The Sommerfeld fine-structure constant $\alpha$ has been determined from a direct measurement of the fine-structure separation in the $2P$ states of atomic hydrogen using the level-crossing technique. From the changes in resonance fluorescence caused by level crossing at 3484 G, we obtain a value for the fine-structure separation $E\left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)-E\left({}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\right)=10\mathrm{}969.13\left(0.10\right)\mathrm{}$ MHz and ${\alpha }^{-1\mathrm{}}=137.0354\mathrm{}\left(6\right)\mathrm{}$. The quoted uncertainty represents our estimate of 70% confidence from the analysis of 84 separate runs.

We have observed transitions between Zeeman levels of fine-structure states of He, excited and aligned by electron impact in a magnetic field, for both the $4p{}_{}{}^3{}_{}{}^{}P$ and $5p{}_{}{}^3{}_{}{}^{}P$ states. An improved apparatus has reproduced the six previously observed $4p{}_{}{}^3{}_{}{}^{}P$ resonance lines with an improved signal-to-noise ratio. It has also made possible observation of two "forbidden" transitions in the $4p{}_{}{}^3{}_{}{}^{}P$ state and the eight corresponding transitions in the $5p{}_{}{}^3{}_{}{}^{}P$ state. The following fine-structure constants have been derived:

$4{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}-4\mathrm{}{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}=3306.4\mathrm{}\pm 0.7$ MHz, $4{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}-4\mathrm{}{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}=270.4\mathrm{}\pm 0.7$ MHz, $5{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}-5\mathrm{}{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}=1660.0\mathrm{}\pm 0.8$ MHz, $5{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}-5\mathrm{}{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}=137.4\mathrm{}\pm 0.7$ MHz.

The anisotropic portion of the diamagnetic Zeeman interaction has been measured and used to derive values for the atomic radius and quadrupole moment. These values are larger than the corresponding expectation values calculated from hydrogenic orbitals. Further calculations and experiments are planned to determine if these discrepancies are apparent or real.

The Fresnel drag has been measured in a triangular ring laser at a wavelength of 0.6328 μ. The drag coefficient in fused silica is $\alpha =0.541\mathrm{}\pm 0.003$, while the theory, including the dispersion term, gives ${\alpha }_{\mathrm{theor}}=1-\left(\frac{1}{n^2}\right)-\beta \left(\frac{\lambda }{n}\right)$ $\frac{\mathrm{dn}}{d\lambda }=0.5423\mathrm{}$ with $\beta =1\mathrm{}$. The coefficient $\beta$ is thus determined as $\beta =0.87\mathrm{}\pm 0.22$, which includes the classical value $\beta =1\mathrm{}$. Thus the magnitude of the drag in a ring laser is within the errors equal to that given in an inertial frame of reference (linear drag).

A general expression for the calculation of pressure broadening for vibrational-rotational lines is derived in the strong-collision model. Classical trajectories and a peaking approximation are used to calculate a unitary scattering operator avoiding perturbation expansions, impact-parameter cutoffs, and straight paths. The latter approximations are not expected to be good when short-range potentials dominate the collision interaction. Use of intermolecular-potential parameters determined from thermodynamics and a simple theory of dispersion forces for ${\mathrm{O}}_2$ calculations gave excellent agreement with experimental data on the magnitude, temperature, and quantum-number dependence of the linewidth parameter.

Lower bounds to the convergence radii of the $\frac{1}{Z}$ expansions are reported for some lowlying states of the isoelectronic series of the helium and lithium atom. It is proven for the first time that the $\frac{1}{Z}$ expansion converges for the ground state of the helium atom. The investigation of the $1{}_{}{}^2{}_{}{}^{}S$ and $1{}_{}{}^2{}_{}{}^{}P_u^{}{}_{}{}^{}$ states of the lithium atom indicated poor convergence properties of the $\frac{1}{Z}$ expansion for systems with more than two electrons. The Brillouin-Wigner perturbation expansion of the ground state of the helium atom is shown to converge if $\frac{1}{(Z-\sigma )}$ is used as perturbation parameter for $\sigma =0.34\mathrm{}$.

The Hylleraas-Scherr-Knight variation-perturbation method is applied to the calculation of oscillator strengths for the dominant transitions from the metastable $2p3p{}_{}{}^3{}_{}{}^{}P$ and $2p3d{}_{}{}^{1,3}{}_{}{}^{}D$ states of helium and the heliumlike ions. The results explain the absence of the $1s2p{}_{}{}^3{}_{}{}^{}P-2p3p{}_{}{}^3{}_{}{}^{}P$ transition of He i from recent beam-foil excitation spectra.

The Born series for the $T$ matrix is considered with the class of potentials $V\left(\mathcal{r}\right)=V_0\int 0^{\infty }\mathrm{dtA}\left(t\right)\mathrm{}\times e^{-t{r}^2}$. An explicit knowledge of $A\left(t\right)\mathrm{}$ is not necessary since the resulting scattering amplitude can be expressed in terms of $V$. The exact expressions for the first and second Born approximations are utilized to approximate the general $n\mathrm{th}$-order term in the series. The series is explicitly summed to yield an expression for the scattering amplitude which reduces at high energy to the previous impact-parameter amplitude of Blankenbecler and Goldberger. The continuation of the series beyond its radius of convergence is discussed and exemplified with an exponential potential $V=V_0{e}^{-\frac{r}{\sigma }}$. A few specific numerical examples are considered to illustrate the behavior of the resulting scattering cross section. Improvement of low-energy total cross sections is noted, particularly for repulsive or weakly attractive potentials.

Compton-profile measurements have been performed on ${\mathrm{O}}_2$, ${\mathrm{N}}_2$, and Ne using silver and molybdenum radiation. An approach is outlined to correct for the breakdown of the impulse approximation for the $1s$ core electrons. A detailed relationship involving experimental corrections is specified by which one can relate the experimentally measured intensity to the Compton profile. Good agreement is found between the silver and molybdenum results on the long-wavelength side of the Compton profile. Comparison of the Ne experimental results both with Hartree-Fock calculations and calculations which include non-Hartree-Fock correlation effects show that within the experimental error agreement is obtained with the latter calculation. The experimental results for ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ are compared with theoretical calculations.

The theory of Eggarter and Cohen for the mobility edge of electrons in dense helium gas is used to perform calculations. The experimental low-field mobility is reproduced over its five-order-of-magnitude range as a function of gas density. The recently measured temperature dependence (4-20°K) is also obtained. The low-field Hall mobility is calculated. Finally, modifications are introduced to yield the electric field dependence of the drift velocity, which is also found to be in good agreement with the experimental measurements.

Methods developed in previous papers are applied to the description of asymmetric charge exchange involving pseudocrossing of energy levels. These methods represent a substantial advance over other classical low-energy models which involve either linear trajectories or the assumption of some mean trajectory.

Absolute cross sections have been measured for the production of Lyman-$\alpha$ radiation by proton impact on ${\mathrm{H}}_2$ in the energy range from 20 to 120 keV. Radiation from slow H atoms produced by dissociative excitation of the ${\mathrm{H}}_2$ molecule was separated from the radiation from fast hydrogen atoms produced by electron capture by using a Doppler-shift technique. Reasonable agreement is obtained with other investigators where the cross sections overlap. The fast-atom emission exhibits a sharp monotonic decrease with energy, characteristic of charge transfer. The slow-atom emission also monotonically decreases with energy but not nearly as rapidly. It is estimated that about 4% of the total charge transfer goes into producting fast atoms in the $2p$ state.

Absolute cross sections for excitation of the $A{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$, $a{}_{}{}^1{}_{}{}^{}\Pi _q^{}{}_{}{}^{}$, and $E{}_{}{}^3{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ metastable states of ${\mathrm{N}}_2$ were deduced from previous time-of-flight studies of metastable nitrogen molecules. The cross section for direct excitation of the $A{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state was determined from threshold to 40 eV and was found to have a peak value of (${5.3}_{-3.0\mathrm{}}^{+4.0\mathrm{}}$) × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ near 11 eV. The total apparent cross section of the $A{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state was obtained by adding cascade contributions from the $B{}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ and $C{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ states and was found to have a value of about 1.2 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at the two peaks near 11.0 and 14.5 eV. The $E{}_{}{}^3{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ state was efficiently excited near threshold and exhibited a resonancelike excitation function with a half-width (full width of half-maximum) at about 0.4 eV and a peak cross section of (7.0 ± 4.0) × ${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ at 12.2 eV. The excitation function for the $a{}_{}{}^1{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ state was obtained from threshold to about 40 eV and was found to differ markedly from two other measurements. Using the present results, a sample vibrational distribution for noninteracting molecules in the $A{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state was calculated at selected electron energies near threshold. For most energies, the lowest vibrational levels are most strongly populated in qualitative agreement with atmospheric observations.

Absolute cross sections have been determined for the production of Lyman-$\alpha$ radiation by 20-120-keV ground-state hydrogen atoms impacting on He, Ne, Ar, and ${\mathrm{N}}_2$. Atom impact on He follows the predicted energy dependence of Levy's Born wave calculation of $2p$ excitation beyond 30 keV. Although the experimental value remains about 25% higher than the theoretical value in this region, the agreement is well within experimental error. For Ne, Levy's scaled Born calculation for $2p$ excitation agrees reasonably well with experiment. However, it is particularly apparent for impact on Ar that the scaled Born calculation underestimates the excitation at the higher energies. All cross sections decrease more rapidly with energy initially than at the higher energies, where a characteristic flattening of the cross-section-vs-energy curve occurs, suggesting the importance of simultaneous excitation of the target and projectile atoms at these energies.

The atomic-beam recoil technique has been used to obtain the ratio of spin-flip to full differential cross sections, for $4{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-4\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},\frac{3}{2}}^{}{}_{}{}^{}$ excitation in potassium by electrons. Data are presented at energies of from 3 to 10 eV, and for electron scattering angles of from $\theta \approx 0° \mathrm{to} 20°$, in 5-deg intervals. Additional data at $\theta \approx 0°$, for energies from threshold to 20 eV, are also presented. Appropriate scattering amplitudes are calculated using the Born, Ochkur, and close-coupling approximations, and comparison with our experiments is made. Exchange is necessary to account for the $\theta \approx 0°$ data; the close-coupling results are in fair agreement with all of the angular data, while the Ochkur approximation gives good agreement at very small angles.

A central-field approximation is used to calculate generalized oscillator strengths (GOS) for a number of discrete and continuous transitions in the noble gases, the alkalis, and Hg, where experimental data exist. The comparisons show that this approximation yields good agreement with experiment except for the first few discrete excitations in low-$Z$ and certain high-$Z$ elements, and in the region of large peaks near threshold in continuum transitions. The reasons for the discrepancies are pointed out, in terms of the approximations made, and the usefulness of this type of calculation is discussed.

A procedure for calculating cross sections for ionization of electrons in various shells of an atom differential in both angle and final electron energy is developed. Calculations for ionization of carbon, copper, and gold for incident energies in the range 100-400 keV are presented and compared with recent experimental results.

The incoherent-scattering factor ($S$) derivation of Heisenberg is extended to include the Thomas-Fermi-Dirac (TFD) model of the atom. TFD neutral-atom calculations of the electron densities and potentials are made with the use of a slope-iteration scheme. The calculations of $S$ show that the TFD values of $S$ are much smaller than the Thomas-Fermi values for small momentum transfers and, therefore, are in better agreement with Hartree-Fock values. The improvement is much greater for small-$Z$ atoms. A comparison of Hartree-Fock and TFD $S$ values is given over a wide range of momentum transfers for the rare gases.

Cross sections for emission of Lyman-$\alpha$ radiation owing to formation of $\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$ and $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ in collisions of 5-25-keV protons and hydrogen atoms with molecular hydrogen have been determined. The intensity of Lyman-$\alpha$ emitted spontaneously from $\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$ was measured at 54.7° or 125.3° with respect to the projectile beam in an essentially field-free collision chamber with an oxygen-filtered photometer calibrated by reference to previous results for ${\mathrm{H}}^{+}$ on Ar. The narrow bandwidth of the oxygen filter allowed separation of the Doppler-shifted Lyman-$\alpha$, emitted by $\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$ formed in electron capture by fast incident protons or collisional excitation of fast incoming hydrogen atoms, and the virtually unshifted Lyman-$\alpha$ emitted by the far slower $\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$ produced in dissociative excitation of ${\mathrm{H}}_2$. The increase in intensity of Lyman-$\alpha$ when an electric field, oriented in the direction of the beam, was applied within the collision chamber has been used to derive separate cross sections for formation of $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ owing to projectile and dissociative excitation. The experimental configuration was designed to minimize the effect of polarization of the light emitted from $\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$ and $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$, and, after small corrections for cascade effects, the data yield cross sections for population of these states. The total cross section for formation of $\mathrm{H}\mathrm{}(n=2\mathrm{})\mathrm{}$ via projectile excitation exceeds that for dissociative excitation in either ${\mathrm{H}}^{+}$ or H impact. ${\mathrm{H}}^{+}$ is generally more efficient than H in the production of Lyman-$\alpha$ at low energies in projectile excitation and at all energies in dissociative excitation, and the cross section for formation of $\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$ usually exceeds that for $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$. Scaling relationships from limiting high-energy-scattering theory are found to have only moderate success in relating our results to previous measurements involving excitation of H to the $n=3\mathrm{} \mathrm{and} 4$ states in projectile excitation and as well as in dissociative excitation by other heavy particles.

The forward-scattered component of the absolute cross sections for proton- and deuteron - impact excitation of the first four vibrational levels of the electronic ground state of ${\mathrm{H}}_2$ have been measured. Excitation cross-section measurements are reported for laboratory energies from 100 to 1500 eV; and, for energies below 100 eV, excitation cross sections are reported for forward-scattered protons from $\theta =0\mathrm{}°$ to $\theta =1.9\mathrm{}°$. The cross sections were measured from the peak intensities observed in the ion energy-loss spectra generated by passing a high-quality proton beam (energy spread <80 meV, angular divergence ≤±1°) through a collision chamber containing the target gas at room temperature. Each excitation cross section (${\sigma }_{0v^{\prime }}$, where the quantum number $v^{\prime }$ refers to the final energy level) is found to reach a maximum value at an energy which decreases with increasing quantum number $v^{\prime }:{\sigma }_{01}\left(max\right)=1.37\mathrm{}\times {10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at 200 eV, ${\sigma }_{02}\left(max\right)=0.342\mathrm{}\times {10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at 140 eV, and ${\sigma }_{03}\left(max\right)=0.078\mathrm{}\times {10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ and ${\sigma }_{04}\left(max\right)=0.021\mathrm{}\times {10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ both at 110 eV. These maxima give collision times and distances which are consistent with the adiabatic hypothesis. For energies beyond the maxima, the cross sections decrease very slowly with increasing energy. Furthermore, the cross sections for excitation to the higher levels decrease more rapidly than the cross sections for excitation to the lower levels, an effect predicted by Shin in a three-dimensional calculation involving a semiclassical theory for the excitation of a classical harmonic oscillator. A comparison of our results with vibrational excitation studies of other systems demonstrates the unique features of the ${\mathrm{H}}^{+}$-${\mathrm{H}}_2$ system. The large values of these vibrational excitation cross sections and their wide effective kinetic energy span show that vibrational excitation must be an important process in a wide variety of physical phenomena.

The energy and angular distributions of electrons produced in the ionization of helium by electrons with energies between 100 eV and 2 keV have been measured in a crossed-beam apparatus consisting of a fixed hemispherical energy analyzer and a rotatable electron gun. Distributions of secondary electrons (those electrons departing with energies less than one-half that of the incident primary electrons) were obtained for a wide range of energies and for angles between 30° and 150° with respect to the direction of the incident primary electron beam. The observed angular distributions were significantly different from the results of two early electron-impact measurements; however, they agreed to the extent expected with more recent results and with similar proton-impact data. For secondary energies above about 50 eV and for primary energies greater than 300 eV, the energy distributions (the cross sections integrated over angle) were observed to be very nearly equal to the distribution given by the Mott formula for free-electron-free-electron scattering multiplied by the number of electrons in the target.