Relativistic corrections are examined for electron capture from a hydrogenlike atom by a bare ion incident with a very high kinetic energy $E$. It is shown that the cross section for nonradiative capture via the double-scattering process suggested by Thomas behaves with $E$ as $E^{-3\mathrm{}}$ in the ultrarelativistic limit. In contrast, the first Born cross section for nonradiative capture behaves as $E^{-1\mathrm{}}$. However, the radiative-capture cross section also behaves as $E^{-1\mathrm{}}$, and has a much larger $E$-independent coefficient. Therefore in the ultrarelativistic limit nonradiative capture may be ignored in comparison with radiative capture.

Cross sections for the ejection of electrons from hydrogen and nitrogen by protons have been measured as a function of the energy and angle of ejection of the electrons at incident proton energies of 5-70 keV and 100 keV for hydrogen. The range of angles measured was 10-160° and the electron energy range was 1.5-300 eV. The doubly differential cross sections were also integrated over angle, over electron energy, or over both to obtain singly differential and total cross sections for electron production. Average electron energies were also calculated from the data. The angular distributions of electrons are peaked in the forward direction but become more isotropic as the proton energy decreases. Nitrogen yields a more isotropic distribution than hydrogen. In this range of proton energies the cross sections integrated over angle are found to fall off approximately exponentially with electron energy, and a simple empirical equation has been found that describes the singly differential and total cross sections within a factor of 2 for several targets. A theoretical interpretation of this result in terms of the molecular promotion model is given in which Meyerhof's method of calculating cross sections for $K$-shell excitation is applied for the first time to the ionization of outer shells of atoms.

Excited-state formation in collisions of ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{2+}$, ${\mathrm{He}}^{+}$, ${\mathrm{H}}_2^{+}$, and ${\mathrm{He}}_2^{+}$ ions with Li atoms has been studied in the kinetic energy range 5-1500 eV. Data were obtained by spectral analysis of near-uv-visible near-ir radiation resulting from spontaneous emission of excited species formed in the collisions. The dominant feature of all collision-produced spectra at all kinetic energies was the 670.8-nm LiI resonance line. Absolute emission cross sections for this line and a number of other spectral features as functions of ion kinetic energy are reported. Although there are no spin restrictions on the final states in the observed charge-transfer processes, only triplet HeI radiation was observed from ${\mathrm{He}}^{+}$-Li collisions. The absence of the corresponding HeI singlet is attributed to nearly inaccessible crossings of the ${\mathrm{He}}^{+}\left(1\mathrm{}{}_{}{}^2{}_{}{}^{}S\right)-\mathrm{Li}\left(2s{}_{}{}^2{}_{}{}^{}S\right)$ potential-energy curve with other singlet ${\mathrm{}\left[\mathrm{HeLi}\right]\mathrm{}}^{+}$ curves. The results for other collision systems are also discussed in terms of curve crossings.

Complex population amplitudes for the excitation of magnetic sublevels of $\mathrm{He}\left(2\mathrm{}{p}^2\right){}_{}{}^1{}_{}{}^{}D$ and $\mathrm{He}\mathrm{}\left(2s2p\right)\mathrm{}{}_{}{}^1{}_{}{}^{}P$ states in 2-keV ${\mathrm{He}}^{+}$ -He collisions have been determined by measuring the energy spectra of the corresponding autoionization electrons ejected at different angles in coincidence with the inelastically scattered ions. It was found that $\mathrm{He}\left(2\mathrm{}{p}^2\right){}_{}{}^1{}_{}{}^{}D$ is excited with a relative probability of 97%. If the direction of the internuclear line at the distance of closest approach is taken as $z$ axis, we find that primarily the $m=0\mathrm{}$ sublevel is populated and that the complete ${}_{}{}^1{}_{}{}^{}D$ excitation can be interpreted as due to pure $m=0\mathrm{}$ excitations with respect to momentary internuclear lines at different points of the trajectory which are symmetric to the turning point. These results are discussed within the framework of the Fano-Lichten promotion model. Quantization along an axis perpendicular to the scattering plane shows an orientation of the excited ${}_{}{}^1{}_{}{}^{}D$ state. From this we find that the angular momentum $L_y$ transferred from the motion of the heavy particles to the electron cloud has an expectation value of $〈L_y〉\approx -\hslash$.

The complex-scaling method is applied to the study of molecular resonances within the framework of the Born-Oppenheimer approximation. In this procedure only the electronic coordinates of the Born-Oppenheimer Hamiltonian are scaled, and thus only the electron-nuclear attraction integrals need be recalculated with explicit complex arguments for each value of the scaling parameter. This method is applied to the study of resonances of ${\mathrm{H}}_2$ and ${\mathrm{H}}_2^{-}$. This represents the first successful application of a complexscaling procedure to the study of a molecular resonance.

The $Z_1^3$ contribution of distant collisions to the average energy loss of heavy charged particles is obtained by extending Bethe's quantum-mechanical calculation to the next highest order in $Z_1$. The second-order Born approximation for the inelastic-collision cross section is simplified by using two major approximations. The infinite summation over terms arising from the coupling to intermediate states of the target atom is approximated with the aid of a parameter and the closure relation. This parameter is proportional to the average excitation energy of the intermediate states as described in the literature. The atomic form factors are simplified through a dipole expansion. Results are obtained in terms of an average excitation energy of the medium. Exemplary results for stopping in Al are presented for estimated values of the average excitation energy of the intermediate states. These results approach the classical and experimental values as the velocity of the penetrating particle increases, agreeing within 20% at $\beta =0.3\mathrm{}$.

Proton-impact-ionization cross sections for argon which are differential in the energy and angle of the ejected electron have been calculated within the framework of the Born approximation using both Hartree-Slater and Hartree-Fock wave functions for the ejected electron. Results of the two types of calculations are compared with each other and with experiment. Differential cross sections for all five sub shells of argon are examined and particular attention is given to some interesting features of the $K$-shell cross sections. The range of applicability of the theoretical models is discussed.

The authors report measurements of the joint distributions in energy and angle for fragments arising from the dissociation of 1.2-MeV ${\mathrm{H}}_2^{+}$ and 3.0-MeV He${\mathrm{H}}^{+}$ in thin carbon foils and in a variety of gases at several pressures. From the foil measurements the distribution of initial internuclear separations in the incident projectiles is derived. These distributions are then used in conjunction with the results for gas targets to determine the role of excited electronic states of the projectile in collisionally induced dissociation. Finally, it is shown how these states also play a vital role in some other phenomena that occur in the interactions of fast molecular ions with foils.

Cross sections have been calculated for electron-impact ionization of singly excited states of the rare gases (neon, argon, krypton, xenon), cadmium, and mercury. The calculations are based upon the symmetric binary-encounter model, together with a semiempirically determined momentum distribution function for the bound, excited electron. Good agreement is obtained with the available experimental data, as well as with existing theoretical results, in the low- to intermediate-energy range.

Cross sections for $n$- (and $l$-) changing collisions of a high-Rydberg atom with a polar molecule are evaluated and found to be of the order of ${10}^{-14\mathrm{}}$-${10}^{-11\mathrm{}}$ ${\mathrm{cm}}^2$. This is based on the model of the quasifree behavior of an excited Rydberg electron, with its interaction with the polar molecule playing a dominant role, and on the mechanism due to energy transfer from molecular rotation to the excited electron. It is shown that the magnitude of the cross sections drastically increases as the energy defect for the collision process becomes small. The calculated results for a symmetric-top as well as a linear polar molecule are in reasonable agreement with recent experimental findings. The possibility of learning about rotational deexcitation of the polar molecule by an extremely slow electron impact from experimental information on these processes is briefly discussed.

Electric dipole polarizabilities and electron-molecule static and adiabatic polarization potentials are calculated by means of ab initio molecular-orbital theory. Nine different basis sets involving 18-48 contracted Gaussian basis functions are used. The authors show that bond-centered basis functions are very efficient for polarizability calculations: a 46-function calculation yields a spherically averaged polarizability ${\alpha }_0$ within (6-7)% of the 56-function calculation of Morrison and Hay and the 76-function calculation of Schneider. As compared to Schneider's calculation, 18 functions underestimate ${\alpha }_0$ by 39% and two 26-function calculations underestimate it by 26% and 31%. These small basis sets may be useful for qualitative purposes, but the results show that the adiabatic polarization potentials at small electron-molecule distances are not less sensitive than polarizabilities to basis-set variations and truncations. Full adiabatic polarization potentials are reported for both 18-function and 47-function basis sets.

The effects of strong magnetic fields on thermal collisions in a vapor are reviewed. Semiclassical and quantum-mechanical symmetry properties of the relaxation matrix are established for resonant collisions between identical atoms and nonresonant collisions with a structureless partner. The variations with field strength of the transfer rates between Zeeman sublevels for $R^{-3\mathrm{}}$ dipole-dipole interaction and $R^{-6\mathrm{}}$ Van der Waals interaction are obtained with an exact semiclassical computation of the collision matrix. These are then compared with those predicted with an approximate formulation by means of the symmetrical correlation function for the potential.

The authors report results of the experimental study of excitation transfer between Zeeman sublevels of the $6{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state of an even isotope of mercury in magnetic fields up to 80 kG, obtained by monitoring the transition from sudden to partially adiabatic collisions. The results are shown to be in good agreement with theoretical evaluations based on a numerical solution of the relaxation problem or on a correlation-function description using a $R^{-3\mathrm{}}$ dipole-dipole interaction.

An experimental study of excitation transfer between certain Zeeman sublevels of the $3{}_{}{}^2{}_{}{}^{}P_J^{}{}_{}{}^{}$ states in strong magnetic fields is reported for $\mathrm{Na}\left(3\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)-{\mathrm{Na}}^{*}\left(3\mathrm{}{}_{}{}^2{}_{}{}^{}P_J^{}{}_{}{}^{}\right)$ resonant collisions. A major decrease in the $M=-\frac{3}{2}\to M=\frac{3}{2}$ transfer rate is observed between 4 and 80 kG. Approximate calculations in the correlation-function framework are performed, and the experimental results and theoretical predictions for the field dependence are in good agreement. Some insights into the mechanisms of the collision process are deduced and the particularly important role of the electronic spin is emphasized. The importance of the symmetry properties of the interaction potential is also directly demonstrated.

A simple model for the effects of polarization is introduced for the study of positron-atom interactions. The model is also used to study positronium-atom interactions by treatment of such systems as the interactions of positrons with polarizable anions. The model depends upon the average dipole polarizability of the atom (or ion) and one disposable parameter, an effective radius. The effective radius is determined by fitting calculated scattering lengths for H and He and the calculated positronium affinity of H to their well-established values, and by interpolating on the ionization potentials for other atoms. The model produces quite satisfactory phase shifts and cross sections for positrons scattering elastically off H, He, Ne, Ar, Kr, and Xe. The model appears to be equal or superior in predictive power to the much more elaborate polarized-orbital model recently formulated by McEachran et al. The model predicts that none of the rare-gas atoms studied will bind a positron. As a measure of how far from binding they are, negative values of the positron affinity are devised by appealing to effective-range theory and a heuristic argument involving the dependence of the calculated scattering length on the disposable parameter in the model.

A previously described model potential for polarization effects in positron-atom interactions is applied to the halogens. The model predicts that (i) each halogen is capable of binding positronium but not a positron, except for iodine, for which the positron affinity has an uncertainty of sign; (ii) no bound excited states for any of the systems exist, except possibly for PsCl; and (iii) the elastic-scattering cross section of positrons off fluorine has a deep Ramsauer minimum at a positron incident energy of about 0.85 eV, as does neon. For (i) results are in substantial agreement with the self-consistent-field results of Cade and Farazdel as corrected for correlation.

Laser isotope separation schemes which require resonant photoexcitation of atoms or molecules with complex spectra will in general involve processes more complicated than a simple chain of transitions between successive pairs of energy levels. In the rotating-wave approximation these situations can be described by excitation graphs with side branches and cycles. For many cases a simple change of basis removes the time dependence of the interaction Hamiltonian and reduces the calculation of level populations and interlevel flows to an eigenvalue problem. By this method it is shown that a side branch with a large matrix element strongly inhibits the flow of population along the path to which it is attached. When several phase-locked lasers are employed, the populations and flows depend on certain linear combinations of the phases, one for each independent cycle in the excitation graph. In the simplest one-cycle example this phase dependence allows a continuous change from no population inversion to complete inversion.

The new results of measurements of coherent scattering of photons by bound atomic electrons over a momentum transfer $q$ range $0-4mc$ together with those from other recent measurements with a coverage in the momentum transfer up to $10mc$ are presented for a critical evaluation of the previous and new calculations on Rayleigh scattering. This evaluation reveals the ranges of applicability of the form-factor formalism in the nonrelativistic and relativistic domain and demonstrates the trend of behavior of the exact theoretical predictions as a function of $\frac{q}{\alpha \mathrm{Zm}}$.

Many-body diagrammatic perturbation theory has been applied to the calculation of ionization energies and multiplet strengths for two highly ionized atoms of the copper isoelectronic sequence. A unified Hartree-Fock zeroth-order Hamiltonian the eigenfunctions of which include both open- and closed-shell orbitals has been constructed for systems with a single open shell. Correlation energies for the excited $4p$ states as well as the ground $4s$ states of Kr VIII and Mo XIV were computed by means of individual basis sets generated for each state. The distribution of the $3l-4l^{\prime }$ correlation energy among second- and higher-order terms differed significantly for the two ions. In Mo XIV, most of the correlation energy was concentrated in second-order, with small third-order effects. In Kr VIII, however, second-order results were substantially changed by higher-order diagrams, particularly in the case of the $4p$ state. Correlated multiplet strengths for the $4s{}_{}{}^2{}_{}{}^{}S-4p{}_{}{}^2{}_{}{}^{}P$ resonance transition were computed, including first-order corrections to the Hartree-Fock zeroth-order wave functions for both initial and final states. The results of these calculations are in excellent agreement with those of recent multiconfiguration Hartree-Fock calculations.

A multichannel relativistic random-pjase approximation (RRPA) for the photoionization of atoms is presented. The RRPA equations are obtained by generalizing the nonrelativistic time-dependent Hartree-Fock equations using the Dirac-Breit Hamiltonian to describe the atomic electrons. The angular decomposition of the RRPA equations to a set of coupled equations for the radial wave functions is given, and the radiative-transition operators are developed for arbitrary electric and magnetic multipoles. Formulas are obtained for the total photoionization cross sections and angular distributions, including all multipoles. The method of constructing multichannel solutions from the RRPA radial wave functions is described and various ways of choosing approximate potentials for the photoelectron are given.