The relation between the dynamical properties of a coupled quasiparticle-oscillator system in the mixed quantum-classical and fully quantized descriptions is investigated. The system is considered as a model for applying a stepwise quantization. Features of the nonlinear dynamics in the mixed description such as the presence of a separatrix structure or regular and chaotic motion are shown to be reflected in the evolu- tion of the quantum state vector of the fully quantized system. In particular, it is demonstrated how wave packets propagate along the separatrix structure of the mixed description, and that chaotic dynamics leads to a strongly entangled quantum state vector. Special emphasis is given to viewing the system from a dyn- amical Born-Oppenheimer approximation defining integrable reference oscillators, and elucidating the role of the nonadiabatic couplings which complement this approximation into a rigorous quantization scheme.

The recently built electron-energy-loss spectrometer (EELS) (typical full width at half maximum of 60 meV) has been employed to measure EELS spectra of neon in discrete and autoionization resonance regions at a 2.5 keV impact energy and a mean scattering angle of 0°. Relative optical oscillator strength density spectra were established by multiplying the EELS spectra by the known Bethe-Born conversion factor of the spectrometer, and then were normalized at a single point in the smooth continuum. Absolute optical oscillator strengths corresponding to these energy regions are reported and compared with previously published experimental and theoretical values. Two forbidden transitions in the autoionization region are observed and identified. One of them has not been previously reported to our knowledge.

Numerical study of the kinetics in metastable antiprotonic helium molecules driven by a sequence of laser π pulses resonant to the adjacent transitions is carried out. The phenomena taking place are shown to be useful for checking the mechanisms of the depopulation of high-n states, for measuring the populations of the individual energy levels, and for slowing down the decay by means of π-pulse-induced inversion.

A boson-realization model and a corresponding q-deformed model are proposed for the vibrations of bent triatomic molecules, where Fermi resonances between stretching and bending vibrations are taken into account. The two models are applied to fit the vibrational energy levels of ${\mathrm{H}}_2$O up to 22 000 ${\mathrm{cm}}^{\mathrm{-}1}$ with the standard deviations 8.198 and 7.157 ${\mathrm{cm}}^{\mathrm{-}1}$, respectively.

We present a self-interaction-free density-functional theory (DFT) for the treatment of both the static properties of the ground states and the photoionization processes of many-electron systems. The method is based on the Krieger-Li-Iafrate (KLI) treatment of the optimized effective potential (OEP) theory and the incorporation of an explicit self-interaction correction (SIC) term. Such an extended OEP–KLI-SIC method uses only orbital-independent single-particle local potentials and is thus computationally more efficient and yet maintains good accuracy. The usefulness of the procedure is examined by the studies of the static properties of the ground states of atoms (Z⩽18) and the dynamical photoionization processes involving autoionizing resonances. Both the energy functionals of the local spin-density approximation (LSDA) and Becke's exchange energy functional and the correlation energy functional of Lee-Yang-Parr (BLYP) are used as the input to the KLI-SIC calculations. It is found that the implementation of the KLI-SIC procedure gives rise to optimized effective potentials that possess the correct behavior in both short-range and long-range regimes. As a consequence, the LSDA and BLYP ionization potentials are significantly improved. For higher-Z atoms, the improvement of the LSDA total energies and the ionization potentials are particularly remarkable, approaching the experimental or exact values. As another test of the KLI-SIC method, we have performed the calculation of the photoionization cross sections of the Ne atom using both the time-independent and time-dependent LSDA (TDLSDA) methods. We found that the TDLSDA results agree closely with the experimental data in the broad peak region, followed by a series of sharp resonances due to the 2s→np resonant transitions. The calculated linewidths and resonance line profile parameters are in reasonable agreement with both the experimental and the configuration-interaction (R-matrix) results, demonstrating the usefulness of the KLI-SIC procedure for achieving accurate DFT calculations in both static properties and dynamical processes.

The major objective of this paper is to make some simple, but numerically useful generalizations of the classical orthogonal functions. The motivation for doing this is to develop accurate, orthornormal basis sets for the expansion of solutions of the Schrödinger equation in multichannel problems. The generalizations are needed for two reasons. First, it is often useful for the set to have a mathematical structure which is unrelated to the classical functions and second, the boundary conditions which need to be satisfied by the solutions to the Schrödinger equation are often not easily represented by the classical functions. In contrast to certain other techniques, such as those based on diagonalizing the overlap matrix, the method we propose is capable of generating very large, orthonormal subspaces in a numerically stable fashion. While it is not possible to demonstrate a one-to-one correspondence between this finite basis representation of the Hamiltonian and a representation based on the points and weights of a Gauss quadrature, the so-called discrete variable representation (DVR), as is true for the classical orthogonal functions, it is still possible to transform to a representation which preserves all of the essential features of the DVR. The method is illustrated by applying it to a few simple one- and two-dimensional problems.

Radiative decay of ${\mathrm{nd}}^{\mathrm{-}1}$${5\mathrm{f}}^{\mathrm{m}+1\mathrm{}}$ excited states in ${\mathrm{UO}}_2$ induced by electron collisions is studied theoretically and experimentally. Energies, transition probabilities, and photoexcitation cross sections for the relevant configurations of ${\mathrm{U}}^{4+}$ are calculated by using the multiconfiguration Dirac-Fock method. Experimental observations are made in the 4d range. Direct recombination of the excited 5f electron to the 4d hole and 4d-6p emission in the presence of the spectator excited 5f electron are observed. From the theoretical results, the spectra are simulated and compared to the observed spectra in the three nd regions. The agreement is correct and describes the evolution of the coupling scheme in the ${\mathrm{nd}}^{\mathrm{-}1}$${5\mathrm{f}}^3$ excited states from n=3 to n=5.

Relativistic large-scale multireference configuration-interaction all-electron calculations, used to study the influence of valence-electron correlation effects on the fine-structure splittings in the Pb atom and the isoelectronic ions ${\mathrm{Bi}}^{+}$ and ${\mathrm{Po}}^{2+}$, are presented. The atomic nucleus was modeled as a finite, uniformly charged sphere. The one-electron basis set consisted of orbitals expressed as a linear combination of kinetically balanced Gaussian basis functions. All four valence electrons were correlated by considering excitations from the ${6\mathrm{s}}^2$${6\mathrm{p}}^2$ configurations and systematically enlarging the virtual space to include unoccupied orbitals of symmetries up to ${\mathrm{f}}_{7\mathrm{/}2}$. The results obtained are in good agreement with experimental data, and remaining disagreements are largely attributed to missing core-valence correlation effects. Comparisons with the results of variational quantum Monte Carlo and multireference configuration-interaction studies based on the relativistic pseudopotential approach are also presented.

We have calculated the ${3\mathrm{s}}^{21}$${\mathrm{S}}_0$-${3\mathrm{s}3\mathrm{p}}^{1,3}$${\mathrm{P}}_1$ transition energies for neutral magnesium and Mg-like ${\mathrm{Ar}}^{6+}$, ${\mathrm{Cu}}^{17+}$, ${\mathrm{Kr}}^{24+}$, and ${\mathrm{Mo}}^{30+}$ using the relativistic configuration-interaction (CI) method. These calculations are based on the relativistic no-pair Hamiltonian which includes Coulomb and retarded Breit interactions and employ finite B-spline basis functions. Quantum electrodynamic and mass polarization corrections are also calculated. For Mg-like ions studied here, intravalence correlations are treated exactly by saturating the basis with all configurations that arise from valence-valence excitations. Contributions from core polarization are also calculated with large-scale CI expansions by including dominant configurations from core-valence excitations. Agreement between theory and experiment are good for all the Mg-like ions studied here.

Recent experimental results on the muon exchange from muonic hydrogen to argon show that the reaction rate is energy dependent near 0.1 eV. A muonic hydrogen atom, formed by muon capture in ${\mathrm{H}}_2$ gas at 15 bars, is thermalized in a few hundreds of nanoseconds. If the muon transfer reaction occurs before that time, the rate is shown to be slightly lower compared to thermalized muonic atoms [${\lambda }_{\mathrm{pAr}}$=(1.63±0.09)×${10}^{11}$${\mathrm{fs}}^{\mathrm{-}1}$]. As an indirect consequence, the muon transfer rate from μp to helium, determined by our group [R. Jacot-Guillarmod and co-workers, Phys. Rev. A 38, 6151 (1988)] is lowered by about 40%. The present value ${\lambda }_{\mathrm{pHe}}$=(0.51±0.19)×${10}^8$${\mathrm{fs}}^{\mathrm{-}1}$ is in good agreement with other experiments. The transfer rate from muonic deuterium to argon shows also an energy dependence. The muon transfer rate to argon from the deuteron is ${\lambda }_{\mathrm{dAr}}$=(0.86±0.04)×${10}^{11}$${\mathrm{fs}}^{\mathrm{-}1}$ at room temperature. The intensity patterns of the muonic Lyman series of argon obtained by muon transfer from both hydrogen isotopes are determined and compared with theoretical predictions.

In view of recent high-precision measurements of transition energies between levels of berylliumlike Rydberg ions of ${\mathrm{S}}^{12+}$ and ${\mathrm{O}}^{4+}$ in (high-angular-momentum) Rydberg states, we introduce a modified polarization model that allows one to estimate level energies even in the case of near degeneracy, that is, when an excitation energy of the Rydberg electron is nearly equal but opposite to that of the ionic core. Estimates as well as rigorous upper and lower bounds for the dominant second-order perturbation-theory dipole contributions to the line shifts (with continuum states included) are given. Agreement with the measured line shifts is very much improved over that of the usual polarization model, but the range of estimates remains, in many cases, rather larger than the experimental uncertainty; our primary purpose is to assist experimentalists planning studies of other Rydberg ions by providing estimates which are improved and which remain trivial to apply.

The pooling of high-resolution laser-induced fluorescence measurements with photoassociation binding energies in ${}_{}{}^6{}_{}{}^{}\mathrm{Li}_2^{}{}_{}{}^{}$ has provided a strict test of models proposed for extrapolation of long-range molecular potential functions. An analytical expression is given for the long-range part of the $0_{\mathrm{u}}^{+}$ molecular states originating from M(ns${\mathrm{}}^2$S)+M(np${\mathrm{}}^2$P) alkali-metal atoms, replacing earlier expressions which assumed negligible spin-orbit coupling. The success of this model is illustrated by the excellent agreement between the experimentally determined dissociation energy ${\mathrm{D}}_{\mathrm{e}}$=9352.032(8) ${\mathrm{cm}}^{\mathrm{-}1}$, and the value 9352.032(12) ${\mathrm{cm}}^{\mathrm{-}1}$ obtained by extrapolation of E(R) values of a Rydberg-Klein-Rees potential for the A${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathrm{u}}^{+}$ state of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}_2^{}{}_{}{}^{}$. The lifetime of the ${}_{}{}^2{}_{}{}^{}\mathrm{P}_{1\mathrm{/}2}^{}{}_{}{}^{}$ atomic level is 27.13(2) ns.

By posing the Hartree-Fock method as a density-functional method, an exchange potential is derived. By approximating the Hartree-Fock orbitals with the Kohn-Sham methods the Krieger-Li-Iafrate approximation to the optimized-effective-potential method is obtained.

We have developed an interesting and widely applicable technique for measuring lifetimes of low-lying levels of neutral atoms and their first few ionization states. The cascade-photon-coincidence method has been extended by using a light source consisting of excited atoms sputtered from a solid by 10-keV argon ions. We have measured the lifetimes of the ${4\mathrm{p}}^2$${\mathrm{P}}_{3\mathrm{/}2}^{\mathrm{o}}$ state of Ca II, the ${6\mathrm{p}}^2$${\mathrm{P}}_{3\mathrm{/}2}^{\mathrm{o}}$ state of Ba II, and the ${4\mathrm{p}}^2$${\mathrm{P}}_{3\mathrm{/}2}^{\mathrm{o}}$ state of Al III. These measurements are in good agreement with earlier work.

Hyperfine quantum-beat spectroscopy has been utilized in a pump-probe configuration to measure magnetic dipole (A) and electric quadrupole (B) coupling constants in the 3d${\mathrm{}}^2$${\mathrm{D}}_{3\mathrm{/}2}$ and 3d${\mathrm{}}^2$${\mathrm{D}}_{5\mathrm{/}2}$ levels of three isotopes of potassium. For many of these levels, the largest hyperfine splitting is smaller than the natural width, and so a subnatural linewidth technique is required. In the experiments, the 3d levels are excited on the 4d${\mathrm{}}^2$${\mathrm{S}}_{1\mathrm{/}2}$→3d${\mathrm{}}^2$${\mathrm{D}}_{\mathrm{j}}$ quadrupole transition with linearly polarized light. Time evolution of the alignment components in the d levels is probed by time-delayed resonant radiation on the 3d${\mathrm{}}^2$${\mathrm{D}}_{\mathrm{j}}$→9p${\mathrm{}}^2$${\mathrm{P}}_{\mathrm{j}}$ transitions. Comparison of the excitation rate for two orthogonal relative polarization directions of the pump and probe laser at each delay time permits derivation of a linear polarization degree. This quantity contains beats at the various hyperfine frequencies in the d levels. Fitting the experimentally obtained time dependence to theoretical expressions allows extraction of the hyperfine coupling constants. For the 3d${\mathrm{}}^2$${\mathrm{D}}_{3\mathrm{/}2}$ level of ${}_{}{}^{40}{}_{}{}^{}\mathrm{K}$ we obtain A=0.96(4) MHz and B=0.37(8) MHz, indicating a typical precision also obtained for the other levels and isotopes.

The experimental ${\mathrm{Ar}}_2$ trace-polarizability collision-induced scattering spectrum is reported in absolute units and over a large range of Raman frequency shifts, up to ν≃400 ${\mathrm{cm}}^{\mathrm{-}1}$. At frequency shifts above 60 ${\mathrm{cm}}^{\mathrm{-}1}$, the measured spectral profile falls off exponentially. We were able to record the far wing down to intensities that are two orders of magnitude smaller than those of the previous work. While the long ago predicted insufficiency of the dipole-induced dipole (DID) or DID-like trace models is confirmed, reliable fully quantum computations based on a modern approach show that the ab initio Dacre's trace [P. D. Dacre, Mol. Phys. 45, 1 (1982)] accounts well for the frequency dependence of the experimental spectrum differing only by a scaling constant.

Full quantum calculations are carried out for the elastic (rotationally summed) integral and differential cross sections in low-energy collisions of positrons with rigid rotor ${\mathrm{CO}}_2$ molecules. The interaction includes an expansion of the exact Coulomb potential on a single-center (SCE) and a parameter-free correlation-polarization (${\mathrm{V}}_{\mathrm{CP}}$) potential given in local form via density-functional theory (DFT) with gradient corrections. State-to-state rotationally inelastic cross sections (integral and differential) are also presented and their behavior is discussed in relation to what is known from similar experiments with electrons as projectiles. The agreement found between computed and measured elastic integral cross sections is rather good and confirms the realistic quality of a DFT treatment for short-range dynamical correlation effects.

By means of differential energy-transfer measurements, excitation processes in ${\mathrm{Li}}^{+}$-Ar collisions have been studied over a wide range of laboratory angles of 2°⩽θ⩽92° and at laboratory collision energies of 70⩽${\mathrm{E}}_{\mathrm{lab}}$⩽2000 eV. The ${\mathrm{Li}}^{+}$ and Li atoms scattered inelastically were observed at reduced angles of ${\mathrm{E}}_{\mathrm{lab}}$θ>5 keV deg, and collision energies of ${\mathrm{E}}_{\mathrm{lab}}$⩾200 eV. At 200⩽${\mathrm{E}}_{\mathrm{lab}}$⩽350 eV, the inelastic signals are exclusively due to one-electron transitions, while for ${\mathrm{E}}_{\mathrm{lab}}$⩾500 eV two-electron excitation as well as one-electron excitation was observed. The electronic transitions in the moderate-energy ${\mathrm{Li}}^{+}$-Ar collisions take place at distances of R<${\mathrm{R}}_{\mathrm{c}}$=0.81 Å. The excitation mechanism for one-electron charge transfer having the largest cross section is investigated in detail by referring to ab initio potentials. The angular dependence of the differential cross sections of two-electron transitions at higher energies shows three different types of excitations: the first transition takes place around ${\mathrm{R}}_{\mathrm{c}}$=0.75 Å, the second around ${\mathrm{R}}_{\mathrm{c}}$=0.47 Å, and the third around ${\mathrm{R}}_{\mathrm{c}}$=0.2 Å. The first and second transitions are due to noncrossing interactions, while the third is attributed to avoided crossing.

In this work we construct a correlated double continuum wave function for the three-body Schrödinger equation valid for large interparticle distances. Genuine three-body effects are considered by taking into account a nondiagonal part of the Hamiltonian written in generalized parabolic coordinates. A solution is found in terms of the confluent hypergeometric function of two variables ${\mathrm{\Phi }}_2$, with similar structure to the first-order Faddeev approximation. The use of such a solution seems to introduce appropriately the interelectronic repulsion.

Using the merged-beams technique, independent, absolute, total electron-capture cross sections have been measured for the ${\mathrm{N}}^{2+}$+H (or D) system in the collision energy range 0.1–4500 eV/amu. For collision energies less than 200 eV/amu, the data are in reasonable accord with recent fully quantal calculations of Herrero et al. [J. Phys. B 28, 711 (1995)], except that the experiment provides no evidence for the existence of a peak in the cross section at 0.25 eV/amu. Additional structure between 10 and 100 eV/amu, as predicted by Bienstock et al. [Phys. Rev. A 33, 2078 (1986)], is not observed either. A comparison is also made with other measurements, which make use of a hydrogen furnace [Phaneuf et al., Phys. Rev. A 17, 534 (1978); Seim et al., J. Phys. B 14, 3475 (1981); Wilkie et al., J. Phys. B 18, 479 (1985)]. Above 2000 eV/amu the agreement is excellent. However, between 200 and 2000 eV/amu the present results are some 30% below the previously published experimental and theoretical cross sections, and a local maximum is found near 200 eV/amu, instead of 360 eV/amu. A possible explanation for this discrepancy is suggested.