Soft-x-ray emission spectra for the La ${\mathit{N}}_{4,5}$${\mathit{O}}_{2,3}$ transitions in lanthanum aluminate ${\mathrm{LaAlO}}_3$ include contributions from several relatively intense multiplet lines near 80 eV. The appearance of this spectrum contrasts sharply with the three diagram lines observed for the ${\mathit{N}}_{4,5}$${\mathit{O}}_{2,3}$ emission spectrum of Ba in ${\mathrm{BaF}}_2$. An atomic model of the La ${\mathit{N}}_{4,5}$${\mathit{O}}_{2,3}$ transition, assuming single occupancy of the 4f shell by a spectator electron, provides a good approximation of the measured spectrum. Emission features due to the low-energy ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ and ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}^{\mathit{o}}$ terms of the 4${\mathit{d}}^9$4f configuration are also apparent in the ${\mathrm{LaAlO}}_3$ emission spectra, but not in emission spectra from ${\mathrm{BaF}}_2$. Reflection measurements indicate that the 4f level is not occupied in the ground state in ${\mathrm{LaAlO}}_3$. The data suggest that charge transfer from ligand orbitals following creation of a 4d vacancy prior to the emission process is the predominant mechanism giving rise to the required 4f occupancy.

The most recent measurements leading to improved Li I energy levels appeared in the late 1950s. Since then, many high- and ultrahigh-precision spectroscopy techniques have been used to measure the fine and hyperfine structures and isotope shifts of this atom. Most previous measurements were made on ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$. Using high- and low-current hollow cathode sources and Fourier-transform spectrometry, we have made measurements in both ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ including nine previously unmeasured infrared lines. Wave-number measurements were obtained on 34 lines from 1829 to 30 925 ${\mathrm{cm}}^{\mathrm{-}1}$. The strongest lines have been determined to ±0.0010 ${\mathrm{cm}}^{\mathrm{-}1}$. We also measured 22 new isotope shifts, and added specific mass shifts for five levels. The resonance lines at 6707 Å in both isotopes, emitted by low-current, commercial lithium hollow cathode sources, were measured to ±0.0005 ${\mathrm{cm}}^{\mathrm{-}1}$. The energy levels have been recalculated using the new data.

We investigate the classical dynamics of the problem of two centers and a finite dipole by means of a common Hamiltonian model. Conditions for trapped orbits are determined first by a qualitative analysis of the effective potential, revealing two types of bifurcation in the two-center problem as a control parameter passes through a critical value ${\mathrm{\mu }}_{\mathit{c}}$. For equal masses there is a pitchfork bifurcation, for unequal masses a tangent bifurcation. Separating the common Hamiltonian in elliptic coordinates shows that the third invariants for the two-center problem and the finite dipole are isomorphic in scaled variables. Explicit trapping conditions are then found in terms of the coefficients of two quartics. A critical-point analysis for the finite dipole shows that a potential well exists for all values of scaled angular momentum below the same critical value ${\mathrm{\mu }}_{\mathit{c}}$, at which the elliptic point runs off to infinity. In this case the existence of the third invariant does not confine any orbits not already trapped by energy conservation. A similar analysis of the effective potential for the point dipole shows that the only trapped orbits besides those impacting the origin are unstable zero-energy trajectories lying on a sphere.

The finite difference expression for the hardness of atoms and molecules, i.e. half the difference between the ionization potential and the electron affinity according to Parr and Pearson [J. Am. Chem. Soc. 105, 7512 (1983)], is expressed here as an explicit functional of the Kohn-Sham orbitals, of the Kohn-Sham eigenvalue differences, of the Coulomb potential, and of certain parts of the exchange-correlation potential. The functional is derived by exploiting the relationship between uniform coordinate scaling of the electron density and a perturbation theory with respect to the electron-electron interaction. The hardness is obtained as a perturbation expansion consisting of terms which each are connected to a specific order of ${\mathit{e}}^2$ with e being the electronic charge. This allows one, in principle, to determine the hardness exactly within the Kohn-Sham method or, in actual applications, up to some chosen order in ${\mathit{e}}^2$. The actual expansion is displayed through second order. To some extent the results are also valid in the case of band gaps of solids.

Explicitly correlated Gaussian functions are applied to extensive variational calculations of the ${}_{}{}^1{}_{}{}^{}$S ground state of the beryllium atom. The convergence of the energy with respect to the basis-set expansion length is investigated. The nonrelativistic clamped-nuclei energy computed from a 1200-term wave function equals -14.667 355 hartree and is in error by about 1 ${\mathrm{cm}}^{\mathrm{-}1}$. This is the lowest variational upper bound to the beryllium ground-state energy reported to date and it shows that recent empirical estimates of the nonrelativistic energy of the Be atom lie slightly too high. Several expectation values, including powers of interparticle distances and the Dirac δ function, are computed. The nuclear magnetic shielding constant, the magnetic susceptibility, the specific mass shifts, the transition isotope shift, and the electron density at the nucleus position are evaluated.

B splines with carefully adjusted knot sequences are used as basis functions in cylindrical coordinates to calculate the energy levels of the low-lying (m=0) states of a hydrogen atom in a uniform magnetic field of arbitrary strength by using the variational method. The strength of the field calculated covers a range from γ=0 to γ=100 000 for the ground state and up to γ=2000 for the 2s and 2p states. A precision of up to ten digits in the region of 0≤γ≤200 and up to eight digits for γ≳200 has been maintained for all the results presented. In order to test the applicability of the B splines for the higher excited states, the energy levels of 3s, 3p, 3d, and 4f states with m=0 in the field region of 0≤γ≤10 have also been calculated. Even though the number of basis sets was kept constant, the accuracy of the results was maintained in the intermediate field regions and also in the very strong field regions, which are known to be difficult for achieving high accuracy. The flexibility of the B splines is demonstrated here by the uniformly accurate results in the transition from spherical symmetry to Landau symmetry as the field strength of the magnetic field is increased. The energy levels of all the low-lying states with various ranges of magnetic field strength have been compared with published values. They are in good agreement with the most updated values and compare favorably with all other published results.

A comparison of nonlinear classical resonances with the nonlinear quantum resonances has been well established for semiclassical systems. However, systems in which tunneling is present are no longer semiclassical and the correspondence between the classical and quantum systems breaks down. We examine nonlinear quantum resonances in a system consisting of a triangular potential well (formed by a static field plus an impenetrable wall) with an attractive δ-function potential well and a weak external time-periodic force. In this system, tunneling is important and nonlinear quantum resonances that have no classical counterpart can occur. In the second part of this paper, we remove the impenetrable wall and consider this system to be a model of a bounded particle subject to a strong external static field and a weak periodic field. The presence of the static field leads to strong enhancement and suppression of the single-photon photodetachment rates for certain frequencies. This effect has been observed experimentally in the photodetachment of ${\mathit{H}}^{\mathrm{-}}$ ions and predicted by theoretical models. The model present here is particularly useful because the photodetachment spectrum can be obtained analytically and leads to greater insight into more realistic models.

Ground-state energies and frequencies of collective modes for the Lipkin model are evaluated within the framework of a microscopic functional approach using functional relations between the ground-state energy, the matrix of the effective interaction R^ between particles in the medium, and the linear response function of a system. A strict functional equation for R^ is derived. A special version of the well-known local approximation is elaborated to transform this equation into a system of integro-differential equations, which is solved numerically. Most of the numerical calculations are carried out in the region of moderate coupling constants, where the ground state possesses the same symmetry as the noninteracting system. The deviation of the calculated ground-state energies from the exact values is found not to exceed 0.1% in a wide region of the variation of the interaction strength, including the vicinity of the phase-transition point. This is better by approximately one order of magnitude than the results from the established many-body approaches.

We use many-body perturbation theory to examine the interaction of positrons with atoms. Our calculations predict positron s-type bound states with binding energies 0.87, 0.23, 0.35, and 0.045 eV for Mg, Zn, Cd, and Hg atoms, respectively. This binding is due to the positron-atom polarization potential and virtual positronium formation. A simple criterion is used to find other atoms that are likely to form bound states with positrons. Among the most probable candidates are Ti, V, Cr, Mn, Zr, Nb, and Mo.

The lifetime of 800-MeV ${\mathrm{H}}^{\mathrm{-}}$ ions against electron detachment in a static electric field was measured over a range of eight orders of magnitude in experiments at the High Resolution Atomic Beam Facility of the Los Alamos Meson Physics Facility. The ions traversed a linear gradient magnetic field of 1.3-T peak strength resulting in a 6-MV/cm peak rest-frame electric field capable of stripping a large fraction of ${\mathrm{H}}^{\mathrm{-}}$ ions. The unstripped ${\mathrm{H}}^{\mathrm{-}}$ ions, neutral ${\mathrm{H}}^0$ atoms, and protons were detected 5.5 m from the magnet. This spectrum was analyzed to determine the lifetime of the ${\mathrm{H}}^{\mathrm{-}}$ ion versus electric-field strength and the results were compared with previous studies. Three parametrizations of the lifetime formula based on an existing theory were used to calculate the stripping probability. The data were fit to the lifetime formula and good agreement with theoretical predictions was found. Finally, a possible experiment for observing excited states of ${\mathrm{H}}^{\mathrm{-}}$ is briefly discussed.

From time-of-flight spectra of metastable ${\mathrm{Ar}}^{\mathrm{*}}$ atoms emerging from sustained discharges in Ar, we observe discrete nonthermal peaks due to excited products of dissociative recombination (DR) of ${\mathrm{Ar}}_2^{+}$ formed by reactions in the discharge. These peaks are in addition to the expected Boltzmann distributions of metastable atoms from direct excitation by fast primary electrons. From the peak velocities, and thus the kinetic energies released in the dissociation, the DR product states are uniquely determined, regardless of subsequent radiation. As we have previously found from ${\mathrm{Kr}}_2^{+}$ [A. Barrios et al., Phys. Rev. Lett. 69, 1348 (1992)], most of the excited DR products are (n+1)s states, but ${\mathrm{Ar}}_2^{+}$ also yields smaller amounts of 4p and 3d states. We have also recently shown [G. B. Ramos et al., Phys. Rev. A 51, 2945 (1995)] that, surprisingly, in studies of ${\mathrm{Ne}}_2^{+}$ and ${\mathrm{Ar}}_2^{+}$ DR, a substantial but undetermined fraction of reactions go to a purely ground-state channel. In addition, we have found that under certain conditions in Ar discharges, the relative amount of the higher excited-state products, including 4p, 3d, 5s, and 5p can be dramatically influenced. The velocity peaks also become narrower than expected from the thermal distribution of the parent ${\mathrm{Ar}}_2^{+}$ as the energy level in the product atom increases. These studies in argon discharges have included variations in source pressure, discharge voltage, and strength of the axial magnetic field.

In a two-step pulsed laser experiment 4${\mathit{f}}_{5/2}$7h J=4,5,6, autoionizing levels of Ba were excited. The 4${\mathit{f}}_{5/2}$7h levels interact with 6${\mathit{d}}_{5/2}$ni levels resulting in complex interference patterns. The excitation spectra were calculated using the eigenchannel R-matrix method in combination with multichannel quantum-defect theory. These R-matrix calculations reproduce the excitation spectra, including the interference patterns which involve q-reversal and stabilization against autoionization in the 6${\mathit{d}}_{5/2}$ni series, very well. The excitation spectra for J=5 are also analyzed using a phase-shifted R-matrix model in which only three channels had to be included to reproduce the main experimental features. The three-channel model clearly shows that the stabilization against autoionization in the 6${\mathit{d}}_{5/2}$ni Rydberg series is a result of interference in the decay of 4${\mathit{f}}_{5/2}$7h and 6${\mathit{d}}_{5/2}$ni levels, autoionizing into the same 6${\mathit{d}}_{3/2}$εi continuum.

Charge-exchange processes in fast collisions of ${\mathrm{F}}^{\mathit{q}+}$ (q=2–9) on Ne and Ar gas targets have been studied using the projectile–recoil-ion coincidence method. The target ionization without a projectile charge change increases with increasing projectile charge approximately as ∼${\mathit{q}}^{1.4}$. This dependence is weaker than the ${\mathit{q}}^2$ dependence predicted by the first Born approximation because of the large ionization probabilities involved. The single-electron-capture cross sections follow the known ${\mathit{q}}^3$ scaling law, while the double-electron-capture cross sections display a ${\mathit{q}}^6$ dependence, as predicted by the independent-electron approximation for small capture probabilities. Single- and double-electron loss from the L shell decreases with increasing q mainly because of the decrease in the number of L-shell electrons, while binding-energy effects play only a minor role. In contrast, the large sudden decrease in electron-loss cross sections once K-shell electrons must be removed is due to the large increase in binding energy.

We have measured the energies and autoionization rates of the Mg 3pnf J=4 autoionizing states and the energies of the 3pnf J=2 states. The J=2 autoionization rates are too small to measure. The observed energies and autoionization rates can be described by a simple independent-electron model based on a ${\mathrm{Mg}}^{+}$ ion and a hydrogenic electron.

The threshold behavior of the single-photon double-ionization cross section of atomic oxygen has been studied using vacuum uv radiation from a synchrotron storage ring. The double-ionization cross section appears to follow a power law ${\mathit{E}}^{\mathrm{\alpha }}$ (where E is the kinetic energy of the two electrons) from its threshold to about 2.0 eV above with an exponent α=1.08±0.03, which is consistent with Wannier’s theoretical value of 1.056. The cross section also shows the influence of the doubly excited 2s2${\mathit{p}}^3$${\mathit{nln}}^{\prime }$${\mathit{l}}^{\prime }$ (n,${\mathit{n}}^{\prime }$≳3) neutral states, among which the first three converge to the 2s2${\mathit{p}}^3$${(}^5$${\mathit{S}}^{\mathit{o}}$)4p${(}^6$${\mathit{P}}^{\mathit{o}}$) ionic state of oxygen.

Electron spin exchange with spin one paramagnetic species has been investigated with particular emphasis on the cases of hydrogen (H=${\mathit{p}}^{+}$${\mathit{e}}^{\mathrm{-}}$), Mu (Mu=${\mathrm{\mu }}^{+}$${\mathit{e}}^{\mathrm{-}}$), positronium (Ps=${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$) colliding with ${\mathrm{O}}_2$. The effects of spin exchange on electron spin relaxation (ESR), muon spin relaxation (μSR), and positronium lifetime measurements are described in terms of the difference in phase shifts between quartet and doublet encounters (Δ), which will allow one to interpret ESR, μSR, and positron data in a unified way and help one to understand isotope mass effects not only in spin exchange but also in chemical reactions, which often compete with spin exchange. For instance, the ESR and μSR relaxation rates in high transverse fields are expressed, in terms of the rate of collisions λ, as ${\lambda }_{\mathit{T}}^{\mathit{e}}$=(32/27)λ ${\sin }^2$(Δ/2) and ${\lambda }_{\mathit{T}}^{\mathrm{\mu }}$=(16/27)λ ${\sin }^2$(Δ/2), respectively, and the so-called statistical factors, such as (32/27) and (16/27), are strong functions of the magnitude and direction of the applied field.

A single-channel distorted-wave approximation is used to calculate the one-electron capture cross section into an arbitrary state (nlm) of ${\mathrm{Ti}}^{22+}$, ${\mathrm{V}}^{23+}$, and ${\mathrm{Fe}}^{26+}$ from the ground state of a hydrogen atom. Since the interaction between the heavy projectile and the target electron is stronger, we represent the initial-channel wave function by a continuum distorted wave while the wave function in the final channel is taken to be a traveling atomic orbital. The nth partial cross sections are found to be in qualitative agreement with previous calculations for some other systems. It is found that at high energies the value ${\mathit{n}}_{\max }$, where the nth partial cross section is maximum, is larger by a few steps than obtained from the ${\mathit{n}}_{\max }$=${\mathit{Z}}^{3/4}$ model. However, for a fixed projectile ${\mathit{n}}_{\max }$ moves towards the smaller values as the energy increases. The l dependence of the cross sections are also studied at different energies at the corresponding ${\mathit{n}}_{\max }$. We have further studied the mth partial cross sections at various energies and at the corresponding ${\mathit{n}}_{\max }$ for several l values. It is found that the contributions from higher m values are decreasing rapidly for m≳5.

The photodissociation of doubly excited ${\mathrm{H}}_2$ has been experimentally investigated. Using the pulsed character of the incident synchrotron radiation, the time analysis of the atomic fragment fluorescence Balmer-α (${\mathrm{H}}_{\mathrm{\alpha }}$) decay was used for identification of the fragments. The measured branching ratios of the H(3l) fragments at a given photon energy contain information about the dynamic behavior of the photodissociation. The states of the first Rydberg series, ${\mathit{Q}}_1$(2pσ,nlλ), dissociating into H(1S)+H(n=3) lead almost to H(1S)+H(3S) fragments; the state involved can be identified from the correlation diagram as the (2p${\mathrm{\sigma }}_{\mathit{u}}$,4d${\mathrm{\sigma }}_{\mathit{g}}$) configuration. The photodissociating states of the second Rydberg series, ${\mathit{Q}}_2$(2pπ,nlλ), lead to H(2p)+H(n=3), the H(n=3) fragments being a mixture of H(3S) and H(3D) in a ratio of about 2:1. In order to identify the relevant ${\mathit{Q}}_2$ state, the energy ordering in the manifold of the molecular states dissociating into ${\mathrm{H}}^{\mathrm{*}}$(n=2) and ${\mathrm{H}}^{\mathrm{*}}$(n=3) has been established by calculating the whole dipole-dipole long-range interaction.

Measurements of the circular polarization of Balmer-α radiation emitted by excited hydrogen atoms, following the transmission of (20–50)-keV protons through thin, tilted amorphous carbon foils, exhibit markedly unexpected behavior as a function of exposure of the foil to the proton beam. Specifically, the circular polarization changes from an initially well understood tilt-angle dependence to a behavior which, for low tilt angles, gives the opposite handedness of circular polarization from that predicted. In addition, the degree of alignment, indicated by the linear Stokes parameter M/I, is enhanced also as a function of dose. These changes in the tilt-angle dependence of the Stokes parameters have been systematically correlated with beam-induced graphitization of the foil, which is observed to occur from Raman measurements.

We analyze above-threshold ionization through an autoionizing resonance and show that this process is strongly enhanced when the photon is tuned near the minimum of the primary photoionization peak; the enhancement occurs also when the free-free transitions are taken into account. We demonstrate that this property can be exploited to enhance the harmonic generation.