The fermion-antifermion equation derived recently is applied here to positronium with the aim of laying the groundwork for a systematic calculation of the higher-order corrections. An equation valid to the fourth order in the fine-structure constant is obtained which is equivalent to the corresponding equation derived within the Bethe-Salpeter formalism. The static-interaction limit of this equation, the Breit equation, is then decomposed into angular momentum states, whereby four second-order differential equations are obtained. The resulting eigenvalue equations are solved numerically using the appropriate boundary conditions at the origin. The resulting spectrum is in agreement with perturbative calculations.

The problem of determining the ground-state energy and wave function of a three-body system is considered anew. It is found that a particular Hylleraas-type expansion for the wave function arises naturally in the present approach. The main problem is seen to be the determination of the action of certain matrices on a vector representation of the trial wave function. A method is introduced which avoids the need for, and hence determination of, long algebraic expressions for matrix elements. As a result, computer programs do not have to be altered when new potentials are considered. It is merely necessary to supply the parameter values characterizing the two-body potentials, which, in general, are a linear combination of a Coulomb potential and terms which are of the form of a polynomial times a Yukawa potential.

The triple-differential cross section for ionization of helium by low-energy electron impact is investigated over the energy and angular variables. Measurements have been made for primary electron energies near 100 eV, ejected electron energies of 5, 10, and 20 eV, and scattering angles 15°, 20°, and 30°. The forward lobe of the triple-differential cross section is found to be approximately cylindrically symmetric.

Total scattering cross sections have been measured for 0.3-31 eV positrons colliding with helium atoms and for 0.25-24 eV positrons colliding with neon atoms using a beam-transmission technique. These measurements have resulted in the first direct observations of Ramsauer-Townsend effects for positrons colliding with helium and neon, and also provide clear indications of the onset of positronium formation in each of these gases. As an overall check of the reliability of the experimental approach for measuring total scattering cross sections for positrons, electron-atom scattering cross sections have been measured in the identical apparatus, using the same target gases, and the same technique as was used for the positron measurements.

A saturated-absorption experiment is used to measure the effects of velocity-changing collisions between Kr* metastable atoms ($4p^{5}5s{\left[\frac{3}{2}\right]}_2$) and He and Ar perturbers. Comparison between experimental profiles and profiles calculated assuming hard-sphere collisions between Kr* and perturber atoms confirms the calculations of Borenstein and Lamb concerning the change of velocity associated with a collision. Furthermore it is found that the rate of velocity-changing collisions is consistent with the predictions of kinetic theory.

Collisionally induced transitions between two electronic states during atom-atom collisions are described in the near-adiabatic formalism. The two-level system, in the semiclassical impact-parameter method, is represented by time-dependent coupled differential equations which have been studied by many workers. We present a method of solving the system of equations under the approximation of slow variation of the matrix elements responsible for the transition. A general formula for the transition probability is obtained with special reference to the problem of charge transfer, though the result is applicable to other two-level systems. The formula reduces under various special conditions to other well-known expressions, such as those found by Vainshtein and co-workers, the Landau-Zener formula, and that for resonance charge transfer.

A method for obtaining scaled collision strengths $Z^2\Omega$ for highly charged ions in terms of scaled results for hydrogenic ions with $Z=\infty$ is modified by a perturbation theory approach to include the major relativistic corrections. The results are then expected to provide useful estimates for ions with $Z$ in the range $3N\lesssim Z\lesssim 50$, where $N$ is the number of bound electrons per ion. Cases in which the modified approach simplifies are considered and numerical results are given for intermediate-coupling fine-structure transitions in highly charged He-like ions involving transitions between $S$ and $P$ levels and between $S$ and $D$ levels with $n\le 5$ for six or more energies. Some comparison is made with previous results of Jones.

The ($e, 2e$) reaction is studied under kinematic conditions designed to test different reaction theories. The problem is reduced to a calculation involving distorted waves for the electron-ion interactions and a two-body operator for the electron-electron interaction. The amplitude factorizes into an $\mathrm{ee}$ factor and a distorted-wave factor if the eikonal approximation is made for the distorted waves. The factorization is tested by choosing kinematics so as to keep the distorted-wave factor constant while varying the $\mathrm{ee}$ factor. The value of the average eikonal potential is established in coplanar symmetric kinematics. The target is helium. At incident energies of 400 and 800 eV, the approximation is good for recoil momenta less than about 1 a.u., provided the effective two-body operator is the $t$ matrix. The $v$ matrix is ruled out. There are strong indications that the impulse approximation itself breaks down for small relative momenta between the outgoing electrons.

We have measured the polarization of the $K{\alpha }^{\prime }$ [$\left(1\mathrm{}{s}^{-1\mathrm{}}2p^{-1\mathrm{}}\right){}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$] to [$\left(2\mathrm{}{p}^{-2\mathrm{}}\right){}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$] x ray from an Al target following bombardment by various ion beams at several different incident energies. The polarization of the $K{\alpha }^{\prime }$ x ray is a measure of the ratio of the $2p$ substate populations ${\sigma }_1(M_L=\pm 1)$ and ${\sigma }_0(M_L=0)$ of the ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ state. We compare our results with recent collision-theory calculations which predict nonstatistical substate populations for simultaneous $K$- and $L$-shell ionization.

The two-state, two-center atomic expansion method of Bates for charge transfer is generalized to calculate cross sections of electron capture from inner shells of multielectron atoms by fast protons. In the limit of small capture probabilities, the connections of the present approach with various first-order Born theories are investigated. It is shown that these Born methods for electron capture of multielectron atoms can be obtained from the present approach by further approximations. The method is applied to obtain cross sections of electron capture from C, N, O, Ne, and Ar atoms by fast protons in the energy region where the projectile velocity is nearly equal to the $K$-shell-electron orbital velocity of these atoms. Results of the calculations are compared with experimental measurements.

Experimental $K$-shell ionization cross sections of ${}_{13}{}^{}{}_{}{}^{}\mathrm{Al}$ and ${}_{28}{}^{}{}_{}{}^{}\mathrm{Ni}$ are reported for ions of ${}_1{}^1{}_{}{}^{}\mathrm{H}$, ${}_1{}^2{}_{}{}^{}\mathrm{H}$, ${}_2{}^4{}_{}{}^{}\mathrm{He}$, ${}_3{}^6{}_{}{}^{}\mathrm{Li}$, and ${}_3{}^7{}_{}{}^{}\mathrm{Li}$ with kinetic energies in the range from 2 to 36 MeV, and of ${}_{28}{}^{}{}_{}{}^{}\mathrm{Ni}$ for ions of ${}_6{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_8{}^{16}{}_{}{}^{}\mathrm{O}$, and ${}_9{}^{19}{}_{}{}^{}\mathrm{F}$ in the range from 4 to 90 MeV. The theory of direct Coulomb $K$-shell ionization, as developed in an earlier paper [Phys. Rev. A 7, 983 (1973)] for projectiles of atomic number $Z_1$, small compared to the target atomic number $Z_2$, and of velocities $v_1$ small compared to the target $K$-shell electron velocity $v_{2K}$, i.e., $v_1\ll v_{2K}$, is extended to intermediate velocities $v_1\simeq v_{2K}$. New effects appear. They add to the $Z_1^2$-proportional cross sections one derives from linear-response theories for direct ionizations. They are attributed to the polarization of the target $K$ shell in the field of the projectile, and to electron capture by the projectile. Guided by the perturbed stationary-state theory of atomic collisions, the polarization effects are incorporated so that the theory retains the unifying aspects of the cross sections derived in the plane-wave Born approximation, but the variables now contain the nonlinear effects as scaling factors. Electron-capture cross sections are added. When $v_1\gg v_{2K}$, such contributions subside, and one retrieves the cross sections of the linear-response approximation. The theory predicts $K$-shell ionization cross sections for projectiles with $\frac{Z_1}{Z_2}<0.5\mathrm{}$ at all velocities in a comprehensive manner. It agrees with experimental data covering six orders of magnitude for collisions partners with $\frac{Z_1}{Z_2}$ ranging from 0.03 to 0.3 and $\frac{v_1}{v_{2K}}$ from 0.07 to 2.

The lowest-lying resonance occurring in $S$-wave positronium-hydrogen scattering is reinvestigated, using the complex-rotation method. By employing a generalized Hylleraas-type wave function that includes all six interparticle coordinates, a very accurate value of the resonance position $E_r$ is obtained, along with a good value of the width. The present result for $E_r(-1.205\mathrm{}\pm 0.001 \mathrm{Ry})$ is lower than the previous result of Drachman and Houston, who omitted the interelectronic coordinate $r_{12}$ in their trial function. In addition, the lowest ground-state energy of positronium hydride is obtained by using 210 terms in the trial wave function. The effect of the $r_{12}$ coordinate and others on both the resonant energy and the binding energy of PsH is discussed.

In an electron-photon coincidence experiment, the angular dependence of the photon linear polarization in the elementary process of atomic-field bremsstrahlung was measured for a fixed direction of the outgoing electron and for coplanar geometry. An electron beam of 300 keV was used, incident on a carbon target. It has been found that for photon-emission angles with large cross section the radiation is almost completely polarized with the electric vector in the reaction plane. A strong decrease of the polarization caused by electron spin-flip radiation was observed for a photon-emission angle near the minimum of the cross section. Within the experimental errors we find agreement with theoretical calculations.

Measurements of the plasma-broadened $H_{\alpha }$ line shape in a wall-stabilized arc show considerable differences between experimental and theoretical line profiles at electron densities below ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The half-width of the experimental profile is up to three times larger than predicted theoretically. At low electron densities (≲ ${10}^{15}$ ${\mathrm{cm}}^{-3\mathrm{}}$), part of such discrepancies can be attributed to the neglect of fine-structure splitting in current Stark-broadening calculations, especially for $H_{\alpha }$, $L_{\alpha }$, and hydrogenic-ion lines.

$U$-branch transitions corresponding to 5←1 and 4←0 in the rotational quantum number $J$ of the ${\mathrm{H}}_2$ molecule have been clearly observed in the infrared fundamental band with a 3.6-cm absorbing path of the solid at ∼ 10 K. These transitions arise because of the hexadecapolar contribution to the intermolecular interaction, and this work represents the first observation of such absorption in solid ${\mathrm{H}}_2$. A measurement of the absorption intensity was made for the case of high-purity parahydrogen.

Semiclassical expressions of two-photon ionization of atoms induced by radiative collisions are derived. The dependence of the ionization yield on the atomic forces, field intensity, and energy gap is derived. Although absorption tends to decrease as the field intensity rises due to stimulated emission at the second crossing, the two-photon ionization yield can be nearly saturated at the first crossing, thus enhancing the absorption. Both regions, ionization in single collisions and ionization between collisions, are treated. In the latter we find that saturation of the ionization can be achieved at much reduced intensities. This process promises an extremely sensitive method for studying radiative collisions, especially when absorption or fluorescence becomes extremely weak.

Multiphoton free-free transition amplitudes are derived from time-dependent perturbation theory for intense laser pulses of finite duration and slowly varying shape. The expressions obtained are general enough to exhibit effects caused by the off-shell behavior of the electron-atom (molecule) system without the laser field. A time-averaging procedure is derived by which the cross-section calculation for a laser pulse with a slowly varying shape is reduced to the knowledge of the single-mode constant-laser-intensity cross section. We find that recent experimental data can be explained qualitatively with the help of this averaging procedure.

Electromagnetic radiation from a classical charge distribution interacts with an incident plane wave, and the interaction terms in the resulting Poynting vector are shown to give a net contribution to the total energy flux exactly in the forward-scattering direction. A simple relativistically valid expression for the interaction energy in the case of a single particle is derived, and we show that energy is conserved in Thomson scattering if radiation-reaction forces are included. A perturbation theory is developed for a particle having its own given unperturbed motion, and the perturbed interaction energy is shown to be proportional to the intensity of the incident wave. We apply this theory to a "free-electron laser" consisting of a relativistic electron in a linear accelerator, and show that stimulated emission or absorption could both occur. The result contradicts that obtained using the Einstein-coefficient method.

There has been a recent claim for the observation of fractionally charged particles. If this evidence is to be interpreted as due to a quark embedded in a heavy nucleus, a natural follow-up is to look for "quark atoms" through their spectral lines. The recent technique of single-atom detection may be one way of doing this. Such searches will require as inputs knowledge of the spectroscopic transitions in the quark-atom. The presence of the quark causes large shifts in spectral lines which fall in the visible and near-visible regions and a simple technique is presented based on interpolations in isoelectronic series for estimating these shifts quickly and accurately for any atom. Results are also presented for the x-ray transitions in heavy atoms and very accurate results for the various series in quark hydrogen. The techniques and results of this paper may also be relevant for searches in laboratory and astrophysical spectra.

Experimental data on collision-induced scattering in the frequency range of the vibrational Raman band ${\nu }_1$ of C${\mathrm{F}}_4$ up to 280 amagat at 296°K are discussed within the framework of dipole-induced dipole (DID) approximation using computer calculations and previous Rayleigh results for the same molecule. Satisfactory agreement between theoretical and experimental results is obtained for the low-frequency line shape at low densities and for the density dependence of the integrated intensity. However, the point-dipole DID approximation in its present form is unable to describe exactly either the whole detailed line shape or the absolute value of the integrated depolarization factor. The different influences of the three- and four-body interactions are discussed for Rayleigh and Raman scattering.