The hyperfine structure of $6snd{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ Rydberg states of ${}_{}{}^{135,137}{}_{}{}^{}\mathrm{Ba}$ is reported for principal quantum numbers ranging between $n=10\mathrm{}$ and $n=50\mathrm{}$. From our data, singlet-triplet mixing coefficients have been deduced. A three-channel quantum-defect model has been used to analyze the resonance in singlet-triplet mixing of $6snd{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{} \mathrm{and} {}_{}{}^3{}_{}{}^{}D_2^{}{}_{}{}^{}$ Rydberg states in the vicinity of the $5d7d{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ perturber. For the determination of the scattering matrix, hyperfine-structure data were found to be essential. Good agreement has been achieved between calculated and experimental singlet-triplet mixing coefficients.

The previously proposed method to obtain classical limits of quantized fields using von Neumann - lattice coherent states as basis states for the projection form of the Schrödinger equation is modified in order to take into account the reaction of the radiation field to the charge in a compact manner. The modification is based on the work of Glauber on the time evolution of coherent states. To illustrate the method, a charged harmonic oscillator with and without initial external electromagnetic field is investigated.

How each state-to-state reactive transition determines nonundulatory "state-to-all-states" angular distribution has not yet been investigated. Here we present a complete exposure of state-to-state distorted-wave Born-approximation angular distributions in order to examine how the nonoscillatory and backward-peaked state-to-all-states reactive scattering angular distribution occurs.

The importance of the resonance contributions to inelastic scattering of electrons from atoms and ions has been appreciated for quite some time. We have used an approximate method to compute the resonance contributions to selected inelastic transitions in O VI and S IV and compare our results with other theoretical calculations. We find that our total resonance-enhanced collision strengths are in very good agreement with other calculations. We also can accurately compute the positions of individual resonances but can sometimes be in error by a factor of 2 on individual resonance widths.

Slowing-down and capture cross sections have been consistently calculated for ${\mu }^{-}$, ${\pi }^{-}$, $K^{-}$, and $\overline{p}$ in collisions with hydrogen and helium atoms and isotopic variants. Capture-energy distributions are determined using the differential-energy-loss cross sections in the laboratory frame. Capture is found to occur predominantly at energies near or below the ionization potential of the target. Ratios of capture on different species are given as a function of the mole fraction of each species present in mixtures. For ${\pi }^{-}$ in a He-H mixture the reduced capture ratio obtained is ∼0.73, slightly less than the experimental value of 0.92 for the ${\mathrm{H}\mathrm{e}-\mathrm{H}}_2$ mixture. In contrast with another recent theoretical calculation and in agreement with experimental analysis, it is found that atomic capture of pions in the helium-hydrogen mixture is only slightly nonlinear. It is pointed out that some prior theoretical treatments are in error because of inconsistent calculation of the slowing-down and capture processes and/or subsequent approximate treatment of the energy transport. Use of capture and transfer rates in muon kinetics, e.g., muon-catalyzed fusion, is discussed.

The Faddeev-Watson expansion (FWE) for the $T$ operator is applied to the study of thermal collisions between Rydberg atom and neutral atom. These collisions are considered as a three-body problem (the perturber, the Rydberg electron, and its parent core) and it is assumed, as already done in most theoretical works dealing with Rydberg-atom-atom collisions, that the core-perturber interaction can be neglected. Then the evaluation of the FWE first- and second-order terms is made tractable by using an appropriate separable potential for the Rydberg-electron-perturber interaction. The evaluation of the second-order term allows us to estimate the importance of taking into account explicitly the Rydberg-electron-core interaction in the expression of the (three-body) $T$ operator for the thermal collisions considered. Detailed calculations for the process $\mathrm{Rb}(n, l=0)+\mathrm{He}\to \mathrm{Rb}(n^{\prime },l^{\prime })+\mathrm{He}$ are presented and discussed. The FWE second-order term has been evaluated for the first time by taking the (two-body) $t$ operator associated with the Rydberg atom (valence electron plus parent core) as the Coulomb potential. The contribution of the FWE second-order term to the scattering amplitude decreases as $n$ increases and is found especially significant when both the momentum transfers involved in the collision are large and the values of $l$ and $l^{\prime }$ are small.

Emission cross sections for ten spectral lines transiting from Cd II low-lying excited states formed by single-electron impact on Cd atoms have been measured with a photon-counting technique. Polarizations of these lines have also been examined. By the use of these results and removing the influence of cascade transitions, direct-excitation cross sections for seven low-lying states ($5p{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},\frac{3}{2}}^{}{}_{}{}^{}$, $5s^2{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2},\frac{5}{2}}^{}{}_{}{}^{}$, $6s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$, $5d{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2},\frac{5}{2}}^{}{}_{}{}^{}$) have been determined as a function of electron energy. They are found to be of the order of ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ for the $5p$ and $5s^2$ states and of ${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ for the $6s$ and $5d$ states at their maxima.

Sodium vapor, in the density range ${10}^{13}$ to 5 × ${10}^{14}$ ${\mathrm{cm}}^{-3\mathrm{}}$, was excited by a cw dye laser, tuned 20-150 GHz from either the $D_1$ or $D_2$ resonance line. We observed a three-peak scattered spectrum, consisting of the Rayleigh component at the laser frequency, and the two fluorescence components (direct and sensitized) at the atomic resonance-line frequencies. Corrections to the Rayleigh signals for anisotropy and polarization effects, and to the fluorescence signals for radiation trapping, were made in order to obtain the ratio of the sum of the total intensities of the two fluorescence components to that of the Rayleigh component. This ratio combined with a measurement of the line-wing absorption coefficient yields the sodium density and the $D$-line self-broadening rate coefficients [$k_{\mathrm{br}}=4.67\mathrm{}\times {10}^{-7\mathrm{}}$ ${\mathrm{cm}}^3$${\mathrm{s}}^{-1\mathrm{}}$ (±15%) for the $D_2$ line and $k_{\mathrm{br}}=3.07\mathrm{}\times {10}^{-7\mathrm{}}$ ${\mathrm{cm}}^3$${\mathrm{s}}^{-1\mathrm{}}$ (±15%) for the $D_1$ line]. Asymmetry in the self-broadened line wings due to fine-structure recoupling was observed. The measured intensity ratio of the $D$ lines, combined with pulsed measurements of the effective radiative decay rates in the presence of radiation trapping, yields the fine-structure collisional-mixing cross section [$\sigma (3\mathrm{}{P}_{\frac{3}{2}}\to 3P_{\frac{1}{2}})=172\mathrm{}$${\mathrm{\AA }}^2$(±18%)] at $T\cong 300°$ C. Our results are compared to other experiments and to theory.

A resonance scattering theory for many-electron resonances is applied to the analysis of the ${\mathrm{He}}^{-} 1s2s2p{}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$ resonance. We have found that multiconfigurational Hartree-Fock theory is applicable even in such cases and predicts the Feshbach nature of the state. Furthermore, by including electron correlation and off-energy-shell pseudostates, we demonstrate the strong energy dependence of the width of this resonance. We suggest that this is the reason for the discrepancy of recent theoretical results with experimental ones. The theoretically predicted cross section is asymmetric, whereas the recent experimental one is symmetric but non-Lorentzian. Defining the position and width of the resonance at maximum and half-maximum values of the cross section correspondingly, we find $E_R=20.26\mathrm{}$ eV and ${\Gamma }_R=600\mathrm{}$ meV, compared to the experimental values of $E_R=20.27\mathrm{}$ eV and ${\Gamma }_R=780\mathrm{}$ meV.

The classical-trajectory Monte Carlo method has been used to calculate ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ electron-capture and ionization differential cross sections in the range 25-200 keV. The results indicate the importance of including excited product states to describe the small-angle electron-capture scattering. Angular scattering of the electron removed by the ionization process has been studied as a function of ejected-electron velocity $v_e$. The classical calculations are in reasonable agreement with coupled-channel results of Shakeshaft [Phys. Rev. A 18, 1930 (1978)] as to the "electron capture to the continuum" (ECC) component of the ionization process where this term is defined as the ejected electron being more closely centered to the projectile than the target nucleus after the collision. The ECC cross section ${\sigma }_{\mathrm{ECC}}$ was studied as a function of collision energy (50-500 keV/amu) and projectile charge state ($q=1-10\mathrm{}$). At high energies, ${\sigma }_{\mathrm{ECC}}$ scales as $\frac{q^{2.3}}{E^{2.5}}$. The maximum value for ${\sigma }_{\mathrm{ECC}}$ was determined to be an energy $E_{max}\cong \left(56\mathrm{} \frac{\mathrm{keV}}{\mathrm{amu}}\right)q^{0.4}$. Restricting the ECC component to small electron-scattering angles, ${\theta }_{\mathrm{lab}}\le 5°$, and electron-ejection velocities $v_e=v_p(1.0\mathrm{}\pm 0.1)$, where $v_p$ is the projectile velocity, indicates this process is a minor component of the total ionization cross section at intermediate energies.

The soft-photon approximation for bremsstrahlung derived some time ago by Low and extended by Feshbach and Yennie to allow for resonances is further generalized, in the framework of nonrelativistic scattering theory, to apply to the case where the scattering potential has a long-range Coulomb tail. The derivation is based on an asymptotic evaluation of the matrix element in configuration space in which electric-dipole, magnetic-dipole, and electric-quadrupole components of the particle-field interaction are accounted for. The $M1\mathrm{}$ and $E2\mathrm{}$ contributions give rise to retardation corrections, of order $\frac{v}{c}$, to the leading $E1\mathrm{}$ term. The Coulomb tail has the effect of introducing certain factors into the approximate bremsstrahlung amplitude which depend logarithmically on the photon frequency. The result obtained here has an immediate application to the problem of Coulomb scattering in a low-frequency laser field and provides a generalization of earlier work based on the electric-dipole approximation.

Some lower-lying doubly excited resonances in electron-hydrogen scattering converging on the $N=3,4,\mathrm{and} 5$ hydrogenic thresholds, as well as some lower-lying $P$-wave resonances associated with the $N=6\mathrm{}$ threshold, have been calculated by a method of complex-coordinate rotation. Hylleraas-type wave functions are used for $L=0\mathrm{}$ and $L=1\mathrm{}$ resonances, and products of Slater orbitals for states with $L\ge 2$. Results are compared with recent calculations. Furthermore, in addition to the usual resonances of parities ${\mathrm{}(-1\mathrm{})\mathrm{}}^L$, resonant states with parities ${\mathrm{}(-1\mathrm{})\mathrm{}}^{L+1\mathrm{}}$ are also calculated. Results are used to construct the "supermultiplet" structures of the doubly excited resonances of two-electron atoms.

A nonadjustable-model potential is proposed for electron scattering that includes both electron exchange and correlation effects in a hybridization of local electron-gas theory and the long-range polarization. The model potential energy function consists of the sum of the energy-dependent electron-gas exchange potential (Hara version) and the energy-independent electron-gas correlation potential smoothly joined onto the long-range polarization interaction. Illustrative calculations of elastic scattering phase shifts and cross sections are described for the rare-gas atoms, where reasonable agreement with accurate calculations suggests usefulness of the model for more complex systems.

The positronium-formation cross section in positron-hydrogen scattering has been calculated by using the distorted-wave approximation in which the total incident wave function is obtained by the method of polarized orbitals. The two variants of the polarized-orbital method, one due to Temkin and Lamkin and the other due to Callaway , have been employed to estimate their relative importance. The present results have been compared with those obtained by elaborate variational methods. The results obtained by using the potential of Temkin and Lamkin have been found to be encouraging.

Forty-eight transition probabilities for lines belonging to the $4p$-$\mathrm{ns}\mathrm{}(n=6,7,8,9\mathrm{})\mathrm{}$ transition arrays of ArI have been determined by means of emission-line-intensity measurements. The single-photon delayed-coincidence method has been used to obtain the lifetime values of the $\mathrm{ns}{\left(\frac{3}{2}\right)}_2\mathrm{}(n=6,7,8,9\mathrm{})\mathrm{}$ levels. With the taking into account of these lifetimes together with theoretical calculation in $\mathrm{jK}$ coupling for the lines beyond the experimental range, the relative transition probabilities were put on an absolute scale. The lifetime values obtained in the present work are original in the literature excepting the $7s{\left(\frac{3}{2}\right)}_2$-level lifetime. Four transition probabilities are also the first values found in the literature.

The dynamic Stark shift of an inhomogeneously broadened spectral transition has been studied. Our measurements show a shift in the observed ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ ground-state hyperfine transition which has a nonlinear dependence on light intensity when the conditions for inhomogeneous broadening are met. The nonlinearity is the result of light-intensity gradients in the signal volume, which produce an inhomogeneously broadened asymmetric microwave transition. We show that our measurements are in full agreement with the second-order perturbation-theory treatment of light-induced energy-level shifts, when the effects of inhomogeneities are properly taken into consideration. The effects of inhomogeneous broadening must be carefully considered when extracting oscillator strengths from light-shift data, or when performing high-precision laser spectroscopy.

Using a three-step laser excitation approach, we have studied the autoionizing ${\left(6\mathrm{}{p}_{j}nd\right)}_{J=3\mathrm{}}$ states of neutral barium. The $6p_{\frac{3}{2}}\mathrm{nd}$ series is essentially unperturbed and exhibits a constant quantum defect and autoionization widths which scale as ${\nu }^{-3\mathrm{}}$, where $\nu$ is the effective quantum number. The $6p_{\frac{1}{2}}\mathrm{nd}$ states are narrower than the $6p_{\frac{3}{2}}\mathrm{nd}$ states and are perturbed by their interaction with the $6p_{\frac{3}{2}}\mathrm{nd}$ states. The perturbation leads to variations in the quantum defects of the $6p_{\frac{1}{2}}\mathrm{nd}$ states and departures from the ${\nu }^{-3\mathrm{}}$ scaling of the widths. The interaction is most apparent in the excitation of the $6p_{\frac{3}{2}}10d$ state which is degenerate with the $6p_{\frac{1}{2}}\mathrm{nd}$ states for $n\sim 20$. The observed excitation spectrum clearly shows the influence of the degenerate $6p_{\frac{1}{2}}\mathrm{nd}$ states and is shown to represent the spectral density of the $6p_{\frac{3}{2}}10d$ state. This spectrum as well as all the above-mentioned observations may be connected by a quantum-defect treatment.

Analytic expressions are obtained which well represent the nonrelativistic single-electron ($nl,n^{\prime }{l}^{\prime }$) dipole transition rates in screened central potentials, not only when both states are inner shell in character, as had been previously achieved, but also when only one of the states has an inner-shell character. The key idea is to expand one of the screened bound-state wave functions (outer shell) in terms of an unbound negative-energy Coulomb wave function with the same energy shift as the screening shift of the inner-shell bound state. The expressions obtained are an analytic continuation (in photon energy) of corresponding bound-free matrix elements.

Many-body perturbation theory has been used to calculate the photoionization cross section of neutral calcium from threshold at 6.11 to 70 eV. Near-threshold resonance structure due to double electron excitation has been included and is compared with the results of several experiments. At higher energy, resonance structure due to $3p$ excitations to bound states with $l=0\mathrm{} \mathrm{and} 2$ has also been calculated and compared with a measurement by Mans-field and Newsom. The $3p^{5}4s^{2}3d{}_{}{}^1{}_{}{}^{}P$ resonance is found to be particularly prominent, in agreement with experiment. Our results are also compared with a recent calculation using the relativistic random-phase approximation.

Dispersion-theory techniques, previously used to calculate the two-photon exchange potential $V_{2\gamma }\mathrm{}\left(R\right)\mathrm{}$ between two neutral systems, are used to study $V_{2\gamma }\mathrm{}\left(R\right)\mathrm{}$ acting between a neutral system $A$ and a charged system $B$. For the case when $A$ is an atom and $B$ an electron, general results are given for all corrections of order $\frac{{\lambda }_e}{R}$ or of order ${\left(\frac{a_0}{R}\right)}^2$ relative to the leading $R^{-4\mathrm{}}$ term.