ni-Ni collisions at beam energies between 24 and 40 MeV. In these transitions one photon carries away the entire two-electron transition energy. The cross sections for the characteristic radiation and the two-electron radiation have been determined. The measured branching ratios between the single- and double-electron transition into the doubly ionized $K$ shell are compared with various theoretical predictions. The theoretical and experimental results are found to be in qualitative agreement.

We discuss the existence of a general Wigner-Eckart theorem for the physical hydrogen-atom problem. The group generators are not a derivation with respect to the physical variables ($r, \theta , \phi$), and thus the eigenfunctions do not qualify as tensor operators. The lack of the derivation property is reflected in disjoint subspaces which for the Coulomb problem are threefold.

Previous theoretical studies of the ground state of three-electron atoms based on $Z$-dependent perturbation theory have yielded values for the third-order energy coefficient which differ by as much as a factor of 2. Estimates of the third-order energy coefficient obtained via a "differencing technique" from variational calculations and from experimental data for the lithium isoelectronic sequence also disagree with each other and with the theoretical results. The present value of the third-order energy coefficient is based on a first-order wave function constructed from accurate, first-order, two-electron wave functions and appears more accurate than these earlier results.

It is pointed out that the Wigner function $f(r, p)$ is $\frac{2}{h}$ times the expectation value of the parity operator that performs reflections about the phase-space point $r$, $p$. Thus $f(r, p)$ is proportional to the overlap of the wave function $\psi$ with its mirror image about $r$, $p$; this is clearly a measure of how much $\psi$ is centered about $r$, $p$, and the Wigner distribution function now appears physically more meaningful and natural than it did previously.

Measurements are reported for the total quenching of metastable hydrogen atoms by neon, krypton, xenon, and molecular hydrogen, in the energy range 0.052-3 keV. The cross sections are found to be on the order of 5 × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ at the lowest energies, and decrease to approximately 2 × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ at the highest energies. The data at low energy are analyzed using a simple theoretical model.

The total cross section for electron capture has been measured for ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{+}$, ${\mathrm{N}}^{+}$, ${\mathrm{Ne}}^{+}$, ${\mathrm{Ar}}^{+}$, ${\mathrm{Kr}}^{+}$, and ${\mathrm{Xe}}^{+}$ incident on a Cs vapor target. The energy range investigated was 40-120 keV for incident protons, 30-140 keV for incident ${\mathrm{N}}^{+}$, and 20-200 keV for the incident noble-gas ions. Also measured was the total attenuation cross section for ${\mathrm{H}}_2^{+}$, ${\mathrm{H}}_3^{+}$, and ${\mathrm{N}}_2^{+}$ incident on Cs in the energy range 30-160 keV. These attenuation cross sections result from either electron capture or breakup of the incident molecular ion. At velocities below 5×${10}^5$ m/sec, the various cross sections are different both in magnitude and velocity dependence. In the velocity range (0.5-1.5)×${10}^6$ m/sec, the cross sections for the various incident ions are almost completely independent of the identity of the incident ion. At velocities above 1.5×${10}^6$ m/sec, the individual cross sections are different from one another again. The behavior of the measured cross sections is discussed in terms of a theoretical model for near-resonant charge transfer.

The formalism developed previously to study electronic transitions by the curve-crossing mechanism is used to obtain a general model for transitions which take place due to the strong coupling of curves which do not cross. This exactly solvable model is a generalization of a model developed by Rosen and Zener. The model is shown to give respectable agreement with exact calculations at low velocities, and to go to the correct resonant-charge-exchange limit at high velocities. Predictions of the model are shown to give good agreement with the measured total cross sections for charge exchange in the sytem ${\mathrm{Li}}^{+}$ + Na⇄Li+${\mathrm{Na}}^{+}$.

The generalized Rosen-Zener model developed in the accompanying paper is used to calculate differential cross sections for a model noncrossing system, and the structure of the cross sections is explained in terms of the deflection functions. It is found that the angular threshold effects that are typical of potential-curve crossings do not appear in this noncrossing system.

Relative muon capture probabilities for the individual elements of compounds and relative muonic x-ray intensities have been measured for a series of ionic solids and some related elements. Marked similarities are observed in relative $K$- and $L$-series intensities of a single ionic species, independent of bond partner (e.g., ${\mathrm{Cl}}^{-}$ in NaCl and Ca${\mathrm{Cl}}_2$). However, significant $K$-series differences are observed for an element in an ionic vs a covalent situation (e.g., Cl in NaCl and in NaCl${\mathrm{O}}_4$), with the higher $K$ x rays from the covalently bound element showing relative enhancements of as much as a factor of 2 over the ion. The measured intensities have been compared to the predictions of a meson cascade code, which allows variation in the muon initial principal quantum number ($N_{\mu }$) and the parameter $\alpha$ in the commonly used modified statistical angular momentum distribution, $P\left(l\right)=(2l+1)\mathrm{}{e}^{\alpha l}$. The fit was quite insensitive to the choice of $N_{\mu }$ (in the neighborhood $N_{\mu }=17\mathrm{}$), but the results could not be well fitted with a single value of $\alpha$. The atomic capture probabilities predicted by recent calculations do not fit the data noticeably better than the Fermi-Teller "$Z$ law."

The $L$ x-ray production cross sections for the $L{\alpha }_{1,2}$, $L{\gamma }_{1,5}$, and $L{\gamma }_{2,3,6}$ transitions in Pt, Au, and Hg have been measured by ionization of the $L$-subshell electrons with 0.4-2.0-MeV proton bombardment. Individual subshell ionization cross sections, ${\sigma }_{L_i}(i=1, 2, or 3)$, have been extracted from the x-ray yields. Comparisons of the x-ray production and ionization cross-section data have been made with the predictions of the plane-wave Born approximation (PWBA), the PWBA with binding-energy and/or Coulomb-deflection effects, and the constrained binary-encounter approximation (CBEA). The binding-energy and Coulomb-deflection effects partially account for the gross quantitative discrepancies between the PWBA and the data for proton energies less than 1 MeV. Substantial discrepancy still exists, as evidenced by the disagreement between the data for $\frac{{\sigma }_{L_3}}{{\sigma }_{L_2}}$ and all the theoretical predictions.

A three-mode microwave afterglow apparatus has been used in conjunction with a high-speed grating spectrometer to study the variation with electron temperature of the recombination coefficient $\alpha \left({{\mathrm{Xe}}_2}^{+}\right)$ and of the Xe* excited states produced by dissociative recombination over the range $300\le T_e\le 8000$ K. At low electron temperatures, 300-700 K, $\alpha \left({{\mathrm{Xe}}_2}^{+}\right)$ varies approximately as $T_e^{-\frac{1}{3}}$, with a smooth transition to a $\sim T_e^{-0.7\mathrm{}}$ variation at higher electron temperatures, 1300-7400 K. At $T_e=T_{+}=T_n=300\mathrm{}$ K, $\alpha \left({{\mathrm{Xe}}_2}^{+}\right)=(2.3\mathrm{}\pm 0.2)\times {10}^{-6\mathrm{}}$ ${\mathrm{cm}}^3$/sec, in agreement with earlier studies at room temperature. At thermal energy (300 K) Xe* excited states up to but not exceeding the energy of the ${\mathrm{Xe}}_2^{+}$ ion in its ground electronic and vibrational state are observed. With microwave heating to $T_e\sim 8000$ K additional, higher-lying Xe* states (up to ∼0.6 eV above the ${\mathrm{Xe}}_2^{+}$ ion ground state) are produced by the dissociative recombination process.

Total cross sections have been computed for $K$-shell ionization in selected multielectron atoms by proton impact using the single-particle Glauber approximation with hydrogenic wave functions. Our single-particle Glauber approximation corresponds to an independent-particle model where explicit coupling with target electrons not directly involved in the interaction is omitted. In principle, the Glauber approximation is valid over a wider region of scattering parameters than is the Born approximation. However, our Glauber results are not in significantly better agreement with observation than simpler Born predictions. For all targets considered at projectile velocities near the peak of the cross section, single-particle Glauber results tend to lie beneath observed cross sections by proton impact, in contrast to previous results for electron impact where, as expected, Glauber results are in better agreement with observations than Born results for low-$Z_2$ targets. Some explanations of the discrepancy and possible extensions of our methods are considered. It is also found that, as the atomic number of the target, $Z_2$, increases, the relative contribution of Glauber corrections to corresponding Born calculations decreases at projectile velocities near and above the peak of the $K$-shell ionization cross section. For $Z_2\gtrsim 5$, the Glauber scattering corrections to Born results for $K$-shell ionization at projectile velocities near and above the peak of the cross section are less than a few percent, e.g., less than errors due to our use of hydrogenic target wave functions. For ${\mathrm{O}}^{+8\mathrm{}}$ + Ne, unlike $p^{+}$ +Ne, significant differences are apparent between Glauber and Born predictions for direct Coulomb ionization.

Ionization continuum cross sections, differential in energy loss, have been determined from the energy-loss spectra of 25-, 50-, 75-, 145-, and 200-keV protons scattered from atomic hydrogen. The theoretical differential cross sections in the Glauber and Born approximations that are presented show that the theory and the experimental results for 200-keV proton impact agree very well, but below 200 keV there are differences. These differences, which are more pronounced at the lower projectile energies, may be explained in terms of charge transfer to the continuum, which is not treated in our Born and Glauber calculations of direct Coulomb ionization. The total ionization cross sections obtained by integrating the differential cross sections are in reasonable agreement with ionization cross-section measurements that have been obtained from crossed-beam experiments.

Cross sections for the collisional ionization of the metastable atoms Ne*, Ar*, Kr*, and Xe* by electrons with impact energy $E$ in the range $6<E<\mathrm{}250\mathrm{}$ eV are determined in the Born and binary-encounter approximations. For low energies $\epsilon$ of ejection, the $s-d$ and $s-f$ bound-free transitions dominate the associated form factor, while transitions to continuum states with progressively higher angular momentum gain importance with increasing $\epsilon$. While up to nine partial waves are normally sufficient for convergence of the bound-free form factor at a given energy $\epsilon$ and momentum change $K$ of the ejected electron, as many as 30 are required for those $K$ in the vicinity of the Bethe ridge at large $\epsilon$. These properties are the origin of the overall closeness obtained between the Born and binary-encounter cross sections. Also inner-shell ionization, as described by the binary-encounter treatment, becomes increasingly important as the target atom becomes more complex. Cross sections for ionization of metastable ${\mathrm{N}}_2$* and CO* are also determined. Good agreement with available measurements (for Ne* and Ar*) is obtained.

Detailed differential cross-section measurements have been performed for production of ${\mathrm{He}}^{+}$ in collisions of metastable ${\mathrm{He}}^{*}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S \mathrm{and} 2{}_{}{}^1{}_{}{}^{}S\right)$ with He at center-of-mass energies of 50, 99, and 199 eV. The product ion distribution contains several distinct features dominated by an intense peak at small angles and an energy-loss value near threshold. The major features of the ionization are shown to be consistent with various calculated processes, each of which follows the ${\Sigma }_g^{+}$ diabatic repulsive potential on the incoming trajectory. Ionization occurs at the crossing into the continuum, at the classical inner turning point, at crossings with higher continua, and through molecular autoionization of doubly excited neutral states. Possible contributions from ${\mathrm{He}}^{+}$ + ${\mathrm{He}}^{-}$ autoionizing states are considered. Evidence is found for significant contributions to the ionization from the small amount of ${\mathrm{He}}^{*}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)$ in the beam.

The mechanism of an observed ionization channel which produces ${\mathrm{He}}^{+}$ at an energy loss of 18.7±0.5 eV in 100-200-eV (c.m.) collisions of metastable He atoms with ground state He atoms was investigated. It is postulated that flux follows the diabatic singly excited ${{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}$ state associated with ${\mathrm{He}}^{*}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)$ projectiles and then transfers to the doubly excited ${{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}$ state corresponding asymptotically to $2{\mathrm{He}}^{*}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$; autoionization follows at large internuclear separations. Ab initio calculations were performed on four ${\mathrm{He}}_2$ states of ${{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}$ symmetry for internuclear separations of $0.72a_0$ to $20.0a_0$. The classical deflection function for the mechanism stated above, generated from the calculated potentials, is consistent with the experimental angular distribution of the product ions.