As a test of the accuracy of numerical techniques used in solving the Bethe-Salpeter equation, we compute the binding energy of a hydrogenlike atom including one-photon exchange only. A 5% deviation from the result predicted from the Dirac equation with a Coulomb potential is in agreement with a result which we derive analytically, $E_b=\left(\frac{1}{4}\right)m{\alpha }^2[1-(\frac{4\alpha }{\pi }\left)\ln \right(\frac{2}{\alpha })+\cdots ]$. $E_b$ cannot be expanded in a power series in ${\alpha }^2$ similar to the series expansion of the Sommerfeld expression for $E_b$ resulting from the Dirac theory. This apparently startling result is not due to a failure of quantum electrodynamics, of course, but to the fact that we have used the relativistic interaction ${\gamma }_{\mu }^{\mathrm{}\left(1\right)\mathrm{}}\left(\frac{1}{k^2}\right){\gamma }_{\mu }^{\mathrm{}\left(2\right)\mathrm{}}$ rather than working in the Coulomb gauge as is usually done. Salpeter remarked in 1952 that doing the calculation as we have done it would result in a slowly convergent series for $E_b$; nevertheless the precise magnitudes involved are surprising.

We show that all the coherence properties of the field in an optical cavity can be transferred to a second cavity by a monoenergetic electron beam. The energy supplied to the second cavity comes from the electron's kinetic energy, as in the klystron.

A time-of-flight technique has been used to measure the quenching of the $2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ metastable state of helium by a static electric field. Neutral ground-state helium atoms effusing from a cooled source slit are immediately excited to the $2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ metastable states by a pulse of antiparallel magnetically focused electrons. The metastable beam is collimated before passing through a uniform electric field region 0.5 m long and is then preferentially detected at the end of the time-of-flight region, 1.825 m from the electron gun. The time-of-flight distribution for the $2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ state is separated from that of the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state by illuminating the beam before the electric field region with an rf-discharge helium lamp. The $2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ state is quenched by resonant absorption of a 20 581-Å photon, raising the atom to the $2{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ state, which then decays to the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ ground state; the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state remains unaffected because it is the ground state for the triplet system. The $2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ time-of-flight distribution is therefore obtained from the difference between the full beam and the quenched beam. The number of $2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ atoms arriving at the detector in specific velocity intervals with the electric field off is compared to the number with the field on to determine the quenching rate ($=k{E}^2$). The result for the quenching constant $k$ for both ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ with $E$ in kV/cm is $k=0.933\mathrm{}\pm 0.005$; this value is in good agreement with theory and with an earlier less accurate experiment. The error in the present experiment arises from a 0.5% uncertainty in the effective length of the electric field region.

We present a treatment of ion-atom and atom-atom potentials based on terms derived from the separated atoms or ions. The method used is an adaption of form-factor techniques developed in particle and nuclear physics. The potentials of the separated atoms or ions are derived from an independent-particle model for atoms and the resulting ion-atom and atom-atom potentials are shown to be representable as sums of exponentially shielded Coulomb potentials, or Yukawa potentials. We then calculate the differential cross sections using an eikonal model which embodies systematic analytic corrections to the Glauber approximation. Analytic results are also obtained for the scattering amplitude at nonforward angles by employing the stationary-phase approximation. The specific case of ${\mathrm{O}}^{+}$-Ar at 100 keV is treated. Exchange effects, polarization, and inelasticity are neglected.

In connection with a recent experiment of Sandars and Stewart, the atomic quadrupole moments for the excited states $n{p}^5{n}^{\prime }s (n^{\prime }=n+1)$ of the rare gases have been calculated, in particular, the induced moment due to the $n^{\prime }s\to d$ excitation produced by the quadrupole potential due to the vacancy in the $\mathrm{np}$ shell. Sandars and Stewart have written the total quadrupole moment ${\Theta }_{\mathrm{atom}}$ as: ${\Theta }_{\mathrm{atom}}=\Theta \mathrm{}\left(\mathrm{np}\right)(1\mathrm{}-R_{\Theta })$, where $\Theta \mathrm{}\left(\mathrm{np}\right)\mathrm{}$ is the quadrupole moment due to the $\mathrm{np}$ vacancy, and $R_{\Theta }$ is a suitable shielding factor associated with $n^{\prime }s\to d$. In the present work, $R_{\Theta }$ was calculated by obtaining the perturbation $\nu _1^{}{}_{}{}^{\prime }(n^{\prime }s\to d)$ of the $n^{\prime }s$ wave function due to the quadrupole potential of the $\mathrm{np}$ vacancy. It was found that the calculated values of $R_{\Theta }$ are in very good agreement with the experimental values for all four cases (Ne, Ar, Kr, and Xe). The calculated values of $R_{\Theta }$ range from 0.82 for Ne to 1.33 for Xe, in good agreement with the experimental results.

The object of the paper is to obtain a perturbation expansion of the wave function which satisfies arbitrary initial conditions. For periodic perturbations, a method is developed to obtain the solution without any secular terms. It maintains the normalization condition for all times, which assures the unitarity of the transition amplitudes.

Consequences of the discontinuity at $Z=30\mathrm{}$ in the Coster—Kronig transition probability $f_{23}$ have been investigated by Auger and photoelectron spectroscopy. The $\frac{L_3-M_{45}{M}_{45}}{L_2-M_{45}{M}_{45}}$ Auger intensity ratio is found to undergo a sudden decrease at $Z=30\mathrm{}$. Relative $L_2$ and $L_3$ level widths of Cu and Zn are derived from photoelectron spectra; while the $L_3$ width increases from Cu to Zn, the $L_2$ width of Cu is greater than that of Zn, contrary to the general trend. The data agree qualitatively with earlier calculations of radiationless-transition probabilities based on hydrogenic wave functions, but substantial quantitative discrepancies are found. New calculations have been performed with numerical single-particle wave functions based on Green's atomic independent-particle model. With suitable assumptions regarding Cu and Zn $M_4$ and $M_5$ electron binding energies in the presence of an $L_2$ vacancy, reasonable agreement between calculated and observed Auger-electron intensity ratios and $L$-subshell level widths is attained.

In view of new high-precision experiments in atomic physics it seems necessary to reexamine nonlinear theories of electrodynamics. The precise calculation of electronic and muonic atomic energies has been used to determine the possible size of the upper limit $E_{max}$ to the electric field strength, which has been assumed to be a parameter. This is opposed to Born's idea of a purely electromagnetic origin of the electron's mass which determines $E_{max}$. We find $E_{max}\ge 1.7\times {10}^{20}$ V/cm.

Using a recent method due to Reiss, the relativistic effect to multiphoton absorption in hydrogenlike atoms in the presence of intense electromagnetic fields of long wavelength is calculated. For an intensity parameter less than unity the corrections are found to be small for any number of photons absorbed. However if the intensity parameter exceeds unity by a considerable amount, corrections become significant.

Electronic dipole and quadrupole polarizabilities and the Sternheimer shielding or antishielding factors are calculated for several closed-shell atomic systems. The calculations are carried out by an effective-field method using the perturbed orbitals, given by the uncoupled Hartree—Fock method, as trial functions. The external field is replaced either by a mean effective field taking into account the mean coupling between the deformations of the various orbitals or by a set of effective fields, each of them being relative to a particular perturbed orbital. Numerical results obtained for the He, Ne, A, and Kr isoelectronic series show a much better agreement with the corresponding coupled values than the initial uncoupled results.

Using the beam-foil technique, we have observed several new transitions in lithium between 100 and 2000 Å. We suggest classifications for some of these transitions in the doubly excited term schemes of Li I and Li II. The lifetimes and wavelengths of the Li II transitions are found to be in reasonable agreement with variational calculations.

The rate coefficient ${\beta }_1$ for the ionizing collision of two metastable helium atoms ($2{}_{}{}^3{}_{}{}^{}S$) is evaluated from measurements in a steadily decaying helium afterglow plasma with three different techniques. The value of ${\beta }_1$ is also determined with a perturbation technique. All the values of ${\beta }_1$ determined by these techniques lie within the range (4.5±1.0)×${10}^{-9\mathrm{}}$ ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$. This value is larger than that observed directly from the decay of the density of the triplet helium metastable atom because the dissociative recombination of $\mathrm{He}_2^{}{}_{}{}^{+}$ is a significantly large source of atomic metastables.

We utilize an atomic independent-particle model to calculate photoionization cross sections for atomic nitrogen and atomic oxygen as a function of the wavelength of the incident radiation, from threshold down to 10 Å. Comparison is made with available experimental data and the results of Hartree-Fock calculations.

The total cross section for scattering of He by He is measured at 100-eV intervals in an energy range from 0.30 to 3.00 keV. Measurements are made using detector angular resolutions of 0.056° and 0.260°. The cross section is found to decrease monotonically from 12.5 to 5.0 ${\mathrm{\AA }}^2$ and from 7.0 to 2.6 ${\mathrm{\AA }}^2$, respectively, as the energy increases. Small-angle differential measurements are also made out to scattering angles of 1.25° at incident energies of 1.80 and 3.00 keV. At 3.00 keV a ${\mathrm{He}}^{+}$ signal is found at sacttering angles beyond 0.8°. The ratio of the ion to the total signal increases to about 10% at 1.25°. The total-cross-section data are used to infer a potential.

Previously described measurements for the scattering of ${}_{}{}^1{}_{}{}^{}\mathrm{H}_{}^{+}{}_{}{}^{}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}_{}^{+}{}_{}{}^{}$, and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}_{}^{+}{}_{}{}^{}$ ions of energies $9<E<\mathrm{}75\mathrm{}$ keV by a thermal beam of Hg atoms have been extended to smaller angles. Angular distributions for $2.8<\mathrm{}{\theta }_L<40\mathrm{}$ deg have been measured for the scattering of all projectiles independent of final charge state. Differential scattering cross sections are in approximate agreement with the theory for scattering in a Thomas-Fermi potential over a range of five orders of magnitude. When the cross sections are reduced by the Lindhard procedure, we find that the Thomas-Fermi interaction is a better approximation to the actual potential than the Lenz-Jensen interaction.

The theory of fine-structure transitions in atom-atom collisions is formulated in terms of the molecular states of the diatomic collision complex. The Born-Oppenheimer (BO) electronic wave functions are implicit functions of the interatomic coordinate $R$, and the molecular theory is analogous to the "perturbed-stationary-state" method. Expansion in molecular channel states incorporates the effects of polarization, exchange, and valence forces on the electronic portion of the scattering wave function and embodies the "adiabatic" contribution of the entire set of closed-channel excited states that are generated in the more usual asymptotic-atomic-state expansion. The channel states are expressed explicity in terms of the body-fixed molecular wave functions, and the resultant interaction matrix elements in the close-coupling scattering formalism are related to the molecular potentials. The theory is developed specifically for proton collisions with the fluorine atom in its ground ${}_{}{}^2{}_{}{}^{}P_{j,\mathrm{mj}}^{}{}_{}{}^{}$ state, with explicit account being taken of the spin-orbit splitting between the $j=\frac{3}{2}$ and $j=\frac{1}{2}$ multiplet states. Use is made of the accurate H${\mathrm{F}}^{+}$ (${}_{}{}^2{}_{}{}^{}\mathrm{II}$) and ${\mathrm{HF}}^{+}\left({}_{}{}^2{}_{}{}^{}\Sigma \right)$ wave functions calculated by Wahl, Julienne, and Krauss. These molecular states asymptotically approach ${\mathrm{H}}^{+}$ +F(${}_{}{}^2{}_{}{}^{}\mathrm{P}$), and accurate quadrupole and induced-dipole interaction parameters which describe the asymptotic interaction potentials are obtained from the calculations. Estimates are made of the BO coupling terms and they are found to be negligible compared to the spin-orbit couplings. In the following paper close-coupling calculations are made of the cross sections for the fine-structure transitions ($j,m_j\to j^{\prime },m_j$).

The results of a close-coupling calculation of the fine-structure transitions ($j,m_j\to j^{\prime },m_j^{\prime }$) are presented for collisions between photons and $\mathrm{F}\left({}_{}{}^2{}_{}{}^{}P_{j,m_j}^{}{}_{}{}^{}\right)$. The theory is formulated in the perturbed-stationary-state approximation using accurate molecular wave functions for the ground ${}_{}{}^2{}_{}{}^{}\mathrm{II}$ and ${}_{}{}^2{}_{}{}^{}\Sigma$ states of H${\mathrm{F}}^{+}$. Comparison is made to the predictions of the Born approximation. The magnetic selection rule ($j,m_j\to j,-m_j$) is strongly violated in the $j=\frac{3}{2}$ state and less strongly violated in the $j=\frac{1}{2}$ state. It is concluded that the important region of interaction for the $j=\frac{1}{2}\to j=\frac{3}{2}$ transition is at short-to-intermediate distances where accurate molecular potentials are required and close-coupling effects are dominant.

The lifetime of the $2 {}_{}{}^3{}_{}{}^{}P_j^{}{}_{}{}^{}$ states in singly ionized lithium has been measured using an rf magnetic-resonance technique; the value is $\tau =45\mathrm{}\pm 5$ nsec. Neutral lithium was ionized and excited by a unidirectional beam of electrons which produced an alignment in the excited state. The cross section for the electron-impact excitation $1s^{2}2s{}_{}{}^2{}_{}{}^{}S\to 1s2p{}_{}{}^3{}_{}{}^{}P$ near threshold was measured to be ${10}^{-22\mathrm{}\pm 1}$ ${\mathrm{cm}}^2$. Implications for the feasibility of rf resonance spectroscopy on the fine and hyperfine structure of the $2 {}_{}{}^3{}_{}{}^{}P$ term will be discussed.

The high-energy Glauber, or eikonal, approximation is used to derive formulas for the scattering amplitude and cross section for the ionization of atomic hydrogen by electron impact. The scattering amplitude is expressed in terms of a double infinite sum of hypergeometric functions which may be evaluated on a computer. Total cross sections may be obtained by squaring the scattering amplitude and integrating over five final-state variables. Three integrals are trival and two must be done numerically. At sufficiently high energies, the Glauber result reduces to the expressions found in the simpler, but more restrictive, Coulomb—Born approximation.

Using an accurate numerical solution of the Thomas—Fermi model with quantum-mechanical corrections, the author obtains a description of coherent and incoherent scattering of x rays by the inert gases, which is in excellent agreement with detailed Hartree—Fock calculations. The results are somewhat better than those given by the Thomas—Fermi—Dirac model, and are a substantial improvement over those given by the Thomas—Fermi model alone.