The cross section of symmetric charge transfer between Gd and ${\mathrm{Gd}}^{+}$ as a function of impact energy (velocity) in the range of 10–1000 eV (3.5×${10}^5$–3.5×${10}^6$ cm/sec) was successfully obtained by a crossed-beam technique, which featured a pulsed ion beam produced by laser photoionization in an atomic gas beam. The absolute values and the impact-energy dependence of the cross sections were obtained from the attenuation rate of the primary ions in the atomic gas and the ratio of the detected charge transferred ions to the primary ions, respectively. The cross sections obtained are larger than those of other elements studied in the past, and the impact-velocity–cross-section curve could be fitted with that obtained from the superposition of the resonant and capture-type probabilities resulting in charge transfer, assuming that the capture-type cross section is inversely proportional to the impact velocity.

The relative photoionization cross sections for the production of the 2${\mathit{s}}^2$2${\mathit{p}}^4$${(}^3$P)3p${(}^4$P°) satellite state of neon has been measured from its threshold at 52.1–60.5 eV. The spectrum is dominated by resonance structure, which can be identified as autoionization of numerous doubly excited neutral states.

Partial and total cross sections of electron-capture processes in collision of ${\mathrm{N}}^{4+}$ ions with H atoms are calculated in the collision energy range from 1 eV/amu to 10 keV/amu. Semiclassical and quantum-mechanical molecular-orbital methods with electron translation factors are employed. Two-electron processes are also considered, but they are found to make small contributions at all collision energies. The dominant electron-capture channels are found to be the ${\mathrm{N}}^{3+}$(3p) state at energies above 300 eV/amu and the ${\mathrm{N}}^{3+}$(3d) state at energies lower than 300 eV/amu. Three experiments that observed only total cross sections have been reported for this system. The agreement of the present calculation with these measurements is excellent at all energies. In particular, an oscillation observed in the experiment of Huq, Havener, and Phaneuf [Phys. Rev. A 40, 1811 (1989)] is reproduced by our calculation in the energy range 10–300 eV, and the origin of the oscillation is discussed.

Dielectronic recombination (DR) via 1s→2p excitation has been measured for ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$ ions using the electron-cooling device in the storage ring at the Institute for Nuclear Study at the University of Tokyo. Resonant maxima from the DR were observed as well as the maximum due to the radiative recombination. The spectral shape and the magnitude of the measured rate coefficients are consistent with available calculations within experimental errors.

We discuss measurements of the angular distributions of photoelectrons produced by photoionizing ground-state rubidium with light of wavelengths between 266 and 285.3 nm. The spin-oribit perturbation in this heavy element affects the ratio of the oscillator strength for excitation to the ${\mathit{P}}_{3/2}$ state to that for excitation to the ${\mathit{P}}_{1/2}$ state. For our measurements the electron energy approaches that of the Cooper minimum in the photoionization spectrum, the effect of which is to reduce the asymmetry parameter from the nonrelativistic value of 2. At the shortest wavelength for which we have measured these distributions, the cross section for ionization to the ε${\mathit{P}}_{1/2}$ state has nearly vanished.

The angular and velocity distributions of the ${\mathrm{HD}}^{+}$ and ${\mathrm{D}}_2^{+}$ fragments resulting from collision-induced dissociation of the ${\mathrm{HD}}_2^{+}$ molecular ion incident on He have been measured in the energy range 1–5 keV. These distributions were used to determine the binding energy of ${\mathrm{HD}}_2^{+}$, some of the main transitions involved in the dissociation process, and the total cross sections for the production of both fragments.

A general formulation of the sojourn-time operator approach is presented, valid for arbitrary scattering systems and free of restrictions to one-dimensional systems present in the previous work of the authors. We show how first-order perturbation theory can be consistently formulated in terms of appropriate sojourn-time operators. Both time-dependent and time-independent perturbations, including coupling between translation and internal degrees of freedom, are considered. The mean values of these Hermitian sojourn-time operators give the mean sojourn time (dwell time) of the particle in spatial regions or, more generally, in certain subspaces of the state space of the system defined by sets of commuting observables. The perturbed S operator and also the effect of the perturbation on the change of observables due to the scattering are, to a first-order approximation, fully expressible in terms of these operators. We also show that this approach provides a unified treatment of the various idealized one-dimensional systems, which have frequently been employed in the debate on tunneling and interaction times. In particular, we provide some insight into the role of complex times, which appear as combinations of matrix elements of the sojourn-time operators.

We investigate the validity of the surface electric-field interaction model in beam-foil experiments where the polarization of the emitted light is measured. After summarizing the theory for expanding the density operator into state multipoles and linking these to the Stokes parameters of the light, we show also how to use symmetries to reduce the size of the calculations. A very simple model is chosen for the electric field: it is perpendicular to the foil and constant over a finite distance, then zero. This model is used to find the initial density matrix for the n=3 singlet states of He i and the electric-field parameters from tilted-foil experiments. Reasonable results are obtained given the unrealistic electric-field model used.

The coherence length of a neutron wave packet depends on the spectral width of the distribution of wave vectors that make up the packet. The coherent overlap of the wave packets traversing the two beam paths in a perfect-silicon-crystal neutron interferometer (NI) is altered by placing a material with a neutron-nuclear optical potential in one of the beam paths in the NI. If the optical potential is positive, it causes a delay of the wave packet and a loss of fringe visibility. By use of an analyzer crystal, we narrow the spectral distribution after the mixing and interference has occurred in the last crystal slab of the NI. This increases the coherence length and restores some of the fringe visibility.

A numerical method for calculating Auger rates is proposed. The continuum wave of the ejected Auger electron is computed by numerical propagation (close-coupling method) and thus accounts for the nonspherical interaction with the molecule. The method is tested by computing the Auger spectrum of hydrogen fluoride. Here initial cationic and final dicationic states are treated on the self-consistent-field level.

A measurement of the 1s2p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$→1${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ resonance transition in heliumlike germanium (${\mathrm{Ge}}^{30+}$) has been made on the Lawrence Livermore National Laboratory electron-beam ion trap to a precision of 21 ppm. The result is compared with theoretical values and confirms a trend previously seen in the differences between experiment and theory for this transition as a function of Z. Results for the 1s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$→1${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ and 1s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$→1${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ intercombination lines and for the 1s2s ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$→1${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ forbidden line are also presented and show similar differences with theoretical predictions.

The size and location of nonlinear-resonance zones, in the one-dimensional model microwave-driven hydrogen, are obtained numerically for the microwave field strengths and frequency used in experiments. Classical simulations show a high correlation between the widths of fractional resonances at the chaos border and the width of regions of suppressed ionization observed in experiments. Numerical evidence is given for the existence of quantum nonlinear resonances in microwave-driven hydrogen.

This paper analyzes the use of Raman transitions to select a narrow velocity distribution of atoms. We determine the evolution of the atomic wave function comprised of both the internal state and the external momentum of the atom in the presence of two counterpropagating laser beams. The effects of a single π pulse, two separated Ramsey π/2 pulses, and a sequence of four π/2 pulses are analyzed.

When an atom or a molecule is exposed to an electric field, the discrete electronic spectrum turns into a spectrum of resonances with complex energies due to the mixing of the bound wave function of each unperturbed stationary state with the asymptotic form of the Airy function. The complex energies are eigenvalues of a non-Hermitian Schrödinger equation whose solutions have a special outgoing-wave asymptotic form, which is derived rigorously. At least three coordinate transformations (rotation, translation, and a combination of these) regularize the dc-field-induced resonance function, the most efficient one being the long-honored rotation, f(x)=${\mathit{xe}}^{\mathit{i}\mathrm{\theta }}$, which causes the function to dissipate asymptotically as ${\mathit{e}}^{\mathrm{-}\gamma \mathit{x}3/2}$. This finding, obtained from first principles, explains previous results that have been obtained either via trial computations or via elaborate mathematical analyses of the spectrum. The theory is further developed toward the efficient computation of such resonances with ${\mathit{scrL}}^2$ functions. Starting from the resonance-wave-function form ${\mathrm{\Psi }}^{\mathrm{res}}$=a${\mathrm{\Psi }}_0$+${\mathit{bX}}_{\mathrm{as}}$, the computation of the localized ${\mathrm{\Psi }}_0$ is carried out on the real axis, and only the free-electron function belonging to ${\mathit{X}}_{\mathrm{as}}$ is rotated and optimized in the complex plane. Two applications are presented. The first involves a numerically solvable one-dimensional model of a shape resonance in a dc field for a large range of field strengths.

The second involves the hydrogen atom in its ground as well as in its first excited state. In the first example, ${\mathrm{\Psi }}_0$ is obtained numerically in an explicitly constructed effective potential containing partly the effect of the field. To this ‘‘dressed’’ ${\mathrm{\Psi }}_0$, the asymptotic part ${\mathit{X}}_{\mathrm{as}}$ is then added as a sum of an only ten back-rotated complex Slater-type orbitals (STO’s), whose coefficients and nonlinear parameter are optimized from the diagonalization of the full Hamiltonian until stability of the complex eigenvalue is achieved. In the second example, ${\mathrm{\Psi }}_0$ was chosen as the exact 1s for the ground state and as the two roots 2s±2${\mathit{p}}_0$ of the total Hamiltonian for the excited state. ${\mathit{X}}_{\mathrm{as}}$ was expressed in terms of angular momentum symmetry blocks up to l=8, with each symmetry expanded in terms of ten complex STO’s. No optimization of θ or other nonlinear parameters was done. Comparison with the exact results for the model potential and with published ones for the H atom shows very good agreement, thereby demonstrating the efficiency and reliability of the theory as well as its potential for treating N-electron systems.

We have observed radiatively assisted collisions between velocity-selected K Rydberg atoms in radio-frequency (rf) fields. The low relative velocity of the atoms leads to long collision times, or equivalently, narrow, 1-MHz, collisional resonances. We have carried out systematic measurements with rf fields in the strong-field regime, and have shown that the cross sections agree quantitatively with the predictions of the strong-field theory. We have also shown experimentally and theoretically that the sum over m of the cross sections for m photon-assisted cross sections is larger than the resonant-collision cross section in the absence of a rf field.

We have explored a genuinely time-dependent problem consisting of periodic crossings of energy levels. The model can be realized in several physical systems, but we refer it explicitly to a two-level ion that swings in a harmonic trap and concurrently interacts with a traveling light wave. We have solved the Schrödinger equation for this model by numerical integration as well as by the use of matrix continued fractions for the steady state. We investigate both the time and the frequency behavior of the model. We have also compared the exact behavior with an intuitive model based on a Landau-Zener description of each crossing followed by a simple relaxation behavior. In addition, the coherent interaction with the field is found to lead to a resonancelike behavior of the population transfer, which we can attribute to the accumulated phase of the Bloch vector. The various time scales of the problem are identified and their physical significance is elucidated.

We set up a level-crossing model with two time scales and compare the numerically calculated probability transfer with several analytic results. We also examine the probability transfer in the adiabatic limit and make a comparison with a calculation based on the approach of Dykhne [Sov. Phys.—JETP 11, 411 (1960); 14, 941 (1962)] and of Davis and Pechukas [J. Chem. Phys. 64, 3129 (1976)]. We find that we can get an improved agreement if we modify their approach.

The influence of an external electric field on the Rydberg states of triatomic hydrogen has been studied from the viewpoint of the structure of the spectra and the dynamics of the excited states. Rydberg states with principal quantum numbers ranging from 30 to 125 were observed, and low-field as well as very-strong-field regimes investigated. A perturbative treatment taking into account the coupling between the core rotation and the Rydberg-electron motion was developed. The good knowledge of the low-l Rydberg series in ${\mathrm{H}}_3$ (ns, np, nd, and nf) allowed us to achieve this treatment without adjustable parameters. The agreement between calculation and experimental results is excellent and reveals features resulting from predissociation of selected members of the Stark manifold. Accidental predissociations due to vibrationally excited interlopers are clearly distinguished from the systematic predissociation induced by the mixing with the ns Rydberg series. This is a complete perturbative treatment of the Stark effect in molecular Rydberg states.

The output intensity of an intracavity-frequency-doubled Nd: yttrium aluminum garnet (YAG) laser can exhibit chaotic variations under certain conditions. It has been predicted that the intrinsic noise due to spontaneous emission present in this laser system can be amplified by the chaotic dynamics. We report here the observation of noise amplification in a mathematical model of this laser system in a parameter regime that produces chaotic intensity variations. The amplification was observed in the evolution of the distribution of an ensemble of noisy trajectories, originating from identical initial conditions. The observed amplification occurred at a rate given by the largest Liapunov exponent and is consistent with the theoretical predictions of Fox and Keizer [Phys. Rev. A 43, 1709 (1991)]. However, anomalous amplification was also observed and occurred at a rate ∼10 times the Liapunov exponent. The mechanism for this effect is elucidated.

We present a uniform method for approximating the functions that appear in the N-photon radial matrix element. This matrix element is required for calculating multiphoton-ionization cross sections and angular distributions in lowest-order perturbation theory. The functions include the initial- and final-state radial wave functions, and the regular and irregular parts of the radial Green’s function. We point out that all of these functions satisfy a differential equation of the same form, and differ only in their boundary conditions. The WKB method is then applied to this differential equation to obtain approximations to all of these functions. We then use these solutions to calculate two-photon-ionization cross sections of hydrogen for photon energies between 8.5 and 13.2 eV. Also presented are two-photon-ionization cross sections for Cs around the minimum near the 7p resonance and comparisons with previous work.