We present the details of a theoretical method for calculating the wave-packet dynamics of a Rydberg electron in a strong electric field. Results for Rb are presented, and are compared to recent experiments that measure the time dependence of the electron flux. These interesting experiments provide a different possibility for the experimental detection of wave packets. The results of fully quantum and classical calculations are compared to each other. Several aspects of this system that are easier to study theoretically are presented. The main property that can only be obtained theoretically is the form of the wave function near the nucleus. We found that the flux of electrons entering the detector accurately reflects the flux of electrons leaving a sphere of radius 2000 a.u. centered on the atomic nucleus. The classification of the autoionizing states contributing to the wave packet is also easier to obtain theoretically.

We present nearly local definitions of correlation energy density, and its potential and kinetic components, and evaluate them for several two-electron systems. This information should provide valuable guidance in constructing better correlation functionals than those in common use. In addition, we demonstrate that the quantum chemistry and the density-functional definitions of the correlation energy rapidly approach one another as the atomic number increases.

An effective Hamiltonian approach is developed for the perturbative calculation of bound state energies in quantum electrodynamics. In this approach a recoil correction of order ${\alpha }^2{E}_F$ to the hyperfine structure of hydrogenic systems with the arbitrary mass ratio is obtained. In the case of the positronium it amounts to $\Delta E=$$\frac{1}{3}$$m{\alpha }^6\left[1.130\right(5)\mathrm{}-$$\frac{1}{2}$$\ln \alpha ]$.

To enhance the current understanding of mechanisms contributing to magnetic hyperfine interactions in excited states of atomic systems, in particular, alkali-metal atom systems, the hyperfine fields in the excited $5{}^2{S}_{1/2}–8{}^2{S}_{1/2}$ states of potassium and $8{}^2{S}_{1/2}–12{}^2{S}_{1/2}$ states of francium atoms have been studied using the relativistic linked-cluster many-body perturbation procedure. The net theoretical values of the hyperfine fields for the excited states studied are in excellent agreement with available experimental data for both atoms. There is a significant decrease in importance of the correlation contribution in going from the ground state to the excited states, the correlation contributions as ratios of the direct contribution decreasing rapidly as one moves to the higher excited states. However, the contribution from the exchange core polarization (ECP) effect is nearly a constant fraction of the direct effect for all the excited states considered. Physical explanations are offered for the observed trends in the contributions from the different mechanisms. A comparison is made of the different contributing effects to the hyperfine fields in potassium and francium to those in the related system, rubidium, studied earlier. Extrapolating from our results to the highly excited states of alkali-metal atoms, referred to as the Rydberg states, it is concluded that in addition to the direct contribution from the excited valence electron to the hyperfine fields, a significant contribution is expected from the ECP effect arising from the influence of exchange interactions between electrons in the valence and core states.

We have studied the Zeeman effect of the resonance transition of atomic potassium vapor in a density range where the collision time is comparable with the time in between collisions. We find that the Zeeman splitting in this density range changes significantly as compared to the value for a free atom. In particular, we observe that the Zeeman effect of the two resonance $D$ lines become equal at the highest densities that we have studied. The modification of the Zeeman splitting is attributed to resonant dipole-dipole collisions between ground-state and excited-state atoms.

The multiconfiguration Dirac-Fock model is employed to evaluate the effects of relativity and electron correlation on the hyperfine interaction constants of the 3$d^2$ ${}^3{F}_3$, ${}^3{F}_4$, ${}^1{G}_4$, and $3d4p$ ${}^3{F}_4$ levels of Sc II. The wave function expansions are obtained with the active space method, where configuration state functions of a specific parity and $J$ value are generated by substitutions from the reference configurations to an active set of orbitals. The active set is then increased in a systematic way, allowing the convergence of the hyperfine interaction constants to be studied. The calculated electric quadrupole hyperfine constants, together with previously computed values for other levels of Sc II, are used to evaluate the nuclear electric quadrupole moment of isotope 45 of scandium, for which the value $Q=-0.231\left(4\right)\mathrm{}$ b is found.

The absorptive part of the susceptibility of a system constituted by a strongly driven two-level atom (interacting with a reservoir) is analyzed when probed by a weak field. Memory effects are taken into account (the correlation time of the reservoir variables is finite) and we verify that they lead to several distinct features for the absorption and stimulated emission of radiation, when compared with those obtained in the Markovian approximation. Moreover, we verify that memory effects lead to a signature, namely, the sensitive dependence of the maxima of the absorption lines on the Rabi frequency at off-resonance pumping. Other characteristics of the spectrum are enhanced, even in the presence of a small but non-null correlation time of the reservoir, for instance, the maxima of the dispersionlike absorption curves at on-resonance pumping. In this work several situations are analyzed for different values of the parameters of the problem: the off-resonance frequencies of the driving field, the Rabi frequency, the memory time, and temperature of the reservoir.

The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i.e., arbitrary errors at known positions. We show that four quantum bits are necessary and sufficient to encode one quantum bit and correct one erasure, in contrast to five quantum bits for unknown positions. Moreover, a family of quantum codes for the QEC, the quantum Bose-Chaudhuri-Hocquenghem codes, that can be efficiently decoded is introduced.

In this paper we obtain a simple analytic formula for the photodetachment cross section of ${\mathrm{H}}^{\mathrm{-}}$ in parallel electric and magnetic fields. The three-dimensional semiclassical approximation predicts oscillations in the spectrum and correlates these oscillations with closed classical orbits. The cylindrical symmetry of the Hamiltonian produces some interesting effects. In particular, at boundary energies the semiclassical approximation fails as a focused cusp approaches the origin.

In the preceding paper, we showed that the semiclassical approximation diverges at a bifurcation, and that this divergence coincides with the passage of a focused cusp through the origin. Here we obtain a wave function in the vicinity of this cusp, and we use that wave function to eliminate the divergences in the photodetachment cross section. To describe the focused cusp, we first discuss the wave function of an ordinary two-dimensional (nonfocused) cusp. This wave function is known as a Pearcey function, and it has been studied extensively. Then we show how the formulas that lead to the Pearcey function have to be modified to describe a cylindrically focused cusp. The resulting wave function turns out to be given by an integral of Fresnel type containing within it a cylindrical Bessel function. This wave function is used to derive a formula for the photodetachment cross section near a bifurcation. That formula is a simple closed-form expression containing a Fresnel integral. Comparison with exact quantum calculations shows that this corrected-semiclassical formula is quite accurate.

The methods developed in the preceding paper (paper II) are used to construct a wave function near a bifurcation of classical orbits of an atomic electron in an electric field. A formula for the recurrence strength near the bifurcation is derived and compared with experimental measurements.

An ab initio calculation, following a hyperspherical partial-wave method [J. N. Das, Aust. J. Phys. 47, 743 (1994)], satisfactorily represents the recent experimental triple differential cross-section results of Röder et al. [Phys. Rev. A 53, 225 (1996)] for electron hydrogen atom ionization collisions at low energies. The qualitative agreement with their theoretical results is also good. Moreover, our results are in absolute units and in some instances our results are in better agreement with the experiments compared to their theoretical results. Here it is also exhibited that the hyperspherical partial wave method is a promising formalism for studying atomic ionization problems.

The electron-impact ionization of atomic hydrogen at intermediate excess energies is considered in the situation where the two continuum electrons escape with substantially different velocities and coplanar with the incident direction. Calculations are performed within a model where the three-body final state is described by a product wave function consisting of three symmetrical, Coulomb-type functions. Each of these functions describes the motion of a particular two-body subsystem in the presence of the third charged particle. A comprehensive comparison with available experimental data is presented, and the results are contrasted with those of other theoretical models. Generally, good agreement is found with the absolute measurements; however, in some cases discrepancies between various theoretical predictions and experimental findings are obvious, which highlights the need for a theoretical and experimental benchmark study of these reactions.

Photodetachment of Al${}^{-}{(3s}^2{3p}^{23}P)$ near the threshold of the first excited state of neutral aluminum has been studied both experimentally and theoretically. A 19-keV mass-resolved Al${}^{-}$ beam was intersected by a frequency-doubled neodymium-doped yttrium aluminum garnet pumped dye-laser beam, and the fast atoms created by detachment processes were detected. Measurements just below the threshold of the first excited state, Al${(3s}^{2}4s{}^{2}S)$, find a large resonance peak in the detachment signal. An eigenchannel $R$-matrix calculation generates a resonance structure that is qualitatively similar to the data and identifies the large resonance peak as resulting from a doubly excited negative-ion state having predominantly ${(3s}^{2}4s4p{}^3{P}^o)$ character. Density plots of the resonance state are presented to demonstrate its structure. Near the Al${(3s}^{2}3p{}^{2}P)$ threshold, theory agrees also with recent relative measurements of D. Calabrese et al. [Phys. Rev. A 54, 2797 (1996)].

A highly accurate measurement of $\Delta n=0\mathrm{}$ dielectronic recombination (DR) resonances with Ar${}^{15+}$ has been carried out at the ion storage ring CRYRING. The absolute energies of the DR resonances were determined by a method that uses the Schottky frequency and the knowledge of the length of the beam orbit in the ring. The accuracy in the absolute energy achieved in this experiment was $\sim 1\%$. Positions and widths of doubly excited states of Ar${}^{14+}$, as well as the DR cross sections, were calculated with relativistic many-body perturbation theory in an all-order formulation. Radiative corrections and mass polarization were needed to obtain good agreement with the experimental results.

The Lindblad approach to open quantum systems is introduced to study the dynamics of a single trapped ion prepared in nonclassical motional states and subjected to continuous measurement of its internal population. This results in an inhibition of the dynamics similar to the one occurring in the quantum Zeno effect. In particular, modifications to the Jaynes-Cummings collapses and revivals arising from an initial coherent state of motion in various regimes of interaction with the driving laser are dealt with in detail.

The electron-impact approximation for the ejection of target electrons by heavy, highly charged projectiles is modified in order to allow for a distortion of the initial state by the heavy perturber. Model calculations for ionization of ${\mathrm{H}}_2$ by 0.5–0.6 MeV/amu ${\mathrm{Cu}}^{5+}$ impact show that the binary-encounter peak is considerably broadened when distortion effects are included. In general, this leads to a better agreement of the peak shape with experimental data than the conventional binary-encounter model.

We present an improved theoretical description of Rydberg electron motion in the presence of an arbitrary ionic core. Through the use of a generalized eigenvalue equation involving Coulomb, multipole, and polarization interactions we are able to describe accurately the physics of the autoionizing Mg $3pnf$ Rydberg states. The vector hyperpolarizability ${\beta }_v,$ the proportionality constant for an interaction term with the operator structure $\overrightarrow{L_c}\cdot \mathcal{l}\to {/r}^6$, where $\overrightarrow{L_c}$ and $\mathcal{l}\to$ are the orbital momenta of the ionic core and the Rydberg electron, is found to be 1.885 a.u., roughly two orders of magnitude larger than in ground-state Ne${}^{+}$. The effects of nonadiabatic radial interactions now emerge clearly. Comparisons with measured autoionization energies and rates, and with those computed using $R$-matrix and multichannel quantum defect theory methods, confirm the accuracy of this approach. The concept of adiabatic torquing of orbital planes is introduced and explored in Rydberg magnesium.

We present double-differential electron distributions, measured in the neighborhood of the velocity of the emerging projectiles, for 45-keV H${}^{+}$ and H${}^0$ incident on a He target. Target thicknesses range from single-collision conditions through a multiple-collision regime up to charge equilibrium in the emerging beam. The convoy-electron emission yield is determined as a function of target thickness. Using a simple rate equation and known cross sections for charge exchange and electron scattering, approximate agreement with experiment is obtained. A smaller electron-He scattering cross section improves this agreement. This result could be interpreted as due to the effect of the projectile Coulomb field in the transport of the electrons.

A quantal reaction-coordinate treatment is employed to calculate charge-transfer cross sections for ${}^{12}{\mathrm{C}}^{2+}{+}^4\mathrm{He}$ collisions in the impact energy range $300\mathrm{eV}<~E<~2.5\mathrm{keV},$ using a molecular basis set. Total cross sections are compared with semiclassical results and with available experimental data.