We explore the classical limit of the hydrogen atom by constructing a minimum-uncertainty wave packet that travels along a Kepler orbit. The dynamics of the wave packet display both classical and quantum-mechanical properties. Over a limited period of time, during which the dynamics of the wave packet may be considered linear, the motion of the wave packet can be described by classical equations of motion. After this time, the quantum dynamics, whose most prominent features are decays and revivals of the wave packet, becomes dominant. We discuss decays and revivals of the wave packet in detail.

An alternative discretization method treating rearrangement and breakup channels on equal footing is introduced for wave-packet description of three-body dynamics. The permutational symmetry for three identical particles is incorporated into the evolution equations of the proposed method. The method is tested on a model three-particle problem that exhibits both rearrangement and breakup channels. Sharp-energy S matrix elements over a broad range of energies above the breakup threshold are extracted from a single wave-packet calculation.

The local convergence and accuracy of wave functions obtained by direct solution of the Schrödinger equation with the help of the correlation-function hyperspherical-harmonic method are analyzed for ground and excited states of the helium atom and for the ground state of the positronium negative ion. The inclusion of the cusp conditions into the correlation function is shown to be of crucial importance, not only near the coalescence points, but also away from them. The proper inclusion of all cusps yields for the ground state of the helium atom the local wave-function accuracy of about ${10}^{\mathrm{-}7}$ for different interparticle distances. The omission of one of the cusps in the excited helium atom reduces the wave-function precision to ${10}^{\mathrm{-}2}$ near the corresponding coalescence point and to ${10}^{\mathrm{-}4}$–${10}^{\mathrm{-}5}$ away from it.

We make another application of a remarkably efficient technique, in which the intermediate states of conventional second-order perturbation theory are replaced by a finite set of pseudostates, and the energy denominators are replaced by the expectation values of the unperturbed Hamiltonian with respect to those pseudostates. In previous calculations (of van der Waals coefficients and frequency-dependent polarizabilities) in which the pseudostates were determined by diagonalization of the unperturbed Hamiltonian, excellent converged results were obtained with as few as five to ten terms representing both bound and continuum states. Following the work of Bassani, Forney, and Quattropani [Phys. Rev. Lett. 39, 1070 (1977)], we use the method to investigate the 2S-1S transition rate using both the E⋅x and A⋅p forms of the interaction. The results mirror closely those obtained in the conventional way, even when only a small number of terms are used, and they are not strongly dependent on the exact form of the basis functions used.

A method of density mapping between position and momentum spaces is developed within the Hartree-Fock framework. The results are applied to the generation of momentum moments 〈${\mathit{p}}^{\mathit{n}}$〉 from the position density for the first- and second-row atoms in their ground states. For the given near-Hartree-Fock position density, the method reproduces the counterpart momentum moments with excellent accuracy, the error being less than 0.1% for the first-row atoms and 0.3% for the second-row atoms except for a few minor cases.

Several problems in atomic physics, such as diamagnetism in high Rydberg states, or the electron-electron interaction in high doubly excited states, and analogous problems at high excitation in nuclear physics or in other branches of physics, display certain characteristic and common features. Among these are the existence of classes of sharply localized states formed through large superpositions of basis states that are degenerate in the absence of the interaction. The asymmetric rotor at high angular momentum J displays these same features: In particular, most of its eigenstates divide into two groups with different localizations (along the directions of minimum and maximum moments of inertia). A few states lie in a ‘‘separatrix’’ region in between, corresponding to localization along the axis with an intermediate moment of inertia. A 1:1 mapping is made from the atomic and nuclear problems into the asymmetric rotor, wherein the principal quantum number n and orbital angular momentum l of the former are put in correspondence, respectively, with J and M, the azimuthal projection of the rotor’s angular momentum. For each given problem, the ‘‘asymmetry parameter’’ of the corresponding rotor is identified, and eigenvalues and eigenfunctions are presented. The concept of a conjugate rotor is also introduced. The key, common feature that underlies localization is the vanishing as l→n of the off-diagonal coupling between the states in a degenerate manifold {nl} just as in the asymmetric rotor where the matrix elements of the step-up and step-down operators in the ‖JM〉 basis vanish when M→±J.

Gradients of the total energy with respect to nuclear coordinates within the linear combination of Gaussian-type orbitals approach to local-density-functional theory are discussed. We explicitly include the effects of the fitting procedures for both the direct Coulomb and the exchange-correlation energies in the evaluation of the energy-gradient expression.

The 877.5-nm electric-field-induced quench radiation on a thermal beam of Ba atoms in the metastable 6s5d ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$ state for transition to the 5${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ ground state has been measured at the 3% precision level. The Stark-enhanced dipole radiation yields a simple relationship between the field-free-decay rates for transitions between the metastable ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$ state and the nearby states that are mixed in by the field. Using the known decay rates, we obtain a decay rate of A(6s6p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$–6s5d ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$)∼7×${10}^3$ ${\mathrm{s}}^{\mathrm{-}1}$.

An asymptotic theory of quasiclassical type is constructed for the quasistationary states and branch points of terms in the problem of two Coulomb centers. In the adiabatic approximation of atomic collision theory, the branch points and the parameters of quasistationary states, respectively, determine the electron transitions between two bound states and between a bound state and the continuous spectrum.

Orientation and alignment parameters for the first excited p state of Li and Na in collisions with He through direct excitation from the ground state are studied theoretically in the energy region up to ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.\mathrm{}}$=100 keV by using a quasi-one-electron theory. Scattering states are expanded in terms of molecular orbitals, which are calculated by using the pseudopotential method and include electron translation factors. The approach appears to work well for Li+He, giving good agreement for the 2p excitation probability and orientation. For alignment, the situation is less clear because of difficulty in experimental measurement. Two-electron effects and cascades from more highly excited states cause our description of Na+He collisions to be less satisfactory. However, agreement with the experimental 3p excitation probability and orientation parameters where all data are available is fairly good at lower energies (${\mathit{E}}_{\mathrm{c}.\mathrm{m}.\mathrm{}}$<1 keV) and at larger impact parameters (b>1.25 a.u.).

For the ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$${\mathrm{-}}^1$${\mathit{S}}^{\mathit{e}}$, ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$${\mathrm{-}}^1$${\mathit{D}}^{\mathit{e}}$, ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{e}}$${\mathrm{-}}^1$${\mathit{S}}^{\mathit{e}}$, and ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{e}}$${\mathrm{-}}^1$${\mathit{P}}^{\mathit{o}}$ double-electron excitation processes of He in high-lying doubly excited states by charged-particle impact, we have evaluated the Born cross sections using the hyperspherical wave functions. Together with our previous results [Motoyama, Koyoma, and Matsuzawa, Phys. Rev. A 38, 670 (1988); Matsuzawa, Atsumi, and Koyama, ibid. 41, 3596 (1990)], we have theoretically found a set of propensity rules for these excitation processes between the doubly excited states with L≤2. These rules indicate that a He atom in a strongly correlated doubly excited state tends to conserve its internal state as a flexible e-${\mathrm{He}}^{2+}$-e linear triatomic molecule during the excitation processes except for the restriction arising from the Pauli exclusion principle. How the exclusion principle modifies the above-mentioned propensity rules for singlet-singlet optically allowed excitation processes depends on the radial correlation of the initial state. The behaviors of the doubly excited atoms in rotationally and/or vibrationally excited states as the flexible linear triatomic molecule tend to deviate from those predicted by the propensity rules so obtained. This is due to the fact that there are no final states available for the propensity rules to specify because of the restriction arising from the cutoff of the quantum numbers.

We calculate first-retardation and multipole corrections to the dipole angular distributions of L-shell photoelectrons ejected by polarized photons. The calculation is performed nonrelativistically in the framework of the independent-particle model. It leads to general expressions for the s and p subshell retardation correction in terms of radial matrix elements and relative phase shifts. In the 2s case the retardation effects may contribute as much as 10–30% to the angular distribution even close to threshold, especially for higher-Z elements. In the 2p case the retardation effects are small close to threshold but can contribute as much as 10–20% for relatively low final electron energies of 1–3 keV. We have also obtained simple semianalytical expressions for the retardation corrections, based on the assumption that for inner shells screening effects beyond normalizations and phase shifts can be treated perturbatively. The semianalytic formulas compare quite well with the results of numerical calculations for the 2s subshell; they are somewhat worse for 2p photoelectrons, especially for lower energies and lower Z. This is due to the fact that in the latter case larger distances become more important in the integrals determining radial matrix elements. In the 2s case the retardation effects result in forward or backward peaking of the angular distributions. For the 2p initial state and linearly polarized photons, they lead to deviations from dipole predictions for a uniform angular distribution of photoelectrons whose momenta are perpendicular to the direction of photon polarization.

Electron scattering from polar molecules is studied in a hybrid approach that uses the recently introduced algebraic-eikonal approach to describe the forward-angle scattering and the results of, for example, a close-coupling calculation for larger angles. The two calculations are matched by making a partial-wave expansion and combining the high partial waves of the algebraic-eikonal approach with the low partial waves obtained in a full close-coupling calculation. The method is illustrated by applying it to electron scattering from a rigid-rotor molecule with a large dipole moment.

Bragg additivity was explored through measurement of Balmer-α emission cross sections produced by the collision of 100–350-keV ${\mathrm{He}}^{+}$ incident on ${\mathrm{H}}_2$, ${\mathrm{CH}}_4$, ${\mathrm{C}}_2$${\mathrm{H}}_2$, ${\mathrm{C}}_2$${\mathrm{H}}_4$, and ${\mathrm{C}}_2$${\mathrm{H}}_6$. The cross-section data show a linear relation on a Fano plot, thus indicating that the Bethe-Born theory may provide an appropriate description of the collision. Evidence for Bragg additivity would be a direct dependence of the value of the emission cross section on the number of hydrogen atoms in the target molecule. Results indicate a failure of strict additivity. Once molecular structure had been taken into account by a calculation of approximate electron densities, the cross sections followed an additive rule demonstrating a dependency not only on the number of hydrogens present, but also on the number of electrons available per hydrogen atom.

Electronic transitions between the spin-orbit states of ${}_{}{}^3{}_{}{}^{}$P and ${}_{}{}^1{}_{}{}^{}$D of ${\mathrm{I}}^{+}$ were observed in the inelastic collisions between ${\mathrm{I}}^{+}$ and Xe. The Landau-Zener model is used to interpret the transfers of translational energies to electronic energies and vice versa at the crossing points of the various potential-energy curves of (XeI${)}^{+}$. Relativistic complete-active-space self-consistent-field followed by first-order configuration-interaction and relativistic configuration-interaction (RCI) calculations including spin-orbit coupling are carried out on the low-lying electronic states dissociating into Xe+${\mathrm{I}}^{+}$ and ${\mathrm{Xe}}^{+}$+I asymptotes. Some of the potential-energy curves correlating into Xe+${\mathrm{I}}^{+}$ were found to be bound, while most of the states correlating into ${\mathrm{Xe}}^{+}$+I were found to be repulsive. RCI calculations explain the observed efficient energy transfers. The spin-orbit-corrected RCI ${\mathit{D}}_{\mathit{e}}$ of ${\mathrm{XeI}}^{+}$ in the $0^{+}$(III) state is calculated as 0.8 eV. Two electronic states of $0^{+}$(II) and $0^{+}$(III) symmetries are found to be strongly bound while 2, 1, and $0^{\mathrm{-}}$(I) states are relatively less bound.

Ab initio cross sections have been calculated for electronic excitation resulting from single collisions in the keV energy range between ${\mathrm{H}}_2^{+}$ initially in the ground electronic and vibrational state incident on He targets. These collisional excitation studies are based on ab initio calculations of the three lowest adiabatic states of the (${\mathrm{HeH}}_2$${)}^{+}$ quasimolecular system and ab initio calculations of the nonadiabatic gradient coupling matrix elements between these three adiabatic states. With use of straight-line trajectories in the classical trajectory approximation, cross sections have been obtained for (1) charge exchange into the ground state of He and (2) collisional dissociation via electronic excitation 1${\mathrm{\sigma }}_{\mathit{g}}$→1${\mathrm{\sigma }}_{\mathit{u}}$ of the ${\mathrm{H}}_2^{+}$ projectile. Furthermore, with a knowledge of the diabatic structure of the (${\mathrm{HeH}}_2$${)}^{+}$ energy levels, (3) the sum of the cross sections for Rydberg excitation of the He target or Rydberg excitation of the ${\mathrm{H}}_2^{+}$ projectile or charge exchange into the repulsive state of ${\mathrm{H}}_2$ was also obtained. The calculated cross sections are in reasonable agreement with available experimentally measured cross sections. The energy thresholds for these cross sections are found to be determined by excitation at level crossings between the ground electronic state and the ${\mathrm{H}}_2^{+}$(1${\mathrm{\sigma }}_{\mathit{u}}$)+He(1${\mathit{s}}^2$) at R≃1.2 a.u. and the ${\mathrm{H}}_2^{+}$(1${\mathrm{\sigma }}_{\mathit{g}}$)+He(1s,2l) at R≃0.7 a.u.

Laser photodetachment on a relativistic ${\mathrm{H}}^{\mathrm{-}}$ beam has revealed several series of resonances in which both electrons are excited. These ‘‘bound states in the continuum’’ appear as dips in the partial production cross sections of various excited states of neutral hydrogen. We present here a detailed account of the experimental observation of the resonances and the results of fits of the measured yields to sets of Fano profiles. A simple analytic formula for the energy-level spacing in this quantum-mechanical three-body system is verified.

A model is developed for the treatment of multielectron ionization and exchange processes in fast ion-atom collisions under the condition that electron-electron interactions may be neglected. The model specifically takes into account ionization and capture from two electron shells of the target and one electron shell of the projectile. The predictions of the model for the case of ionization accompanied by loss of 1–4 electrons from the projectile are compared with experimental results for 40-MeV ${\mathrm{Ar}}^{4+}$ on Ar.

Surface light-induced drift arises under velocity-selective excitation of a low-pressure gas if the accommodation coefficient α for tangential momentum transfer to the surface depends on the state of the gas particles. A kinetic description of this effect is presented. Experiments were performed for rovibrationally excited ${\mathrm{CH}}_3$F colliding with a quartz surface at 300 K. It is found that α depends on the rotational state (J,K) of the molecule much more strongly than on the vibrational state. For the transition (J,K)=(4,3)→(5,3), α is found to increase by δα=1.9×${10}^{\mathrm{-}3}$. This result is shown to be primarily due to the change in magnitude of the rotational angular momentum J, while its orientation with respect to either the molecular figure axis or the surface normal plays a negligible role.

From previous experiments on surface light-induced drift it was found that the coefficient for tangential momentum accommodation in molecule-surface collisions can increase with increasing angular momentum of the molecule. By contrast, various molecular-beam-type experiments yielded the opposite result. These seemingly conflicting data are reconciled in a unified picture describing various phenomena related to molecule-surface interaction for rotating molecules. Using physical arguments it is demonstrated that the accommodation as a function of rotational quantum number should peak around the thermal value, decreasing both for lower and higher rotational quantum numbers of the incoming molecule.