In the calculation of atomic hyperfine structure, it is generally assumed that core polarization effects and relativistic effects can be calculated separately. We examine in detail the validity of this assumption and obtain the lowest-order corrections to such an approach. This correction is described by new operators to be added to the hyperfine Hamilionian, as well as second-order perturbation terms. The systematic effects of the second-order terms are investigated using the effective-operator approach.

The fine-structure separations for the $n{d}^{2}D$ and $n{f}^{2}F$ terms ($n=4,5\mathrm{}$) in singly ionized beryllium have been determined from the modulations present in the beam-foil lifetime-decay curves. Comparison with theory shows good agreement. Relationships between cross sections for the magnetic sublevels are established.

A simple atomic model, with features characteristic of the screening-theory approach, is constructed and provides simple analytic trial wave functions ${\psi }_t$ which describe the motion of the inner electrons particularly well. Basing our model on the energy-extremum principle, in contrast to a semiempirical or phenomenological approach, we can judge improvements in the model in a consistent manner. The single-particle orbitals from which ${\psi }_t$ is constructed are taken to be orthogonal hydrogenlike functions with effective nuclear charges ${\tilde{Z}}_l$ which depend on the quantum number $l$; the ${\tilde{Z}}_l$ serve as variational parameters. By a succession of reasonably good upper bounds the evaluation of the expectation value of the $\frac{1}{r_{\mathrm{ij}}}$ interelectronic terms is reduced to trivial algebraic expressions involving only the occupation number of electrons for each of the ($n,l$) subshells; no numerical work is necessary to determine the energy-optimized set of ${\tilde{Z}}_l$ With the resulting ${\psi }_t$, which is most appropriate for closed-shell atoms, a variety of atomic entities can be obtained directly in analytic form. This model is considered physically more realistic than the Thomas-Fermi model, yielding results of greater accuracy in general. (For large $Z$, the results obtained yield the usual Thomas-Fermi scaling laws.) Much more importantly, these wave functions will be shown elsewhere to be very useful in exploratory analytic studies to judge the effectiveness of variational techniques in the evaluation of the expectation values of various atomic operators. Also, a straightforward adaptation of the present approach will be shown elsewhere to provide a much better understanding of atomic structure in the presence of the intense magnetic fields characteristic of pulsars, a regime in which studies of the heavier atoms have been limited to a statistical Thomas-Fermi-like approach.

A novel method for measuring the hyperfine interval $\Delta \nu$ of muonium in zero magnetic field is described. It consists in applying two successive coherent microwave pulses (lengths $\tau$, separation $T+\tau$) to muonium, and observing the change in muon polarization at $t>T+2\mathrm{}\tau$. By linearly extrapolating two low-pressure runs in Kr together with earlier Chicago data, we obtain $\Delta \nu \mathrm{}\left(0\right)=4463301.2\mathrm{}\left(2.3\right)\mathrm{}$ kHz (0.5 ppm). A joint fit of all available data in Ar and Kr yields $\Delta \nu \mathrm{}\left(0\right)=4463304.4\mathrm{}\left(2.3\right)\mathrm{}$ kHz. With $\frac{{\mu }_{\mu }}{{\mu }_p}=3.183349\mathrm{}\left(15\right)\mathrm{}$ the latter implies (a) ${\alpha }^{-1\mathrm{}}-137=0.03631\mathrm{}\left(32\right)\left(2.4\mathrm{} \mathrm{ppm}\right)$, and (b) a proton polarizability ${\delta }_p^{\prime }=5.4\mathrm{}\left(4.8\right)\mathrm{}$ ppm.

A general formula is derived for two-photon coincidence rates. The result obtained is a function of the orientation of linear polarizers, of the solid angles subtended, and of the relative position of the photon detectors. It applies to both cascade emissions and resonance flourescence when the transitions are of electric dipole type. Allowance is made for anisotropic initial-state populations. It is shown that a single parameter describes the atomic transition when the initial states are isotropically populated. This parameter is found to have a particularly simple form, even when the nuclear spin is nonzero. It is the product of two Racah coefficients and an $E$ coefficient defined here. Tables of the required Racah and $E$ coefficients are provided so that this parameter can be easily determined when the states in the transitions have $J$ values 0, 1, 2, 3, 4, 1/2, 3/2, 5/2, 7/2, or 9/2, and when the nuclear spin is 0, 1, 1/2, 3/2, 5/2, 7/2, or 9/2. Experiments to test hidden-variable theories which are possible in view of these results are discussed. Experiments to determine the effective quantum efficiency of photon detectors using these results are described.

Proton, $\alpha$-particle, and oxygen-ion beams are used to induce $K\alpha$ x-ray spectra in the elements Ca, Sc, Ti, V, Cr, and Mn. The target dependence of the satellite structure for $Z=20\mathrm{} \mathrm{to} Z=25\mathrm{}$ is studied. The relative intensity ratios for the production of one $K$ -shell and multiple $L$ -shell vacancies are measured. These ratios are compared with the predictions of the binary-encounter approximation (BEA) and the semiclassical approximation (SCA) for multiple ionization. The data strongly reflect the statistical approach used in the theories. The BEA theory agrees well with the proton and $\alpha$-particle data but does not give good agreement with the oxygen data.

A collision-type formalism for spectral theory, described by Lu and applied originally to Xe, is improved and is applied to analyze the strongly perturbed absorption spectrum of Ar. The analysis expresses experimental data in terms of three sets of empirical parameters: five eigenquantum defects ${\mu }_{\alpha }$, one 5 × 5 orthogonal transformation matrix ${\updownarrow \updownarrow }_{i\alpha }$, and five dipole matrix elements $D_{\alpha }$. The energy dependence of the parameters is studied and is found to be approximately linear for the ${\mu }_{\alpha }$ and insignificant for ${\updownarrow \updownarrow }_{i\alpha }$ and $D_{\alpha }$. With these parameters thus determined by fitting to the experimental data, the mixing coefficients of the Rydberg levels have been determined and their oscillator strength have been predicted and compared with available experimental data.

The probability of simultaneous $K$-plus-$L$-shell ionization in collisions between Ca, Ti, and Fe target atoms and projectiles of 1.5 - 12.5-MeV/amu deuterons and $\alpha$ particles has been investigated. The results show that the fraction of $K\beta$ x rays emitted in the presence of an $L$-shell vacancy (a) decreases with increasing projectile velocity above a projectile-to-$L$-shell-electron velocity ratio of 1; (b) decreases with increasing target atomic number; and (c) increases with projectile charge (approximately as $z_1^2$). The projectile velocity dependence is in fairly good agreement with a simple classical model based upon the assumption that multiple-vacancy production results from simultaneous Coulomb collisions with $K$-and $L$-shell electrons during the ion's passage through the atom.

We analyze elastic electron-atom scattering at intermediate and high energies by combining the Born series and eikonal series to get a consistent picture of the scattering amplitude through order ${k_i}^{-2\mathrm{}}$. Our eikonal-Born-series approach is compared with the usual Glauber approximation, which is shown to be seriously deficient. We also discuss the Schwinger variational principle, exchange effects, and forward dispersion relations. Applications are made to the elastic scattering of electrons by atomic hydrogen and helium. The agreement between our results and the experimental data is very good.

A Glauber-type eikonal approximation with the classical trajectories taken as two intersecting straight-line segments (called "angle" trajectories) is examined and applied to the $2s$ and $2p$ excitation of hydrogen atoms by electron impact. The calculated differential and total excitation cross sections are compared with experimentally measured and "straight-line" Glauber-eikonal cross sections. The angle approximation does provide a significant improvement over the straight-line approximation for the differential cross section at angles >40°.

The cross sections for the production of forward scattered molecular ions in collisions of ${\mathrm{H}}_2$ on ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ on ${\mathrm{D}}_2$ have been measured at lab kinetic energies between 50 and 500 eV. The cross section for the ${\mathrm{H}}_2$ reaction ranges from 2.2 × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ at 500 eV to 5.0 × ${10}^{-19\mathrm{}}$ ${\mathrm{cm}}^2$ at 50 eV. The ${\mathrm{D}}_2$ cross section varies from 1.7 × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ to 3.8 × ${10}^{-19\mathrm{}}$ ${\mathrm{cm}}^2$ in the same energy range. The angular dependence of the ions was found to be highly peaked in the forward direction for energies above 100 eV. The cross sections for ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$, when plotted versus incident velocity, are found to approach the same values at the highest velocities. The two cross sections diverge toward lower velocities as they approach their respective cutoffs, where each process becomes energetically impossible. These cross sections have been found to fit a theoretical model based on ideas first presented by Demkov and Komarov, in which ionization is presumed to take place via a series of pseudocrossings of the initial state into the continuum of the adiabatic states of the collision complex. For the interaction of two hydrogen molecules, the internuclear separation of each molecule is assumed fixed and the adiabatic states are defined in terms of the distance between the two molecular centers ($R$). Best agreement between the observed cross sections and those predicted from the model are obtained assuming the transition region to be centered around $R=0.43\mathrm{}$ Å, 16.5 eV above the energy of the ground state at large $R$. For the purpose of monitoring the neutral-beam intensity, the secondary-electron emission coefficients ($\gamma$) were measured for ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ impinging on a brass surface. The $\gamma$ values were found to vary from 0.77 and 0.65 at 500 to 0.045 and 0.020 at 50 eV for ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$, respectively.

Under the distorted-wave close-coupling approximation, an expression for the scattering amplitude is obtained. Assuming a Hartree-Fock solution for the atomic wave function, a parametrization of the inelastic scattering cross section in terms of integrals over radial functions is derived. The formalism is then applied to singly ionized argon, using the distorted-wave appoximation.

The cross section ${\sigma }_1(\epsilon ;E)$ has been calculated for the direct impact ionization of hydrogen atoms by protons, ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to 2{\mathrm{H}}^{+}+e^{-}$, for low relative collision energies $E$ between 100 and 500 eV, and all electron energies $\epsilon$ for which it is significant. Fundamental theory and most electronic matrix-element calculations were presented in earlier papers of the series. In the present paper we complete the electronic matrix-element calculations (in particular, the "optimization" of Coriolis or angular coupling matrix elements for ionizing transitions, through introduction of an angular velocity electron-translation factor); and we perform the final integrations over classical trajectories and impact parameters to obtain the cross sections. The cross sections ${\sigma }_1(\epsilon ;E)$ show the expected steep falloff with increasing $\epsilon$ and decreasing $E$, owing to the increasing inefficiency of momentum and energy transfer from the heavy particles to the electron under such changes; ${\sigma }_1$ decreases by about two orders of magnitude from $E=500\mathrm{} \mathrm{eV}$ to $E=100\mathrm{}$ eV, and by four orders of magnitude from $\epsilon =0\mathrm{}$ a.u. to $\epsilon =1.0\mathrm{}$ a.u. A strong dependence of cross section on isotopic mass at fixed $E$ is also predicted thereby. Finally, the most significant conclusion is that the cross section for ionization from the $1s{\sigma }_u\left(2p{\sigma }_u\right)$ molecular electronic state is about 500 times greater than that for ionizing a $1s{\sigma }_g$ molecular electron, the main source of transitions being the Coriolis coupling operator.

The multichannel ($p^{+}$, H) collisions are investigated in the three-state approximation. In our formulation, precautions are taken to ensure that the state function has the correct asymptotic behavior. Consequently, the spurious long-range interactions coming from the nonadiabatic interactions do not appear in our coupled equations. These coupled equations are solved in the straight-line eikonal approximation. The calculated differential elastic, electron-transfer, and $2p\pi$-excitation cross sections are compared with recent experimental data and other theoretical results.

The energies of some metastable states of ionized oxygen and fluorine with three, four, or five electrons are computed. The spectra of Auger electrons, emitted during the autoionization of these states, are obtained and compared with the experimental measurements of Pegg et al. The energies of some of the associated x-ray transitions are tabulated.

We report the results of spectroscopic studies of electrons associated with the decay in flight of metastable autoionizing states in three-, four-, five-, and eleven-electron heavy ions. The binding energies of a large number of observed states are found to be in good agreement with theoretical predictions (c.f. the companion paper of Junker and Bardsley) where such values are available. The lifetime of the lowest-lying quartet state, $\left(1s2s2p\right){}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^o{}_{}{}^{}$ has been measured in three-electron oxygen, fluorine, chlorine, and argon ions. Competition between autoionizing and (in some cases forbidden) radiative-decay modes is discussed. There is evidence that the formation of metastable autoionizing states is quite a general phenomenon, occuring in a wide variety of atomic systems. A need for more extensive energy-level and lifetime calculations is readily apparent.

The cross section for excitation of atomic hydrogen to the $2s$ state by electron impact has been remeasured in a crossed-beam experiment in the energy range from threshold to 12.3 eV. An electron monochromator of the cylindrical type with a full width at half-maximum of 110 meV has been used. The $2s$ atoms were detected by quenching in an electrostatic field and observing the emitted Lyman-$\alpha$ photons. Absolute values for the cross section were obtained by normalizing to the close-coupling calculations of Burke et al. at 10.8 eV. Resonance structure at 11.7 eV, which is a superposition of the ${}_{}{}^1{}_{}{}^{}S$ and ${}_{}{}^3{}_{}{}^{}P$ resonances predicted by theory, has been detected. There is good agreement between the present experiment and the experiment by Oed.

The excitation of states in A1 with single $K$-plus multiple $L$-shell vacancies formed by collisions with 0.4-3.0-MeV helium ions is studied by observing the x-ray decay associated with filling of the $K$-shell vacancy. The observed $K$ x rays come from initial states with one $K$-shell and 0, 1, 2, and 3 $L$-shell vacancies. The absolute cross section for each of these transitions is determined and compared to a calculation using multiple Coulomb ionization. An important result of this experiment is the observation that the ratio of double to single ionization exhibits a maximum at a bombarding energy near the maximum for $L$-shell ionization.

A procedure is developed for computing cross sections for the multiple ionization of atoms by the impact of protons or other fully stripped nuclei. The ionization probability, as a function of energy and impact parameter, $P(E,b)\mathrm{}$, is computed at several beam energies in the binary-encounter approximation for a ground-state hydrogenic electron scattered by an incident proton. Scaling laws are given which may be used to extend these results to other projectiles, other targets, and other hydrogenlike filled atomic shells. It is shown that $P(E,O)=〈\frac{\sigma \mathrm{}(E,r)\mathrm{}}{2\pi r^2}〉$ for isotropic, but otherwise arbitrary, electron-density distributions. A formulation for multiple-ionization cross sections is developed in terms of the single-electron probabilities $P(E,b)\mathrm{}$ for each atomic shell, assuming that both the electrons and the shells are mutually independent. Numerical calculations are compared to recent predictions in the semiclassical Coulomb approximation and to recent satellite and hypersatellite x-ray data. The discrepancies are generally within those resulting from uncertainties of 30-200% in the single-ionization cross sections, when the ionization probability is much less than one. Then, approximating $P\left(\mathrm{Eb}\right)\mathrm{}$ vs $b$ as a step function, the multiple-ionization cross sections are reduced to simple combinations of single-ionization cross sections. These single-ionization cross sections may be evaluated in the binary-encounter approximation by applying scaling laws to the usual universal curve that we tabulate. Multiple-ionization cross sections may thus be estimated without the aid of a computer.

Quantum-mechanical, three-state, close-coupling calculations of the inelastic cross sections for $1{}_{}{}^1{}_{}{}^{}S\to 2{}_{}{}^3{}_{}{}^{}S$ excitation of ground-state He atoms in collision with ${\mathrm{He}}^{+}$ ions have been carried out for energies between 25 and 50 eV (c.m.). Differential, partially integrated (over small angles), and total inelastic cross sections were obtained. The calculations were performed using linear combinations of three single-configuration, valence-bond-type electronic wave functions as the basis of a diabatic representation. The diabatic coupling in the vicinity of the well-established ${}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ curve crossing at $R\simeq 1.5a_0$ was found to be small, and it was verified by comparison with the close-coupling results that the Stueckelburg-Landau-Zener (SLZ) theory was applicable. Several SLZ model calculations were performed using the best available adiabatic potential curves and modeling the crossing region. The resulting differential and partially integrated (over small angles) cross sections were found to be in good qualitative agreement with the measurements. In particular, the strange hump apparent in the small-angle cross sections versus energy curve, which was first found by Utterback, and recently confirmed by MacVicar-Whelan and Borst, was reproduced in our calculations. The interesting nature of the small-angle scattering is discussed, and the sensitivity of the cross section to details of the potential curves near the crossing is examined in detail.