$Z_2$ (target atomic number) dependence of the electronic stopping powers for MeV helium-ion beams is investigated where the charge-state fractions before emerging from matter play a significant role. The electronic stopping powers for a single helium ion in various charge states and a proton ($S_{{\mathrm{He}}^{q+}}$, $q=1\mathrm{} \mathrm{and} 2$, $S_{{\mathrm{H}}^{+}}$) are calculated on the basis of Lindhard-Winther theory with the local-electron-density model. The ratio $\frac{S_{{\mathrm{He}}^{+}}}{S_{{\mathrm{H}}^{+}}}$ shows the $Z_2$ oscillation as well as $S_{{\mathrm{He}}^{+}}$ and $S_{{\mathrm{H}}^{+}}$. The relation between the effective charge $q_{\mathrm{eff}}$ and the mean charge $\overline{q}$ is elucidated in some cases of the incident energy where $q_{\mathrm{eff}}>\overline{q}$ is valid regardless of $Z_2$ and the $q_{\mathrm{eff}}$ values show the oscillatory $Z_2$ dependence with a small amplitude in contrast with a strong $Z_2$ oscillation of $\overline{q}$.

A new theoretical approach to calculate electron-capture cross sections is developed to deal with asymmetric collisions. The method consists of introducing the correct Coulomb asymptotic conditions to the peaking impulse approximation. The approach is elaborated to be meaningful, not only at high projectile energies, but also in the intermediate region (i.e., when the ion velocity, in atomic units, is much larger than the smaller Coulomb charge, but about the same order of the larger charge). An integral expression of the $T$-matrix element is obtained after performing a peaking approximation. This element has a closed form for any transition. $K-K$ charge exchange total and differential cross sections are calculated and compared with experimental results. The approach seems to be more reliable than the continuum distorted wave and peaking impulse approximation.

In the interaction of $N$ spin-$\frac{1}{2}$ particles, the possible types of dependence of the cross section on polarization and momentum three-vectors and/or on two-spinor components may be defined with the use of angular-momentum-coupling trees with $j=1\mathrm{}$ and/or $j=\frac{1}{2}$ external labels, respectively. We show, using integrity-basis theory, that all such trees with spin-$\frac{1}{2}$ labels only may be expressed as sums of products of Kronecker delta functions and $2jm$ symbols in the spinor component labels; this is related to Kramers's method of spinor invariants. The integrity-basis method also identifies the nature of inter-relationships between the spinor invariants. Explicit reductions of angular momentum trees of degree $2N$ in spin-$\frac{1}{2}$ labels are given for $N\le 4$. As simple illustrations of the application of such trees, we discuss the Dirac and Anderson spin Hamiltonians of nonrelativistic exchange theory in this context and also develop a concise description of the polarization dependence of Mφller scattering in QED.

We discuss a multichannel formulation of the Schwinger and a related variational principle (of one order higher than the Schwinger principle) in a form suitable for application to the scattering of low-energy electrons by both linear and nonlinear molecules. The theory includes the effects of polarization straightforwardly and should be particularly useful for obtaining electronically inelastic cross sections. An expansion of the trial scattering wave function in a discrete basis is possible. With certain choices for these basis functions this feature can be particularly advantageous.

As a first application of the Schwinger multichannel theory, we have calculated integral and differential cross sections for electron-impact excitation of the transition $X {}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\to b {}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ in ${\mathrm{H}}_2$ for scattering energies from 13 to 30 eV at the two-state level. We find good agreement between our integral cross sections and the results obtained previously in a two-state close-coupling study. Our method does not rely on single-center expansions to calculate the body-frame scattering amplitude and is designed to be applicable to molecules of arbitrary geometry.

Extensive configuration-interaction calculations for the transitions $\left(1s{2p}^{2}3p\right){}_{}{}^5{}_{}{}^{}S_{}^o{}_{}{}^{}\to \left(1s2s2p3p\right){}_{}{}^5{}_{}{}^{}P$ and $\left(1s{2p}^{2}4p\right){}_{}{}^5{}_{}{}^{}S_{}^o{}_{}{}^{}\to \left(1s2s2p4p\right){}_{}{}^5{}_{}{}^{}P$ of neutral beryllium yield $\lambda =2273.1\mathrm{}\pm 0.5 \mathrm{and} 2305.9\pm 0.07$ Å, respectively. These results agree, to within experimental error, with the wavelengths of two lines observed in the beam-foil spectra of Be. Transition probabilities are also reported.

We present a technique that yields in analytic fashion the quasienergy spectrum of bounded quantum systems in the presence of time-periodic perturbations. It also allows for the calculation of statistical averages using simple algebraic manipulations and provides tractable solutions even for systems with a large number of levels. We also report on numerical calculations for systems with few number of levels in and out of resonance, and which show the recurrences predicted by the Hogg-Huberman theorem [Phys. Rev. Lett. 48, 711 (1982); Phys. Rev. A 28, 22 (1983)].

Light-absorption and -emission spectroscopy were used in the studies of the time dependencies of the Cu II spectral emission, Ne I spectral emission, and ${\mathrm{Ne}}^m\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)$ and $\mathrm{Cu}\left(4s {}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)$ densities in the stationary afterglow of a sputtered Ne-Cu hollow cathode discharge. Transitions from 16 Cu II energy levels were monitored in the afterglow. The three Cu II levels between 21.16 and 21.41 eV are produced, either directly or by cascading, by charge exchange between ${\mathrm{Ne}}^{+}$ and Cu. The one Cu II level at 19.58 eV is predominantly produced by charge exchange between ${\mathrm{Ne}}_2^{+}$ and Cu. The remaining Cu II levels are produced by both reactions. No evidence was found for the production of Cu II excited states by the Penning ionization of Cu by ${\mathrm{Ne}}^m\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)$. A value of 220 ±8 ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$ Torr was measured for the diffusion coefficient of $\mathrm{Cu}\left(4s {}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)$ in neon.

We present both experimental and theoretical studies of resonantly enhanced multiphoton ionization of cesium atoms. Photoelectron angular distributions for two-photon ionization via the one-photon-allowed $7p{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},\frac{3}{2}}^{}{}_{}{}^{}$ and $8p{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},\frac{3}{2}}^{}{}_{}{}^{}$ intermediate states and three-photon ionization via the two-photon-allowed $8d{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2},\frac{3}{2}}^{}{}_{}{}^{}$ resonant intermediate states are reported. The photoelectrons are energy analyzed with a spherical-sector electrostatic energy analyzer with an energy resolution of ~ 0.1 eV and angular resolution of ~ ±2°. A straightforward calculation based upon a finestructure scheme gives excellent agreement with the measured angular distributions for the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ states. The laser pulse duration is comparable to the hyperfine precession period which allows the hyperfine coupling to partially destroy the anisotropy initially produced in the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ resonant intermediate states. Quantitative calculations including hyperfine coupling take this into account and provide an expression which gives a reasonable fit to the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ data.

Experimental and theoretical results are presented for resonantly enhanced three-photon ionization of cesium atoms in the wavelength range from 830 to 950 nm. The accidental near resonance of the $6p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2},\frac{1}{2}}^{}{}_{}{}^{}$ levels at the one-photon energy and the near resonance at the two-photon level with the $6d{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2},\frac{5}{2}}^{}{}_{}{}^{}$ states gives rise to large ionization signals and interesting anomalies in the relative intensities of the fine-structure levels. "Hybrid resonances" are observed which involve the production of $6p {}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ atoms from molecular cesium. One hybrid resonance involves ionization of the $6p {}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state via an electric quadrupole transition ($6p {}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}-7p {}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$). Both experimental and theoretical photoelectron angular distributions are compared for all of the observed resonances except for the $6p {}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state where the signals were too weak for such a measurement. Agreement between experiment and theory is fair for three-photon ionization via the $6p{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state. Comparison of experiment and theory for the case of the $6d{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2},\frac{5}{2}}^{}{}_{}{}^{}$ states indicates that hyperfine coupling during the laser-pulse duration may be important. The angular distributions for the hybrid resonances show the general behavior predicted by theory but the features appear broadened.

Photoelectron branching ratios and angular distributions have been measured for the six outermost levels of ${\mathrm{BF}}_3$ in the range $17\le h\nu \le 28$ eV with the use of synchrotron radiation. Comparisons are made with a recent multiple-scattering model calculation which indicates that a shape resonance in the $e^{\prime }$ electronic continuum should appear in five of the six channels studied. Good agreement between experiment and theory is found in a majority of the comparisons; however, experimental evidence for the expected $e^{\prime }$ shape resonance is clear in some cases but absent in others. The results are discussed in the context of other cases in which shape resonances, well known from inner-shell spectra, are obscured in valence-shell properties. Experiments which would help clarify the role of the $e^{\prime }$ shape resonance in the photoionization dynamics of ${\mathrm{BF}}_3$ are suggested.

Several authors have recently discussed and observed optical-pumping dips in inhomogeneously broadened spectral lines. We have observed a qualitatively similar, but fundamentally distinct phenomenon: optical-pumping dips in a homogeneously broaded $D_1$ line of ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$. To our knowledge this represents the first observation of homogeneous-optical-pumping dips.

The photoionization of the excited Na and K $3d$ states have been calculated with use of various numerical and analytic Hartree-Fock wave functions. Particular attention was paid to the zeros in the $3d\to \epsilon p$ dipole matrix elements and their sensitivity to slight changes in the initial-state wave functions. It was found that only the numerical wave functions were reliable. In addition, it was found that these zeros had virtually no effect on the total subshell cross sections; however, they had a strong influence on the photoelectron angular distributions.

The influence of ac Stark shifts on the three-photon ionization of cesium in a moderate-intensity laser beam is investigated. The ionization process involves a two-photon resonance with the $8d$ fine-structure levels. The work consists of two related parts. In the first part, atomic parameters, such as the two-photon Rabi rate and the ac Stark shift, are calculated in the nonrelativistic Hartree-Fock approximation. In the second part, the atomic parameters thus obtained are used as coefficients in a system of coupled differential equations representing the time evolution of the density matrix. Ionization line shapes are generated for a transform-limited pulsed laser of moderate intensity with a single-mode transverse structure. As the time history of the intensity profile is varied from square to smooth, the ionization line shape becomes asymmetric due to the time dependence of the ac Stark shift. The effects of varying the spatial intensity distribution of the laser light to include transverse centering and longitudinal focusing are also studied.

The fine-structure intervals of selected $\mathrm{np} \mathrm{}(n=18-83\mathrm{})\mathrm{}$ and $\mathrm{nf} \mathrm{}(n=14-28\mathrm{})\mathrm{}$ Rydberg states in neutral Cs have been measured by Doppler-free resonantly enhanced two-photon laser spectroscopy with a thermionic diode detector. One cw dye laser was tuned near resonance with a $6s-5d$ electric quadrupole transition while a second was scanned through the relevant $5d-np$, $\mathrm{nf}$ transitions. This is the first Doppler-free study of these series by strictly optical methods. The experimental fine-structure intervals are in good agreement with splitting formulas derived by other authors from fine-structure measurements of lower-lying $\mathrm{np}$ and $\mathrm{nf}$ levels. Our results and the best previous data have been fitted with several expressions that have been used or suggested for the representation of fine-structure data. A recently proposed expansion formula including inverse even powers of the effective quantum number is found to have little practical significance for the description of experimental intervals.

The technique of harmonic generation with circularly polarized light is applied to study the Landé $g$ factor of the two-quantum excited states of ${\mathrm{I}}_2$ molecules. Systematic and abrupt changes in the $g$ factor are observed. The large change in the $g$ factor is interpreted in terms of perturbation by a level that has no bound state. Enhancement of harmonic generation in a high magnetic field with linearly polarized light is also observed in some resonances that have a small $g$ factor in the two-quantum state. The enhancement is interpreted in terms of constructive interference of resonances originating from the ground state and the first thermally excited vibrational state.

The total photoionization cross section of the $3p$ subshell of atomic chlorine is presented with use of the recently developed open-shell transition-matrix method of Starace and Shahabi. The role of electron correlations is studied by comparison with Hartree-Fock and close-coupling calculations. In contrast to $3p$-subshell photoionization of argon, it is shown that, in chlorine, final-state interchannel interactions are very strong while virtual pair excitations have a weak effect on the shape of the cross section, serving mainly to reduce the discrepancy between length and velocity results. Our results are compared in detail with other theoretical results above the ${}_{}{}^1{}_{}{}^{}S$ threshold as well as with experimental relative-intensity measurements at 584 Å. While our results are lower than the others at the ${}_{}{}^1{}_{}{}^{}S$ threshold ($\hslash \omega =0.6\mathrm{}$ a.u.), at photon energies $\hslash \omega >1\mathrm{}$ a.u., our geometric mean cross section is in essentially exact agreement with unrelaxed ionic core results of Brown, Carter, and Kelly and of Fielder and Armstrong.

In strong ($\frac{1}{3n^5}<?<\frac{1}{16n^4}$) electric fields, Ba autoionizing states converging to the ${\mathrm{Ba}}^{+}$ $6p_{\frac{1}{2}}$ limit have autoionization rates which do not exhibit the familiar $n^{-3\mathrm{}}$ scaling but rather have an $n^{-4\mathrm{}}$ scaling which is independent of the field. This is consistent with the interpretation that most of the autoionization rates come from a few low-angular-momentum zero-field states. In addition, the observed excitation spectra imply that the spectral distribution of the stabilizing radiation in dielectronic recombination is narrower in the presence of an electric field than without it. This implies that the notions used to describe dielectronic recombination in zero field are valid in the presence of a field.

We present a new interaction geometry for optical Ramsey fringes comprised of four traveling waves instead of the three usual standing waves. First, we demonstrate experimentally that the new method leads to an improved contrast, using the optothermal detection of the vibrational excitation of ${\mathrm{SF}}_6$ in a supersonic beam illuminated by a waveguide ${\mathrm{CO}}_2$ laser. Second, we give a simple theoretical description of the method, using evolution matrices of spinors and pseudospin-vector representations of these spinors. Finally, we introduce strong-field density-matrix diagrams to discuss the differences between the various interaction geometries as well as between the Ramsey fringes and the usual stimulated photon echoes.

A two-laser theory is formulated for the photoionization of Li atoms. The first laser is tuned above the ionization threshold of $\mathrm{Li}\mathrm{}\left(2s\right)\mathrm{}$. The second laser probes the ionized target. Stimulated recombination into $\mathrm{Li}\mathrm{}\left(\mathrm{ns}\right)\mathrm{}$ occurs near the Raman-type resonance point ${\epsilon }_{\mathrm{ns}}-{\epsilon }_{2s}-{\epsilon }_1+{\epsilon }_2=0\mathrm{}$ (where $n>\mathrm{}2\mathrm{}$ and ${\epsilon }_q$ is a photon energy). Near the resonance point the ionization probability is characterized by a line profile which resembles that for an autoionizing resonance.