The dielectronic recombination amplitude is given in the resonance approximation by a product of the radiationless capture amplitude $S$ to one of the resonant intermediate states and the radiative decay amplitude $R$ of that resonant state. For highly charged ionic targets, both $S$ and $R$ are expected to scale approximately in the nuclear core charge $Z_C$ for each isoelectronic sequence, and we study the scaling property and its breaking as the number of electrons in the ion increases. The effects of Coulombic and exchange correlations as well as the relativistic correction are considered. Based on the explicit evaluation of the $S$ and $R$ amplitudes using Hartree-Fock wave functions, we have determined an effective scaling function, which has been used to predict the radiation and Auger-emission probabilities $A_r$ and $A_a$ for Ar, Mo, and W from the available values for Fe.

Self-energy corrections for $1s_{\frac{1}{2}}$ levels of heavy muonic atoms are calculated to all orders in the external field using numerical techniques to evaluate the bound-muon propagator. The resulting values of the self-energy are about 10% larger than previous estimates.

Relations, important in some physical applications of the phase-integral method developed by Fröman and Fröman, are derived. For the case of a single well potential these relations are then used for obtaining general phase-integral formulas for level densities, normalization factors, and quantal expectation values, under differing assumptions concerning the behavior of the potential. The derivation of those formulas is based on the phase-integral quantization conditions pertinent to the potentials considered. The wave functions themselves do not occur in the final simple formulas obtained, which can, furthermore, in general be expected to be more accurate than corresponding formulas involving wave functions. Some of the results have been obtained in earlier papers, but the present treatment covers more general situations. To illuminate the application of the phase-integral formula for expectation values, the radial Schrödinger equation is considered, and certain exact relations are discussed within the framework of the phase-integral formulas.

We have calculated the second-order interaction between the spin-orbit coupling perturbation $H_{\mathrm{SO}}\propto r^{-1\mathrm{}}\left(\frac{\mathrm{dV}}{\mathrm{dr}}\right)\overrightarrow{\mathrm{l}}·\overrightarrow{\mathrm{s}}$ acting on the core electrons and the exchange Coulomb interaction between the valence and core electrons. This calculation was previously carried out for two alkali $\mathrm{nd}$ states (Na $3d$ and Rb $4d$) and was shown to result in the observed inversion of the fine-structure interval $\Delta \nu$ for these $d$ states. In the present paper we have evaluated the second-order correction $\Delta {\nu }_2$ for the $\mathrm{nf}$ states of Na, and we have found that $\frac{\Delta {\nu }_2}{\Delta {\nu }_1\simeq -0.07\mathrm{}}$ for Na $11f$ and Na $14f$, in good agreement with the experiment of Gallagher et al., who have observed that the fine-structure interval of Na $11f$, $13f$, and $14f$ is normal, i.e., noninverted, and slightly smaller than the hydrogenic value $\Delta {\nu }_1$ (by ∼ 5%). Calculations have also been carried out for Na $3d$, $4d$, $5d$, $11d$, and $14d$, and the results for $\Delta {\nu }_1+\Delta {\nu }_2$ are negative, in good agreement with the observed inverted fine structure for these states. Additional calculations have been carried out for Cs $4f$, $5f$, and $6f$.

We calculate the differential and the total cross sections for the direct excitation of the $3{}_{}{}^3{}_{}{}^{}S$ state of helium from the metastable $2{}_{}{}^3{}_{}{}^{}S$ state by electron impact using the Glauber and Born methods. For the Glauber cross-section calculation we use the analytic method of Thomas and Chan to reduce the Glauber amplitude for charged-particle-neutral-atom collisions to a one-dimensional integral representation involving modified Lommel functions. The calculations are made for incident electron energies between 3 and 1000 eV, and for two different sets of $3{}_{}{}^3{}_{}{}^{}S$ wave functions. The results of the differential and the total excitation cross sections are compared with all other available theoretical calculations.

Projectile $K$ x-ray production cross sections have been measured for 15-60-MeV ${\mathrm{Si}}^{2+-11+}$ ions incident on a thin He gas target. The data are well reproduced by the plane-wave Born approximation theories of $K$- shell ionization in addition to $1s-2p$ excitation when charge-state dependent fluorescence yields ${\omega }^{\mathrm{}(q+1\mathrm{})\mathrm{}}$ are used as fitting parameters. After normalizing the mean fluorescence yield at the lowest charge state to the results obtained for neutral Si atoms, the ${\mathrm{Si}}^{\mathrm{q}+}$ fluorescence yields vary from 0.044 to 0.528 (±20%) for $2<q<\mathrm{}11\mathrm{}$.

The elastic scattering of electrons with incident energies from 20 to 500 eV from the metastable $2s$ state of atomic hydrogen is calculated by using the Born and Glauber approximations (including the exchange effect). The results for the angular distributions are compared with some other theoretical calculations. It is found that the Born and Glauber integrated elastic-scattering cross section is well represented by ${\sigma }_{\mathrm{elastic}}^{\mathrm{B},\mathrm{G}}(2s\to 2s; K_i)=\left(\frac{4162}{105}\right)\left(\frac{\Pi a_0^2}{K_i^2}\right)$ for $E_i\ge 20$ eV.

Cross sections for electron capture by ${\mathrm{N}}^{+q}$, ${\mathrm{O}}^{+q}\left(1\mathrm{}\le q\le 5\right)$, and ${\mathrm{C}}^{+q}\left(1\mathrm{}\le q\le 4\right)$ incident on atomic and molecular hydrogen have been measured in the velocity range (0.3-5.2) × ${10}^8$ cm/s. The capture cross sections for the higher incident charge states are large, in many cases exceeding 1 × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$. For relative velocities above the Bohr velocity, all the measured cross sections were found to decrease monotonically with increasing velocity and to scale in magnitude roughly as $q^2$. Furthermore, for these higher velocities the cross sections for electron capture from ${\mathrm{H}}_2$ are systematically larger than the corresponding cross sections for electron capture from H. For relative velocities below the Bohr velocity, no simple behavior of the measured cross sections was observed. The behavior of the cross sections at low velocities is discussed qualitatively using the Landau-Zener formalism. For higher velocities reasonable agreement was found with the classical trajectory Monte Carlo calculations of Olson and Salop.

A model is developed to describe collisional quenching in the presence of a radiation field within a close-coupled formalism. In this model the collision dynamics are treated in a simplified manner, ignoring Coriolis and angular-potential coupling, thus reducing the computational complexity of the problem. The model hence focuses on the radial coupling of the collision system to the radiation field. The process investigated with this model is the quenching of fluorine by xenon in the 248-nm radiation field of a KrF laser. The mechanism for the radiative contribution to the quenching cross section is absorption of a photon by XeF followed by stimulated emission of a photon to the XeF ground state, the intermediate state being an excimer state of the XeF molecule. Thus, there is no net loss of photons from the radiation field and (in the language of perturbation theory) the process is of second order. The quenching cross section is calculated for collision energies in the range 0.05 to 0.25 eV and for field intensities of 0, 10, 100, and 1000 GW/${\mathrm{cm}}^2$. Results indicate that field intensity of 10-100 GW/${\mathrm{cm}}^2$ should have an experimentally observable effect on the quenching of fluorine by xenon at thermal collision energies.

We have measured the relative optical-excitation functions and polarizations of the K, Rb, and Cs resonance lines, using crossed electron and atom beams, for electron energies from threshold to 1500 eV. The electron energy resolution was ∼0.25 eV for energies below 13 eV, and the atom beam was optically thin. The atomic resonance-level ($n^{2}P$) excitation functions have been normalized to the Born theory in the high-energy limit. Comparisons are made with other measurements and calculations. The polarizations and total cross sections for H, Li, Na, K, Rb, and Cs are also compared with each other in reduced units to investigate systematic behavior.

We present an experiment studying the nonadiabatic passage of the $F=1\mathrm{}$ hyperfine component of the $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ metastable state of atomic hydrogen through a reversing solenoidal magnetic field. The nonadiabatic region is compared to the model field of Hight, Robiscoe, and Thorson. The measured transition amplitudes are fitted by the calculated amplitudes and the results are discussed.

Based on the impulse approximation, the radiative charge-exchange process in high-energy ion-atom collisions is studied with an application to the collisions between protons and hydrogen atoms, as well as collisions between various uranium ions (${\mathrm{U}}^{+2\mathrm{}}$, ${\mathrm{U}}^{+36\mathrm{}}$, ${\mathrm{U}}^{+92\mathrm{}}$) and various target atoms (N, Ne, Ar, Kr). The dependence on the incident-ion charge state and the target atom is discussed.

Rotational and rotational-vibrational ($v=0\mathrm{}\to 1$) excitation in ${\mathrm{N}}_2$ have been studied with a crossed-beam electron-impact apparatus. In the energy range 1-4 eV, the elastic and vibrational energy-loss peaks show large rotational broadening compared with the apparatus profile (full width at half-maximum, 18 meV). The branching ratios for rotational transitions with $\Delta j=0, \pm 2, \pm 4$ are obtained with a line-shape analysis applied to the energy-loss profiles. The results for rotational-vibrational excitation at 2.27 eV and scattering angles 30-90° are in good agreement with the calculations using the resonant $d\pi$ waves and the rotational impulse approximation. The corresponding results for pure rotational excitation show that the branches with $\Delta j=\pm 2 \mathrm{and} \pm 4$ are predominantly excited via resonances, while the branch with $\Delta j=0\mathrm{}$ contains a large contribution from direct scattering. The absolute rotational cross sections for $\Delta j=\pm 4$ are measured; they exhibit a large magnitude (${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$) and peak and valley structures in the 1-4 eV range, reminiscent of well-known resonant vibrational excitation. The energy dependence and the absolute magnitude of the rotational cross sections for $\Delta j=\pm 4$ can be understood in terms of a "boomerang" calculation. A comparison of the experiment with the relevant theoretical calculations is made.

Lifetime spectra of slow positrons in helium gas at low temperatures and high densities have been calculated using a Monte Carlo technique. Spectra are calculated both with and without applied electric fields using a two-parameter model based on the picture of helium cluster or droplet formation around the positron. The model is remarkably successful in reproducing the observed peak in the low-temperature spectra, the changes in the peak with variation of temperature and electric field, and the behavior of the "equilibrium" decay rate under a variety of conditions. At 5.5°K, the optimal model parameters, independent of electric field, are found to be $E_R=0.005\mathrm{}$ eV for the threshold energy of droplet formation, and $Z_R=18.2\mathrm{}$ for the enhanced decay-rate parameter. The simple slowing-down approximation is relatively successful in explaining the high-temperature spectra and in predicting the position of the peak in the low-temperature spectra when no electric field or only very small fields are present. The approximation breaks down at low temperatures and high electric fields, and consideration of the average positron energy and the width of the energy distribution as functions of time shows why this breakdown occurs.

A nonperturbative approach to the problem of charge transfer in proton-hydrogen collisions is developed in which the wave function corresponding to the outgoing scattered wave in the incident channel is evaluated by solving the Schrödinger equation it satisfies. The present formulation has the advantage of bringing into the theory not only the effects that are due to the Coulomb distortions but also those due to the polarization of the target atom. Our calculation of the capture cross section ($1s\to 1s$), which has been done with neglect of the polarization effect, agrees well with experiment in the low-energy region between 8 and 100 keV. A new interesting feature of our theory is that the cross section for capture shows a maximum at an energy of 9 keV. For proton energies below this value the cross section starts decreasing, finally approaching zero. For higher energies it starts falling with increasing energy in the usual way.

Angular and energy correlations for electrons produced in the ionization of neon and xenon by electrons with energies between 400 eV and 2.5 keV have been measured using symmetric noncoplanar kinematics. The reaction yields information about the atomic orbitals and their correlations when analyzed with the distorted-wave off-shell impulse approximation. In the past, either plane waves or various eikonal approximations have been used for the distorted waves, and in the cases where the eikonal parameters are approximately related to elastic scattering, the spectroscopic sum rule has been approximately verified. In the present work, calculations have also been carried out using partial-wave-expanded optical-model wave functions which describe the elastic scattering in detail. The detailed calculation confirms the spectroscopic sum rule, and hence the validity of the structure determination in the case of neon. For xenon the full distorted-wave calculation gives a much improved fit to the shape of the cross section, but overestimates the effect of absorption, and hence underestimates the cross section for ejecting an electron from the valence $s$ state. The plane-wave and eikonal approximations considerably overestimate the magnitude of the valence $s$-orbital cross section relative to the probability of ejecting an outer $p$ electron. The latter two approximations improve as the energy is increased, but they are still inadequate for neon at 2.5 keV.

The coplanar symmetric ($e, 2e$) cross section has been studied in the intermediate-energy region for the valence states of the inert gases He, Ar, and Ne. Experimental measurements at 200, 400, 800, and 1200 eV for He, and at 400, 800, and 1200 eV for Ne and Ar, are compared with calculations based on the factorized half-off-shell distorted-wave impulse approximation. Calculations are carried out using partial-wave-expanded optical-model wave functions which describe elastic scattering for the distorted waves, the eikonal approximation, and the plane-wave approximation. The latter two significantly overestimate the cross sections at small angles and the valence $s$-orbital cross section relative to the valence $p$-orbital one. They also predict the small-angle peak in the $p$-orbital cross section to be at an angle significantly smaller than is observed. Of the two, the eikonal approximation provides the better description of the data. The full calculation, on the other hand, underestimates the cross sections at small angles and the cross section for the more tightly bound $s$-orbital relative to the small-angle $p$-orbital cross section. It also underestimates the ratio of the large- to small-angle peak heights in the $p$-orbital cross section. All three approximations improve as the energy is increased. The full calculation shows that the factorized distorted-wave impulse approximation cannot provide an adequate description of the reaction.

Doppler-free two-photon transitions between the $3s$, $J=2\mathrm{}$ metastable state and the subconfiguration $7d^{\prime }$ of neon are studied with a pulsed-dye-laser oscillator-amplifier system which was synchronized with a chopped rf discharge in neon vapor. The isotopic shifts for these transitions are measured, and based on these measurements we have made a systematic study of Ne-Ne and Ne-He collisional broadening and shift of these very narrow Doppler-free two-photon resonances.

This paper describes a new class of techniques, called time-delayed laser saturation spectroscopy, which combine frequency- and time-domain methods of laser spectroscopy to provide a way of studying a molecular system as it evolves from an initially prepared stationary state to a second, final state. The specific example analyzed here is three-level free induction decay, in which the time-dependent gain of a Doppler-broadened molecular transition is probed after the sudden termination of an intense field resonating with a coupled transition. The theoretical calculation is based on the coupled density-matrix equations of motion in the slowly-varying envelope approximation. The time-delayed line shapes, which may be studied in either transmission or side fluorescence, exhibit linewidth asymmetries, line-shape deformations, Ramsey-type fringes, power broadening and dephasing, and dynamic Stark splittings and oscillatory decays. The technique provides a unique way of distinguishing the influence of Raman-type processes from that of population saturation and a means to separately measure the associated decay rates. The relationship of the present work to other studies is also discussed.

The photodetachment cross section of ${\mathrm{F}}^{-}$ is calculated using the method of Stieltjes imaging. This technique constructs the photodetachment cross section from the finite number of transition energies and oscillator strengths obtained in a calculation employing discrete basis functions only. The cross sections are obtained at various levels of approximation which assess the importance of the coupling between channel components and of correlation effects. These effects are not found to play an important role in the determination of absorption cross sections by the Stieltjes-imaging method for the particular case under study. The calculated cross sections agree quite well with the measured cross sections.