Experimental $K$-shell ionization cross sections are reported for low-velocity heavy projectiles of atomic number small compared to the target atomic number. For such projectile-target combinations, the Coulomb interaction between the projectile nucleus and the $K$-shell electrons dominates the $K$-shell ionization process at all projectile velocities. The data can disagree by orders of magnitude with the primary predictions of the nonrelativistic quantum theory in the plane-wave Born approximation. Important physical processes are shown to be at the root of the discrepancies. They derive from the finite charge of the moving projectile, and thus do not contribute in the plane-wave Born approximation. They are the Coulomb deflection of the projectile in the field of the target nucleus and the perturbation of the target atomic states by the projectile. A theory for these processes is developed in an approximate manner. When incorporated with the theory in the plane-wave Born approximation, it accounts quantitatively for the data. A method results for reducing cross-section data in a comprehensive way. A universal graph of cross sections emerges which, in effect, constitutes an extrapolation of the data to the conditions of zero projectile charge. It comprises cross sections ranging over six orders of magnitude measured on different targets for various projectiles with a wide range of velocities, mostly below the mean $K$-shell velocities. The locus of this universal graph coincides with the prediction of the plane-wave Born approximation.

The bremsstrahlung radiation from electron-ion collisions is emitted anisotropically in directions dependent on the electron kinetic energy and the photon energy. We consider here the radiation from electrons confined in magnetic mirrors. In particular, the magnitude of this anisotropy is examined as a function of the electron energy, the photon energy, the electron pitch angle, and the angle of a detector with respect to the magnetic-mirror midplane. The calculations are performed in the Born approximation with the cross sections developed by Gluckstern and Hull. We also compute the temperature of a bi-Maxwellian distribution from the slope of the log of the intensity vs photon-energy curve and consider the effects of pitch-angle distribution and detector angle on the anisotropy of the radiation.

An analytic expression for the differential pair-production cross section is obtained using full Furry-Sommerfeld-Maue wave functions for the electron and positron. It is shown that this expression reduces to the Bethe-Maximon approximation and the Born approximation in the appropriate limits, and that it goes into the corresponding Elwert-Haug approximation for bremmstrahlung via the substitution rule. It is found that the cross sections of the Born approximation and the Bethe-Maximon approximation may be related to the cross section of the present approximation by a normalization theory similar to that used to relate point-Coulomb and screened "exact" calculations for pair production. No such theory works for bremsstrahlung because a larger-$r$ region is of importance in the bremsstrahlung process. The region of validity of each approximation is found by comparison with "exact" numerical calculations. There exists a region of low energies and small $Z$ where the present theory for pair production and the Elwert-Haug approximation for bremsstrahlung are valid and are significantly better than the Born and the Bethe-Maximon approximations. The failure of these calculations at low energies for intermediate and high $Z$ is attributed to the fact that the lowest partial waves for the electron and positron, which are dominant at low energies, are very poorly represented in the Furry-Sommerfeld-Maue approximation.

The lifetimes, oscillator strengths, and coherence narrowing of the $\mathrm{}\left(6p8s\right)\mathrm{}{}_{}{}^3{}_{}{}^{}P_1^0{}_{}{}^{}$ and $\mathrm{}\left(6p7s\right)\mathrm{}{}_{}{}^1{}_{}{}^{}P_1^0{}_{}{}^{}$ states of ${\mathrm{Pb}}^{208}$ were measured in this work by zero-field level-crossing spectroscopy. For the $\mathrm{}\left(6p8s\right)\mathrm{}{}_{}{}^3{}_{}{}^{}P_1^0{}_{}{}^{}$ state the lifetime $\tau =1.26\mathrm{}\left(5\right)\mathrm{}\times {10}^{-8\mathrm{}}$ sec and the absorption oscillator strength for the 2053-Å transition to the ground state was 0.041(8). For the $\mathrm{}\left(6p7s\right)\mathrm{}{}_{}{}^1{}_{}{}^{}P_1^0{}_{}{}^{}$ state, $\tau =4.8\mathrm{}\left(3\right)\mathrm{}\times {10}^{-9\mathrm{}}$ sec, and the absorption oscillator strength for the 2022-Å transition to the ground state was 0.020(12).

The Rydberg constant has been determined from absolute wavelength measurements on two fine-structure components of the He II $n=3\mathrm{}-4$ transition. The He II transition was excited in a liquid-nitrogen-cooled hollow cathode. A pressure-scanned Fabry-Perot spectrometer was used to compare the He II wavelengths with a ${}_{}{}^{198}{}_{}{}^{}\mathrm{Hg}$ standard source. The measured value of the Rydberg is $R_{\infty }=109\mathrm{}737.3208\pm 0.0085$ ${\mathrm{cm}}^{-1\mathrm{}}$, where the uncertainty is one standard deviation.

The hyperfine structure of the spectrum of Dy I was studied by means of a Fabry—Perot etalon. The dipole- and quadrupole-coupling constants of the levels $4f^{10}\left({}_{}{}^5{}_{}{}^{}I_{7,8}^{}{}_{}{}^{}\right)6s6p\left({}_{}{}^3{}_{}{}^{}P_{2,1}^{}{}_{}{}^{}\right)$ with $J=9\mathrm{}$ were deduced; these levels were found to be free from configuration mixing. From the quadrupole-coupling constant of the level ${\left[4\mathrm{}{f}^{10}\right({}_{}{}^5{}_{}{}^{}I_7^{}{}_{}{}^{}\left)6s6p\right({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\left)\right]}_9$ the contribution of the $6p$ electron alone was separated, from which it was deduced that $Q^{163}=+2.46\mathrm{}\left(21\right)b$ and $Q^{161}=+2.33\mathrm{}\left(20\right)b$, the Sternneimer correction being taken into account.

Direct sum-over-states methods are used to evaluate the frequency-dependent polarizability and anisotropy for ground-state ${\mathrm{H}}_2$. Rayleigh and rotational and vibrational Raman cross sections for photon scattering and depolarization ratios are given for Lyman-$\alpha$ radiation. An assessment of the accuracy obtainable by the direct use of sum-over-states methods indicates its high promise as a technique for accurate computation of molecular properties. The Dalgarno—Epstein [J. Chem. Phys. 50, 2837 (1969)] technique for obtaining a finite-set representation of components of the resolvent operator is shown to be effective for molecules.

The feasibility of many-body perturbation-theory (MBPT) calculations with hole and particle states expanded in a finite set of bound-type functions is investigated. The correlation energy of atomic beryllium is used as a test case. Particle states with negative and positive energy values are treated uniformly. We find that convergence of individual diagrams to better than ${10}^{-4\mathrm{}}$ a.u., and similar agreement with Kelly's numerical results can be obtained using basis sets composed of $9s$, $7p$, $5d$, and $4f$ Slater orbitals for intrashell correlation and a $10s8p6d4f$ set for the intershell effects. The total correlation energy calculated with these basis functions is in good agreement with experiment. These results indicate that MBPT calculations by the expansion method are indeed feasible. While this method may not be more convenient than the numerical approach for atomic systems, it should be useful for molecular calculations, where finding a suitable complete set of numerical orbitals presents difficult problems.

The radiation emitted when a beam of electrons passes over the surface of a perfectly conducting metal is discussed. The electrons constituting the beam all move with the same velocity in the same straight line but the charge density along the beam may vary in an arbitrary manner. The metallic surface considered is any surface which may be obtained by a small perturbation of a plane. Perturbation theory is used to derive explicit expressions for the electromagnetic field generated. The mathematical techniques employed involve the use of the angular-spectrum-of-plane-waves representation of the electromagnetic field. The results obtained go far beyond those of previous (two-dimensional) theories. The special case of a sinusoidally varying surface is treated in detail and a numerical calculation yields the physically important quantity—the number of optical photons emitted per charge per unit path length—for a particular arrangement.

Calculations are presented of the combined Zeeman- and Stark-effect level shifts in the $n=2\mathrm{}$ excited states of positronium, for positronium moving perpendicular to an applied magnetic field. Lifetimes of the Zeeman- and Stark-mixed $n=2\mathrm{}$ states are also calculated. The electric field results from the Lorentz transformation of the magnetic field to the rest frame of the positronium and is perpendicular to the magnetic field. The level shifts and lifetimes are calculated by diagonalizing the 16×16 Hamiltonian matrix for positronium in crossed electric and magnetic fields. The unperturbed energy eigenvalues calculated by Fulton and Martin are used as the diagonal elements of the Hamiltonian.

The Hamiltonian for a many-particle system in a homogeneous magnetic field is constructed by a straightforward extension of previous work on hydrogenic atoms by Grotch and Hegstrom. Relativistic-correction terms of order ${\alpha }^2{\mu }_{B}H$ are identical to those obtained many years ago by Abragam and Van Vleck and by Perl and Hughes. In addition, higher-order terms due to the anomalous moments and to nuclear motion are explicitly formulated in the present work. These terms are of orders ${\alpha }^3{\mu }_{B}H$ and ${\alpha }^2\left(\frac{m}{M}\right){\mu }_{B}H$, respectively, and are coming to be within the range of present experimental measurements.

The linear polarization of bremsstrahlung from thin targets (∼ 50 ${\mathrm{\mu }\mathrm{g}/\mathrm{c}\mathrm{m}}^2$) of Al, Cu, Ag, and Au was measured for incident electron energies of 50, 75, and 100 keV. The polarization was measured as a function of photon energy at four emission angles ($\theta ={22.5}^{\circ },{45}^{\circ },{90}^{\circ }, \mathrm{and} {135}^{\circ }$). Data presented were obtained with a Compton polarimeter having a large asymmetry ratio (from 35 to 150) and high resolution. The results have been found to be in general agreement with the predictions of various bremsstrahlung calculations.

The ratio $B$ between the transfer rates ${\lambda }_{\mu p,\mathrm{Xe}}$ and ${\lambda }_{\mu d,\mathrm{Xe}}$ of muons from $\mu p$ and $\mu d$ muonic atoms to xenon has been directly measured by stopping negative muons in a gaseous target containing deuterated hydrogen and small xenon admixtures at a total pressure of 6 atm abs. and at 293 °K. The results were obtained by analyzing the differential time distribution of the decay electrons coming from muons stopped within the gaseous mixture. In this way one gets $B=1.98\mathrm{}\pm 0.12$, which supports the dependence of the transfer rates on the mass of the primary muonic atom within 6%. More precise values for ${\lambda }_{\mu p,\mathrm{Xe}}$ and ${\lambda }_{\mu d,\mathrm{Xe}}$ are also given, i.e., ${\lambda }_{\mu p,\mathrm{Xe}}=(4.53\mathrm{}\pm 0.15)\times {10}^{11}$ ${\sec }^{-1\mathrm{}}$ and ${\lambda }_{\mu d,\mathrm{Xe}}=(2.30\mathrm{}\pm 0.17)\times {10}^{11}$ ${\sec }^{-1\mathrm{}}$. A lower limit for the scattering cross section $\sigma$ of $\mu d$ atoms against xenon is obtained, i.e., $\sigma \ge {10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$.

Measurements are reported of the absolute absorption coefficients in the wings of the 8944-, 8521-, 4593-, and 4555-Å resonance lines of cesium in the presence of argon at densities between about 6 × ${10}^{18}$ and 2 × ${10}^{19}$ atom ${\mathrm{cm}}^{-3\mathrm{}}$. The data extend from about 0.7 Å to as much as 600 Å from the line center and were obtained using cesium densities between 7 × ${10}^{11}$ and 2 × ${10}^{15}$ atom ${\mathrm{cm}}^{-3\mathrm{}}$ and temperatures between 390 and 470°K. The measured absorption coefficients are proportional to the product of the cesium and argon densities as expected from line broadening produced by binary collisions between cesium and argon atoms. Using the quasistatic theory as a guide for interpretation, the line profiles for wings of the first resonance doublet show a transition from a wavelength dependence determined by long-range van der Waals forces to a dependence determined by the short-range internuclear potentials discussed by Hedges, Drummond, and Gallagher (HDG). The far-wing absorption profiles obtained in the present experiments are in good agreement with those calculated from the fluorescence data of HDG.

Spin-dependent perturbations from intermediate ${}_{}{}^3{}_{}{}^{}P$ states are calculated by expanding the perturbations to the wave function in terms with one negative power of one of the electron or interelectron coordinates, in addition to standard Hylleraas terms. The nonstandard terms reflect singularities of the Breit operators. A method for solving linear equations with "almost-singular" coefficient matrices is devised. Significant improvement in accuracy is achieved for five contributions, but the procedure does not work well in all cases where the coefficient matrix is unsymmetrical.

When fast beams of oxygen and fluorine ions are incident on carbon and metal foils thick enough to produce charge-state equilibrium, a significant portion of the lithiumlike beam fraction emerges in excited metastable autoionizing states. We have studied the yield of these states with beams in the range 2-20 MeV incident on nominal ${10-\mathrm{\mu }\mathrm{g}/\mathrm{c}\mathrm{m}}^2$ carbon foils and on various metallic foils. The decay in flight of the lowest of these states, the $\mathrm{}\left(1s2s2p\right)\mathrm{}{}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^0{}_{}{}^{}$, is monitored with observation of the spectrum of ejected electrons. We find, for example, that the maximum yield of this single state per incident beam particle is approximately 0.8% and 0.6% for oxygen and fluorine, respectively, on carbon. The energy dependences and target-material dependences are measured and discussed. Comparison is made to related work of Dmitriev et al.

The single-particle model for atoms and ions is used to calculate the transition probabilities to bound and continuum electronic states. The projection operators in the semiclassical approximation derived previously are applied to treat the large numbers of final states involved. Ionization cross sections of atoms and ions by high-energy-electron impact are then estimated. The ionization cross sections result both from direct transition to the continuum and from inelastic scattering followed by Auger emission.

Theoretical results are given for the application of the distorted-wave approximation to electron-atom impact excitation for transitions from an $L-S$ coupled initial state to an arbitrarily coupled final state. Expressions for the differential cross section and spin polarization of the emitted electrons are given for unpolarized electron beams incident upon unpolarized atoms. These results are applied to excitation of helium from its ground state to the $1s2p{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ excited state for incident-electron energies between 26.5 and 300 eV. The results are compared with previous theoretical and experimental works. It is found that the distorted-wave calculation is superior to previous calculations in fitting the absolute magnitude and angular distribution of the experimental data. The improvement over the plane-wave calculations is greater at large angles, where the plane-wave approximations fail by several orders of magnitude.

The results of the distorted-wave theory for electron-impact excitation of atoms are applied to the excitation of the $6s6p{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ state of mercury. The spin polarization and the differential cross section are given for unpolarized incident electron beams with energies between 25 and 180 eV. The distorted-wave results are compared with experimental data, and good agreement is found for both the spin polarization and differential cross section.

A rapid numerical technique for the determination of bound states of a partial-wave-projected Schrödinger equation is presented. First, one needs to integrate the equation only outwards as in the scattering case, and second, the number of trials on ${\kappa }^2 \mathrm{}(=-E)\mathrm{}$ necessary to determine the eigenenergy and the corresponding eigenfunction is considerably less than in the usual method. As a nontrivial example of the technique, bound states are calculated in the exchange approximation for the $e^{-}-{\mathrm{He}}^{+}$ system and $l=1\mathrm{}$ partial wave.