The spin-orbit interaction for the $P$-state continuum of heavy alkali metals was investigated in a photoionization experiment using spin-polarized alkali atoms and circularly polarized light. From the asymmetry in ion-counting rates corresponding to the two photon helicities, Fano's spin-orbit perturbation parameter $x$ was determined over a range of several hundred angstroms for K, Rb, and Cs. The spin-orbit perturbation was found to increase from K to Rb to Cs as expected, and the nonlinear behavior of $x$ as a function of the photon energy $E$ was demonstrated for K. Knowledge of $x\left(E\right)\mathrm{}$ was used to establish accurate values for the position of the Cooper minimum and to estimate the magnitude of the cross section at the minimum. In addition, the $x\left(E\right)\mathrm{}$ data for Cs were used to gain information about the spin polarization of photoelectrons in a Fano-type polarized electron source. Finally, extrapolation of $x\left(E\right)\mathrm{}$ for cesium into the discrete spectrum indicated the existence of a pole in the function $\rho \mathrm{}\left(E\right)\mathrm{}$ which corresponds to the doublet line-strength ratio $\rho \left(E_{\mathrm{nP}}\right)=\frac{S\left(n{P}_{\frac{3}{2}}\right)}{S\left(n{P}_{\frac{1}{2}}\right)}$ at the discrete energies $E_{\mathrm{nP}}$. According to our extrapolation, the pole lies in the region of $n=10\mathrm{} \mathrm{to} 15$, in agreement with the early spectroscopic work of Sambursky (1928) and Beutell (1939), whose measurements were discounted by later investigators.

We develop a detailed theory to calculate multiple-quantum transition probabilities. It is shown that the quantum electrodynamical (QED) approach must be used in order to explain quantitatively the experimental observations of Kusch. The anomalous behavior of shifts in resonance frequency and saturation of widths of transition probabilities can be explained on the basis of a QED renormalization principle. In this paper, we work out the detailed calculations for the case of a double-quantum transition quantitatively. The agreement between QED calculation and Kusch's observation is remarkable. We conclude that the renormalization principle of QED is important even for low-frequency and finite-intensity fields.

The Schlosser-Marcus stationary principle for discontinuous approximate wave functions is shown to be the "finite part" of the energy expectation value. The divergent terms in the expectation value of the kinetic energy are second order in the discontinuity, which explains why the energy expression obtained when they are omitted remains stationary.

The problem of the evolution in time of a system of two-level atoms that are coupled through their electromagnetic fields, is studied and solved in the framework of semiclassical radiation theory. The atoms may be in any initial states and the radiation reaction is fully taken into account. Both superradiance and time-dependent frequency shift or chirping effects are found. The assumption that all the atoms see the same field is shown to place severe constraints on the evolution of the system, in the form of constants of the motion. These constraints are most easily pictured in terms of the Bloch-vector representation of the atomic system, and they lead to explicit solutions for the time development of each atom. It is shown that the evolution of the complex system is describable by means of a collective super Bloch vector, whose behavior is similar to the behavior of the Bloch vector for a single isolated atom. The constraints on the motion also imply that the system cannot radiate all its energy coherently; some of it remains trapped, to be dissipated ultimately by incoherent processes. Some curves are presented to illustrate the behavior of the system in special cases.

The cross section for the photoejection of a proton from a hydride molecule is derived using the Born approximation for $h\nu \gg I$, and using the long-wavelength approximation for $h\nu \simeq 1$, where $\nu$ is the frequency of the incident photon and $I$ is the ionization potential of the proton. The cross section is negligible in the high-energy case. Near threshold, the probability for one photon being adsorbed in a path length of 1 cm is $\tau =1.4\mathrm{}\times {10}^2\frac{\rho N^{\frac{1}{2}}}{Z^{2}M}\left(\frac{\nu }{b{\nu }_0}\right){\left(\frac{b{\nu }_0}{\nu -{\nu }_c+(b-1\mathrm{})\mathrm{}{\nu }_0}\right)}^{\frac{\mathrm{}(6N+5)\mathrm{}}{3}}{f}_N^2$ where $\rho$ is the density $M$ is the molecular weight, $Z$ is the orbital exponent of the Slater function describing the proton, $b$ is a number between 1 and 2, $N$ is the principal quantum number of the proton, $h{\nu }_0=I$, and $h{\nu }_c$ is the kinetic energy of the center of mass plus the kinetic energy of the relative coordinate in the direction of the motion of the center of mass. The coefficient $f_N$ oscillates as $N$ increases. For the range in $N$ considered (88-125), $f_N$ varies from a minimum of 7.793 at $N=103\mathrm{}$ to a maximum of 175.4 at $N=115\mathrm{}$ beyond which it decreases again. Since $N$ is large, $\tau$ is large only near threshold.

A 250-keV pulsed electron accelerator was constructed for the excitation of noble gases, so that resonance radiation and continuous emission could be studied under conditions of good geometry with vacuum-ultraviolet spectroscopic techniques. For argon gas, time-dependent studies were carried out at the wave lengths of the ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ resonance line, the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ resonance line, the 1100-Å continuum, and the 1250-Å continuum over a wide range of gas pressures. The ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ resonance line decays exponentially with a lifetime which seems to be governed by the escape of resonance radiation to the walls of the apparatus and by three-body destruction of resonance states. The 1100-Å continuum, on the other hand, decays exponentially with a lifetime more characteristic of two-body Franck-Condon collisions. The main continuum near 1250 Å reaches a maximum well after the pulse of exciting electrons is terminated and then decays with a lifetime which is very long at low pressure but decreases to a constant value of 2.8 μsec at high pressures(about 1000 torr). From the data we suggest that the ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ states, which are richly populated with charged particles, are converted to argon metastable molecules and these in turn are converted by collisions to a molecule which radiates the 1250-Å continuum with the 2.8-μsec lifetime. Better fitting to the time-dependent emission at 1250 Å is obtained by also including the known channel starting with ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ metastable atoms which are converted to a radiating molecule by three-body collisions.

The average values of the powers of $r$ for the $4f$ orbital, ${〈r^n〉}_{4f}$, were calculated using accurate analytical self-consistent-field wave functions. The results were compared with experimental and other theoretical values.

An explicit expression is derived which permits the exact inclusion of nuclear motion in calculations of second-order optical and magnetic molecular properties within the Born-Oppenheimer approximation. Explicit calculations are carried out on the model problem of the hydrogen molecular ion for the exact $\mathrm{zz}$ component of the Rayleigh and vibrational Raman scattering tensors and for several approximations to these tensors. The result is somewhat sensitive to the approximate expression employed but the semiclassical approximation is accurate to within a percent in both cases.

The influence of Čerenkov-radiation loss on the emission spectrum and motion of an electron passing near the surface of a semi-infinite plane dielectric is treated on the basis of several simplifying assumptions. Equations of motion are obtained and solved for electron velocities just above radiation threshold in a region of anomalous dispersion. Expressions are found for the spatial and temporal dependence of the emission spectrum. A determination is made of the electron's total angular deflection which may exceed ${10}^{-2\mathrm{}}$ deg; this result is shown to be in reasonable agreement with an estimate based on measured emission levels. Possible corrections resulting from induced bremsstrahlung and inelastic interactions with the dielectric are discussed.

An algorithm is presented to calculate electronic levels and the equation of state of atoms suitable for arbitrary matter density and temperature. The self-consistent-field treatment starts with relativistic Thomas-Fermi-Dirac model in the iterative procedure. The Fermi statistics and the central-field approximation are maintained, giving an average atom representation. The broadening of upper electronic levels into bands is taken into account in a simple approximation. Calculations are presented for the ${\mathrm{Fe}}^{26}$ and ${\mathrm{Rb}}^{37}$ atoms at several temperatures and matter densities.

Multiconfiguration self-consistent-field calculations were performed on the following states of boron: $2s^{2}2p$, ${}_{}{}^2{}_{}{}^{}P$, $2s2p^2$, ${}_{}{}^4{}_{}{}^{}P$, ${}_{}{}^2{}_{}{}^{}D$, ${}_{}{}^2{}_{}{}^{}P$, $2s^{2}3s$, ${}_{}{}^2{}_{}{}^{}S$, and $2p^3$, ${}_{}{}^4{}_{}{}^{}S$. For each state, only configurations resulting from the replacement of the valence-shell orbitals were used, and consequently only the valence-shell correlation was calculated adequately. The correlation orbital set consisted of one orbital in each of the symmetries $s$, $p$, and $d$ (except for the $2s^{2}3s$, ${}_{}{}^2{}_{}{}^{}S$ state, where there were two orbitals of $p$ symmetry). For the ground state, the value of 0.067 hartree was obtained for the valence-shell correlation energy. From the wave functions obtained, the term energies and the oscillator strengths for the allowed transitions were calculated and found to be in general agreement with the results of more elaborate calculations and experiments.

Four forbidden decay modes of hydrogenlike argon (${\mathrm{Ar}}^{+17\mathrm{}}$) and heliumlike argon (${\mathrm{Ar}}^{+}$16) have been observed and the lifetimes of the states decaying via these modes have been measured by a beam-foil time-of-flight technique. The decays are the two-photon decay $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\to 1{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ of ${\mathrm{Ar}}^{+17\mathrm{}}$, the two-photon decay $2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\to 1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ of ${\mathrm{Ar}}^{+16\mathrm{}}$, the relativistically induced magnetic dipole decay $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\to 1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ of ${\mathrm{Ar}}^{+16\mathrm{}}$, and the magnetic quadrupole decay $2{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\to 1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ of ${\mathrm{Ar}}^{+16\mathrm{}}$. The measured lifetimes of the levels are $\tau \left(2\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)=3.54\mathrm{}\pm 0.25$ nsec, $\tau \left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)=2.3\mathrm{}\pm 0.3$ nsec, $\tau (2\mathrm{}{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}=1.7\mathrm{}\pm 0.3$ nsec, and $\tau \left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\right)=172\mathrm{}\pm 30$ nsec. From the agreement between the measured and calculated lifetimes it is possible to place an upper limit on the amount of parity impurity in the $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$-state wave function of hydrogenlike ${\mathrm{Ar}}^{+17\mathrm{}}$. Writing $\psi \left(2\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)=\Phi \left(2\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)+\epsilon \Phi \left(2\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\right)$, where the $\Phi \text{'}\mathrm{s}$ are the Schrödinger solutions to the hydrogen atom, we obtain $\left|\epsilon \right|\le 6\times {10}^{-4\mathrm{}}$.

Using plane waves to describe the incident and scattered particles, and screened hydrogenic and Coulomb functions to describe the atomic electrons before and after ejections, we have calculated the differential and total ionization cross sections of 11 atoms and one ion by electron impact, and ionization of helium by proton impact. The effective charges of the screened hydrogenic functions are fixed by the Hartree-Fock calculations. Calculations have been carried out for the atomic $s$, $p$, and $d$ electrons. For low atomic numbers we find reasonable agreement with the experimental data. For intermediate atomic numbers we expect our results to overestimate the actual cross sections, since our choice of a unit charge for the Coulomb function of the ejected electrons will overestimate the atomic dipole potential strength, and in turn the high-energy cross sections. Our results agree closely with the calculational results of Peach, based on a model similar to ours except that the atomic electrons before ejections are described by the Hartree-Fock wave functions. For intermediate atomic numbers and inert gases, the calculated results of McGuire seems to agree better with the experimental data compared to other calculations. The advantage of the method presented here is that the ionization amplitude is given in analytic form. This may allow further analysis on this amplitude, and facilitates extension of the numerical integration for the cross section to high impact energies. We have also given some cross sections for the production of doubly charged ions due to the single ionization.

Electron-capture and -loss cross sections have been measured for fluorine ions passing through nitrogen gas in the energy range from 5 to 54 MeV. Cross sections for multiple electron transfer in a single collision have been obtained in the analysis with quadruple capture and triple loss determined in some cases. The velocity dependence of the capture cross sections is discussed, and capture by the bare fluorine nucleus is in good agreement with theory. The ratio of the cross sections for double to single capture are discussed in terms of a geometry-independent component of the electron-capture process. The cross sections for electron loss are presented and a comparison is made between the velocity dependence observed and an elementary theoretical model.

The simultaneous ionization and excitation of helium to the $n=4\mathrm{}$ level of ${\mathrm{He}}^{+}$ by 200-eV electron impact on helium has been studied by time-resolved spectroscopy of the $\lambda =4686\mathrm{}$-Å ($n=4\mathrm{}\to 3$) line of ${\mathrm{He}}^{+}$. The study revealed that the excitation process is complex. It appears that only about 70% of the excitation of the $\lambda =4686\mathrm{}$-Å line can be accounted for by direct simultaneous ionization and excitation of the helium atom to the $n=4\mathrm{}$ level of ${\mathrm{He}}^{+}$ under single electron-atom collision conditions.

$K$-shell ionization cross sections have been measured for elements between $Z=26\mathrm{}$ and $Z=92\mathrm{}$ using 160-MeV protons as incident projectiles. The results are compared with two theoretical models, the plane-wave-Born-approximation calculations of Khandelwal, Choi, and Merzbacher and the binary-encounter model of Garcia. The results are in qualitative agreement with both these nonrelativistic models. The necessity for a relativistic theory is emphasized by comparison with recent high-energy-electron measurements.

Differential and total cross sections for electron-transfer rearrangement collisions are calculated in the first-order Faddeev-Watson multiple-scattering approximation for a number of three-body atomic systems. For the ($p^{+}$, H) system, it is shown that the inclusion of the pure $p^{+}-p^{+}$ interaction to all orders (including the contributions coming from the on-shell Coulomb cuts) cancels only part of the effect given by the bare $p^{+}-p^{+}$ interaction so that the present electron-transfer cross section lies in between the Brinkman-Kramers and Jackson-Schiff cross sections and asymptotically approaches the Jackson-Schiff cross section from above in the high-energy limit (where the nonrelativistic approximation is no longer expected to be valid). The knock-out contributions to the electron-transfer amplitude at large angles are particularly important for the equal-mass resonant ($e^{+}, e^{-}{e}^{+}$) electron-transfer collision. Owing to the $e^{+}-e^{+}$ knock-out contribution, the total ($e^{+}, e^{-}{e}^{+}$) electron-transfer cross section exhibits an $E^{-3\mathrm{}}$ energy dependence in the high-energy limit.

The energy and angular dependences of the differential elastic scattering cross section are investigated in the first-order Faddeev-Watson multiple-scattering (FWMS) approximation for a number of three-body atomic systems. The anomalies in the first-order Born approximation are not present in the first-order FWMS approximation. Significant differences are found between the elastic ($e^{-}$, H) and ($e^{+}$, H) scattering at energies as high as 10 keV. The elastic ($e^{+}, e^{-}{e}^{+}$) and ($p^{+}, e^{-}{e}^{+}$) scattering cross sections which are incorrectly predicted to be zero in the first-order Born approximation are calculated. The forward-angle peaking of the elastic scattering cross section is accounted for in the first-order FWMS approximation by allowing the system to participate in the intermediate inelastic scatterings. In general, significant differences are found in the magnitude of the cross sections obtained in the first-order FWMS and Born approximations at energies where the first-order Born approximation has been extensively used for normalizing experimental results. The energy for the first-order Born approximation, to be accurate, can be determined experimentally by locating the energy above which the difference between the ($e^{-}$, H) and ($e^{+}$, H) scatterings ceases to be appreciable.

We consider electron spin-exchange collisions between an atom with an electron spin of ½ and a target atom with an arbitrary electron spin. The cross sections that describe the collision are expressed in terms of generalized direct and exchange amplitudes and are shown to depend only on the electron spin, polarization, and alignment of the target atom. We include the effects of an external magnetic field and the nuclear spin of the spin-½ atom on the collision. We calculate the cross sections connecting the initial and final states of the free Hamiltonian describing the spin-½ atom, with analytic results being displayed for the two limiting cases of the external magnetic field. For the general case, graphical results are presented for several common values of nuclear spin that allow the cross sections to be evaluated for arbitrary magnetic fields. The results are applied to several situations of current interest.

In previous work, the stabilization method of calculating resonance parameters was applied to potential scattering and to elastic scattering from a target. The method is here extended to compound-state resonances in inelastic scattering and its application to a model problem for a target with three bound states is examined. The eigenfunctions associated with eigenvalues ${\epsilon }_j$ obtained from the diagonalization of the exact Hamiltonian in appropriately chosen sets of square-integrable basis functions are good approximations, in the inner region, to particular linear combinations of the degenerate exact scattering solutions at $E={\epsilon }_j$ (above inelastic threshold). The partial widths are calculated from a Fermi's-"Golden-Rule"-like formula involving the matrix elements of the exact Hamiltonian between the square-integrable eigenfunctions representing the resonance state and potential-scattering solutions at the same energy. The slowly varying (as a function of $E$) potential-scattering $S$ matrix, knowledge of which is required in the calculation of the decay widths, is determined using the criterion that several good approximations to the resonance state yield exactly the same widths. For the exactly soluble model problem studied here, the resonance parameters obtained with the stabilization method compare well with the exact values, especially for narrow resonances. The theoretical limitations of the method are discussed.