A study is made of the observables of a quantum system in a state which is a wave packet of the discrete spectrum eigenfunctions. An explicit formula is obtained for the time dependence of the observables which is expressed through the elliptical θ functions of time.

The properties of a hydrogen molecule under spatial confinement are studied by diffusion quantum Monte Carlo simulations. The ground-state energy and the bond length of the molecule are evaluated under an equilibrium spheroidal-box condition. Since the calculations of the ground-state properties for this specific system are exact from the diffusion quantum Monte Carlo simulations, the results obtained here can also serve as a criterion to any approximate or variational method applied to highly correlated electronic systems. The possibility of further work to calculate the vibrational frequency and other pressure-dependent physical quantities is discussed.

Using a procedure originally due to Hylleraas, a convenient expansion in coupled spherical harmonics which terminates in a very small number of terms is applied to the treatment of fully correlated two-electron wave functions of any symmetry (total angular momentum, parity, and spin). Coupled equations satisfied by these wave functions are derived which are well adapted to computation and which we discretize on a numerical lattice utilizing the basis-spline collocation method. Use of this method which relies on very flexible basis functions is intended to facilitate subsequently the consideration of time-dependent rearrangments such as autoionization, photoionization, and electron-impact excitation and ionization. Here, we describe the underlying theoretical and computational methods concerning our treatment of the two-electron problem, the lattice discretization, and partial eigensolution by damped relaxation. Results of explicit calculations are given regarding the ground state and two low-lying singly excited states of helium.

The relativistic Fock-space coupled cluster method for the direct calculation of ionization potentials and excitation energies (including fine structure) is presented and applied to atomic Au and its ions. The no-pair Dirac-Coulomb-Breit Hamiltonian is taken as the starting point. The CCSD approximation is implemented (where CCSD indicates coupled cluster with single and double excitations), which includes single and double virtual excitations in a self-consistent manner, incorporating therefore the effects of the Coulomb and Breit interactions to all orders in these excitations. A rather large basis set (21s17p11d7f) of kinetically balanced Gaussian spinors is used to span the atomic orbitals. All calculated energies (ionization potential and electron affinity of Au, excitation energies of Au and ${\mathrm{Au}}^{+}$) agree with experiment to 0.1 eV or better, with an average error of 0.06 eV. Fine-structure splittings are accurate to better than 0.01 eV.

We have calculated sixfold differential (γ,2e) double-photoionization cross sections (6DCS) for helium and for the alkaline-earth atoms Mg and Ca. We use configuration-interaction wave functions for the initial state and two sets of wave functions for the final state: (1) smoothly joined final-state wave functions corresponding to the Coulomb potential at large r and to a pseudopotential at small r and (2) wave functions that are the same as (1) but multiplied by the factor [1-exp(-${\mathit{r}}_{12}$/${\mathit{r}}_{\mathit{C}}$)] to account for the singularity at ${\mathit{r}}_{12}$=0 and the short-range correlation in the final state. To see the effects of the initial-state correlation on the 6DCS, sample calculations are performed with Hartree-Fock initial-state wave functions. In contrast to the results of Le Rouzo and Dal Cappello [Phys. Rev. A 43, 318 (1991)], our 6DCS plots for cases in which both electrons escape with equal energy ɛ=ɛ’=15 eV differ significantly from the cross sections for the case in which the electrons escape with different energies ɛ=5 eV and ɛ’=25 eV. The results show that approximate correlation by means of inclusion of a Coulomb hole into the final-state wave function has a significant effect in some cases for Mg and Ca, but has little effect in the cases studied for He. Comparison with the results of a very recent experiment is made.

We consider the laser-assisted scattering of an electron by an attractive one-dimensional δ-function potential, and solve analytically a coupled-channel Lippmann-Schwinger equation for the full scattering amplitude. Energy, in multiples of the laser frequency, can be absorbed or emitted by the electron during the scattering, and the corresponding superelastic and inelastic, as well as the elastic, scattering amplitudes are all determined exactly. Stimulated recombination resonances are observed in all channels, if the laser irradiance is not too high (${\mathit{I}}_0$≤${10}^{16}$ W/${\mathrm{cm}}^2$, for a binding energy of 0.5 a.u.) The resonance widths are a direct measure of the multiphoton ionization rates from the bound level. For stronger fields the resonances broaden and disappear into the background. For ultrastrong fields (${\mathit{I}}_0$>${10}^{17}$ W/${\mathrm{cm}}^2$) narrow structures reemerge just below multiphoton thresholds. An analytic continuation of the scattering amplitude into the complex energy plane is performed, and the poles of the scattering amplitude are located as a function of laser frequency and irradiance. The question of stabilization for this potential is reconsidered in the light of the present information.

Cross sections for positron- and proton-impact ionization of atomic helium have been calculated using a coupled-state method. The single-electron Hamiltonian of the helium atom was diagonalized in a finite Hilbert space. We included nine radial pseudostates for each s, p, d, and f angular momentum. The time-dependent Schrödinger equation was solved by using a unitary matrix, U matrix, and a hyperbolic trajectory for both projectiles. Our positron results, covering the energy range 60–1000 eV, are compared with available measurements and theoretical calculations. Agreement with the most recent measurement is reasonably good over the entire positron energy range. The proton-impact cross sections are obtained for the proton energy range 10–1000 keV and also show good agreement with the measurements over the entire energy range. We conclude that the lower ionization cross sections for positron impact in comparison with those for proton impact are due to the bigger deflection suffered by the positron in the collision.

This work presents a theoretical study of rovibrational excitation in electronically elastic collisions of He on either ${\mathrm{H}}_2$ or ${\mathrm{D}}_2$ in the collision energy range 100 eV≤${\mathit{E}}_{\mathrm{inc}}$≤2 keV. Earlier classical trajectory collision calculations, which predicted the rovibrational excitation energy to follow a universal scaling law, are here generalized to (1) encompass vibrational excitation caused by a three-body force representing the He interacting with the ${\mathrm{H}}_2$ covalent bond, and (2) incorporate quantization of vibrational excitation by a semiquantal ansatz imposed on the otherwise classical calculations. Quantization of vibrational excitation is shown to cause a breakdown of the scaling law predicted by the fully classical theory. The collisional excitation calculations utilize straight-line trajectories in the framework of the impulsive approximation, and are based on an improved parametric fit to the ab initio interaction energy surface for the ${\mathrm{HeH}}_2$ triatomic molecular system. In addition to the usual two-body Bohr and Born-Mayer terms describing the He-H interactions, the new interaction potential incorporates a three-body term to describe the contribution arising from the He interacting with the H-H covalent bond. The three-body force gives rise to some vibrational excitation phenomena, which are here explored. Good agreement is obtained with experimental measurements on rovibrational excitation energies produced in quasielastic collisions of He on ${\mathrm{D}}_2$

Differential cross sections have been determined in two ways for electron transfer and elastic scattering in collisions between protons and ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$ (1s) ions at center-of-mass energies from 4 to 25 keV. First, the transition coefficients in the eikonal expression for the scattering amplitudes have been calculated using a triple-center, atomic-state approach. Second, a double-center, Sturmian-pseudostate approach has been used. The agreement between the two sets of differential cross sections is outstanding at all energies. A crossed-beam experiment is now underway to measure the differential cross section for electron transfer.

Recently, experimental evidence for the existence of a bound state of the ${\mathrm{HeH}}^{2+}$ molecular ion was reported by Ben-Itzhak, Gertner, Heber, and Rosner [Phys. Rev. Lett. 71, 1347 (1993)]. This three-body system was predicted by Bates and Carson to have bound vibrational states in the 2pσ electronic state despite the strong repulsion potential between the two nuclei. These 2pσ vibrational states decay via an electronic transition to the 1sσ repulsive ground state with a mean lifetime of about 1 nsec. We have used the ‘‘fragment-fragment’’ coincidence method to measure the mean lifetime of the ${\mathrm{HeH}}^{2+}$ molecular ions which dissociate in flight before reaching the detector. The yield of these molecular ions was measured as a function of the distance between the target cell and the analyzer exit. From this measurement a mean lifetime of 3.9±0.4 nsec was determined. The 2pσ→1sσ transition rates for all vibrational states have been calculated within the Born-Oppenheimer approximation using available oscillator strengths. It is shown that the transition rates decrease with increasing vibrational energy because of the ‘‘stretch’’ of the molecular ion. The distribution of 2pσ vibrational states populated by vertical transitions from stripping the ${\mathrm{HeH}}^{+}$ electronic ground state was evaluated, and the resulting decay curve compares well with the measured one.

The contributions of Coster-Kronig resonances to the electron-impact excitation rate coefficients have been calculated for six F-like ions with Z=26, 34, 42, 47, 54, and 63. The calculations are carried out using the relativistic distorted-wave approximation and the multiconfiguration Dirac-Fock model. We found that resonance excitation via Coster-Kronig transitions is the dominant excitation mechanism at low temperatures for Z≤34 and is as important as the direct excitation for heavier ions. In addition, we found that the effects of relativity can reduce the rate coefficients by more than an order of magnitude at electron temperatures T<100 eV.

A 15-state R-matrix calculation has been carried out at 530 energies ranging from the n=2 threshold up to n=5 threshold at 13.06 eV to map out the resonant profiles for the n=2 inelastic integral and differential cross sections, and the angular distribution of the spin asymmetry in the inelastic scattering of spin-polarized electrons by the spin-polarized hydrogen atoms at angles 0°, 30°, 55°, 70°, 90°, 125°, and 180° for the 1s→2s transition. The calculations are compared with the experiments and the feasibility studies of using the electron-energy-loss experiments in the investigation of resonances with positions higher than the n=2 threshold have been carried out.

By exciting the M shell of atomic zinc in the 80–110-eV photon energy range with synchrotron radiation, and by using photoelectron and photoion detection, we have located the 3${\mathit{p}}^5$3${\mathit{d}}^{10}$4${\mathit{s}}^2$ns (and nd) excited states in the 91–99-eV region. Resonant satellites are observed, allowing us to demonstrate the dominant role played by the 3${\mathit{p}}^{\mathrm{-}1}$${\mathit{ns}}^1$→3${\mathit{d}}^{\mathrm{-}2}$n’lɛf interaction upon the decay of the 3p→ns excited states. The 3${\mathit{p}}^{\mathrm{-}1}$${\mathit{ns}}^1$→3${\mathit{d}}^{\mathrm{-}2}$n’lɛf super-Coster-Kronig processes produce a large broadening of the 3p excited states which form series of overlapping states. The resonant satellites lying in the high-energy region are singly ionized states of 3${\mathit{p}}^6$3${\mathit{d}}^8$4${\mathit{s}}^2$n’l configurations, which autoionize into the various 3${\mathit{p}}^6$3${\mathit{d}}^9$4p or 3${\mathit{p}}^6$3${\mathit{d}}^9$4s states of ${\mathrm{Zn}}^{2+}$. Ab initio calculations using intermediate coupling have been performed and display good quantitative agreement with the experimental results.

Electron-capture and deexcitation processes in collisions of excited ${\mathrm{Na}}^{\mathrm{*}}$(3p) atoms with ${\mathrm{He}}^{+}$ ions are studied in the energy range 0.1–7 keV/u by using the molecular-orbital-expansion method within the semiclassical framework. The integral alignment (${\mathit{A}}_{20}$), alignment angle (γ), and orientation (O) parameters of excited He(2 ${}_{}{}^1{}_{}{}^{}$P,2 ${}_{}{}^3{}_{}{}^{}$P) orbitals resulting from electron capture are also determined. Furthermore, the effects of the initial alignment of the ${\mathrm{Na}}^{\mathrm{*}}$(3${\mathit{p}}_{\mathit{m}}$) orbital on the cross sections, O, and γ parameters are investigated. The present results show that the ratio of theoretical cross sections for electron capture by the ${\mathrm{He}}^{+}$ ion in collisions with the ${\mathrm{Na}}^{\mathrm{*}}$(3p) atom and the ground state Na(3s) atom, respectively, is nearly equal to unity in the energy range studied here. The results also show that the O and γ parameters are significantly different for the singlet and triplet manifolds, implying that different collision dynamics for He(2p) formation govern in each manifold. These parameters can be effectively controlled by adjusting the initial alignment of the ${\mathrm{Na}}^{\mathrm{*}}$(3p) orbitals.

A unified treatment for electron-ion recombination has been developed and applied to detailed calculations for cross sections and total recombination rate coefficients for a number of atoms and ions. The ab initio calculations are carried out in the close-coupling approximation employing the R-matrix method for the bound and the continuum states of the electron-ion system. All final states of the recombined system are taken into account and the present method subsumes both the radiative and the dielectronic recombination (RR and DR) processes over all energy and temperature ranges of practical importance. Recombined states of the electron-ion system are divided into two groups: (a) n≤${\mathit{n}}_0$ and (b) ${\mathit{n}}_0$<n≤∞. Photoionization cross sections are calculated for all bound states of group (a), typically a few hundred bound states, referred to as low-n states, including a detailed energy resolution of the several infinite series of autoionizing resonances converging onto the various excited states of the core ion included in the close-coupling expansion. High-n states of group (b) are treated primarily through the theory of DR developed by Bell and Seaton [J. Phys. B 18, 1589 (1985)]. DR collision strengths with detailed resonance structures are presented.

The detailed and the resonance-averaged DR collision strengths show characteristic peaks at the target thresholds of the core ion corresponding to dipole-allowed transitions. Individual bound states of the e+ion system with dominant contribution to low-energy recombination are described. The present results demonstrate the importance of (i) recombinations to excited states (particularly the metastable states), and (ii) low-energy autoionizing resonances, both of which result in large contributions to effective electron-ion recombination. The individual contributions of the excited bound states of the e+ion system are calculated and their relative contribution to the total are discussed. The general pattern of the recombination rate, as a function of electron temperature, is studied along an isoelectronic sequence. It is found that while the low-energy (temperature) recombination increases with ion charge z, the relative high-energy (temperature) contribution to the total decreases; i.e., viewed as independent processes, the RR part increases while the DR decreases with z. Total recombination rate coefficients for several atoms and ions (C ii, S ii, C ii, N ii, O iii, F iv, Ne v, and Si ix) are obtained over the entire temperature range of possible interest in applications. Comparisons are made with earlier works on RR and DR.

Resonance-enhanced two-photon dissociation from the ground ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ (${\mathit{v}}_{\mathit{g}}$=0,${\mathit{J}}_{\mathit{g}}$) state of ${\mathrm{H}}_2$ to the final continua of EF, GK, and I states has been studied using both linear parallel and crossed polarizations of the two-photon fields. The first field creates an aligned population in the intermediate resonant state B ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ (${\mathrm{v}}_{\mathrm{i}}$=0,3,${\mathit{J}}_{\mathit{i}}$) for which the reduced density-matrix description has been adopted. This intermediate state is dissociated through coherent excitation of a number of near-resonant discrete vibrational levels, bound and quasibound, of HH¯ and I, respectively, as well as by direct transition to the continua of EF, GK, and I by absorption from the second field. The nonadiabatic interaction of the HH¯ and I levels with the continuum of GK gives these states predissociating characteristics and the whole process can be formulated in terms of overlapping Fano resonances. The nonadiabatic couplings of the continua of I and EF with the HH¯ bound levels have been neglected because of their smallness. The interference of the transition amplitudes to different overlapping predissociating resonances gives the resultant structure in the dissociation probability which is studied for the second photon wavelength covering a range between the dissociation threshold of the final states and the ionization threshold of ${\mathrm{H}}_2$. The dissociation cross section obtained from these nonadiabatic calculations are found to be drastically altered from the adiabatic and Born-Oppenheimer results.

X rays produced in the collisions of 94–222-MeV ${\mathrm{O}}^{8+}$ ions with ${\mathrm{H}}_2$ and He targets have been measured. Resulting spectra have been analyzed to determine absolute yields, profile widths, and energies for x rays emitted in the process of radiative electron capture (REC). These measurements are compared with predictions based on impulse-approximation calculations, using differential cross sections for radiative recombination (RR) folded with target Compton profiles. Measured absolute peak energy positions and profiles are found to be in good agreement with these simple theoretical estimates. Cross sections derived from REC yields are compared with other measurements and with theoretical RR values. A small systematic discrepancy between experimental and theoretical cross sections is noted.

Differential cross sections and angular-correlation parameters relating to elastic scattering and electron-impact excitation of hydrogen atoms to the n=3 and n=2 states are presented for energies of 16, 20, 35, 54, and 100 eV. Results are obtained from a close-coupling calculation using a 17-state target basis including seven exact states and ten pseudostates. Comparisons are made with experiment and with other calculations.

Two independent types of ab initio calculations for three electrons in the field of a proton have been carried out. Neither calculation shows any evidence for the existence of a resonant state of ${\mathrm{H}}^{2\mathrm{-}}$ contributing to e+${\mathrm{H}}^{\mathrm{-}}$ inelastic scattering, at energies above the three-electron escape threshold. One of the methods used is based on an eigenchannel R-matrix calculation carried out within a reaction volume of finite radius ${\mathit{r}}_0$, followed by an averaging procedure over ${\mathit{r}}_0$. A second method is based on a configuration-interaction study of the dependence of the 2${\mathit{s}}^2$2p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ resonance on the nuclear charge Z. These calculations suggest that previous experimental and theoretical studies of this system were in erroneous agreement that two ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ resonances exist in ${\mathrm{H}}^{2\mathrm{-}}$ above the three-electron escape threshold. We also show that the earlier apparent agreement between experimental and theoretical resonance properties would violate unitarity of the collision matrix.

Radiative electron capture (REC) from a low-Z target atom into a bare high-Z projectile is described in the impulse approximation for the momentum distribution of the captured electron in the initial target state. Otherwise the treatment is rigorous by using exact relativistic Coulomb wave functions for the bound and continuum projectile states. As an application of the computer program, photon spectra and differential cross sections have been calculated for 295-MeV/u ${\mathrm{U}}^{92+}$+N collisions. The angular distributions for K-shell REC as well as for L-shell REC show pronounced deviations from ${\sin }^2$θ. Cross sections for radiative recombination with capture into the K shell and into the L subshells are presented for projectile charges between 20 and 100 and for energies between 100 MeV/u and 2 GeV/u.