We have obtained solutions from the state-specific complex eigenvalue Schrödinger equation (CESE) for the dc-field-induced energy shifts and widths of the Li 1${\mathit{s}}^2$3s ${}_{}{}^2{}_{}{}^{}$S, 3p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$, 3d ${}_{}{}^2{}_{}{}^{}$D, Na KL3s ${}_{}{}^2{}_{}{}^{}$S, 3p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$, 4s ${}_{}{}^2{}_{}{}^{}$S, and 3d ${}_{}{}^2{}_{}{}^{}$D states. These allowed us to compute tunneling rates and scalar and tensor polarizabilities and hyperpolarizabilities. Our values for the polarizabilities are compared with earlier theoretical and experimental ones. We have also computed the tunneling rates using a previously published semiclassical formula and have compared the ab initio results with the semiclassical ones. Due to electronic structure and spectral effects, quantitative as well as qualitative differences occur.

We have measured the dielectronic satellite spectrum for heliumlike Co xxvi trapped and excited in an electron-beam ion trap using a high-resolution x-ray spectrometer in the von Hámos geometry. By sweeping the electron-beam energy across the individual dielectronic recombination resonances, we have determined the relative resonance strengths of the strongest resonances populating doubly excited levels in lithiumlike and berylliumlike cobalt. Most measured dielectronic satellite strengths compare well with theory. A discrepancy with theoretical values is noted for the resonance strength associated with levels (1${\mathit{s}}_{1/2}$2${\mathit{p}}_{3/2}^2$${)}_{3/2}$ and (1${\mathit{s}}_{1/2}$2${\mathit{s}}_{1/2}$2${\mathit{p}}_{1/2}$${)}_{1/2}$. Their values of 49.8±3.2×${10}^{\mathrm{-}20}$ ${\mathrm{cm}}^2$ eV and 22.9±6.4×${10}^{\mathrm{-}20}$ ${\mathrm{cm}}^2$ eV, respectively, are almost twice the size predicted by theory.

In this paper we investigate Coulomb correlation effects in the He atom by studying the structure of the static and dynamic Coulomb hole charge distributions as determined by the analytical 39-parameter correlated wave function of Kinoshita. The static Coulomb hole, which is defined in terms of the radial electron-electron distribution function, shows that as a result of Coulomb repulsion there is a reduction in probability of electron approach within a distance of one atomic unit and an increase in this probability for greater separations. The dynamic Coulomb hole defined directly in terms of the pair-correlation density describes the probability of finding one of the electrons given the position of the other. We thus demonstrate how the two electrons are correlated as a function of the nonuniform density of the atom. We also investigate the correlation potential ${\mathit{W}}_{\mathit{c}}$(r) of the work formalism, which is the work done to move an electron in the force field of the dynamic Coulomb hole charge. The structure of ${\mathit{W}}_{\mathit{c}}$(r) is similar to the exchange potential ${\mathit{W}}_{\mathit{x}}$(r) (which is the work done to move an electron in the force field of the Fermi hole), in that it is attractive, monotonic, and has zero slope at the nucleus. However, as a result of the structure of the Coulomb hole for asymptotic electron positions, and the fact that its total charge is zero, the potential ${\mathit{W}}_{\mathit{c}}$(r) vanishes rapidly in the classically forbidden region.

Thus, the asymptotic structure of the exchange-correlation potential ${\mathit{W}}_{\mathit{x}\mathit{c}}$(r) of the work formalism is that of ${\mathit{W}}_{\mathit{x}}$(r) which is (-1/r). We also detemine via the Kinoshita wave function the correlation potential ${\mathrm{\mu }}_{\mathit{c}}$(r) of Kohn-Sham theory, which differs from ${\mathit{W}}_{\mathit{c}}$(r) in that it also incorporates the effects of the correlation contribution to the kinetic energy. Consequently, it is less attractive than ${\mathit{W}}_{\mathit{c}}$(r), but also has zero slope at the nucleus. However, as is known, the potential ${\mathrm{\mu }}_{\mathit{c}}$(r) is nonmonotonic, since it goes positive within the atom, then becomes negative in the classically forbidden region, finally vanishing asymptotically as a negative function. Since the exchange potentials of the work formalism and Kohn-Sham theory are the same for this atom, and because ${\mathit{W}}_{\mathit{c}}$(r) is strictly representative of Coulomb correlations, we attribute the nonmonotonicity and positiveness of the Kohn-Sham potential ${\mathrm{\mu }}_{\mathit{c}}$(r) to the correlation kinetic energy. This conclusion is consistent with the result that the difference between the correlation energies determined within the work formalism from the dynamic Coulomb hole and Kohn-Sham theory is equal to the correlation contribution to the kinetic energy.

In this paper we consider the time evolution of wave-packet tunneling through a potential barrier. Using a path-summation approach, we can describe the quantum evolution in terms of particle trajectories both in the allowed and forbidden regions. Near the barrier edges, where the potential changes rapidly, the wave aspects dominate. These make the trajectories branch into infinite families of paths, which have to be included in the summation. Combining these features, we treat correctly the complementary aspects of the full quantum process, and this allows us to obtain a computational method that gives accurate numerical results with considerably less expenditure of computer time than a direct integration of the Schrödinger equation. We test the method on a simple rectangular potential by comparing the calculations with both conventional wave scattering results and computations from the Schrödinger equation. A general potential can be approximated by a staircase, which allows the application of our method. A simple adiabatic extension is shown to work excellently for the case of a periodically modulated barrier.

In this paper isotope shifts (IS’s) and hyperfine structure hfs in 16 transitions of singly ionized samarium are presented. The IS’s, which, to our knowledge, have not been determined previously, and the hfs are measured by collinear fast-ion-beam–laser spectroscopy. The ions are excited from metastable levels in the 4${\mathit{f}}^6$${(}^7$F)5d configuration to levels in the 4${\mathit{f}}^5$ 5d6s? and 4${\mathit{f}}^6$${(}^7$F)6p? configurations with laser light in the red and orange part of the visible spectrum. The IS’s between the isotopes ${}_{}{}^{147\mathrm{-}150,152,154}{}_{}{}^{}\mathrm{Sm}$ ii are measured for two transitions while the IS’s between the even isotopes ${}_{}{}^{148,150,152,154}{}_{}{}^{}\mathrm{Sm}$ ii are measured for the other 14 transitions. Three of the 14 transitions are not tabulated in the literature. Tentative compositions of the upper levels are evaluated from the IS’s by using the sharing rule. The IS’s measurements are also used in an absolute calibration of the acceleration voltage within an accuracy of 0.1%. The hfs of 10 levels are recorded. Corresponding magnetic-dipole and electric-quadrupole coupling constants, A and B factors, are evaluated. The A and B factors have not been determined before for three of the levels, and for the other levels they are determined with improved accuracy.

Knowledge of bounds and equalities for the exact density-functional exchange-correlation potential δ${\mathit{E}}_{\mathrm{xc}}$[n]/δn(r) is necessary for its accurate approximation. With this in mind, it is shown, for λ→0, that ${\lambda }^{\mathrm{-}1}$F${\mathit{d}}^3$rn(r)δ${\mathit{E}}_{\mathrm{xc}}$[${\mathit{n}}_{\lambda }$]/ δn(r)≥2${\lambda }^{\mathrm{-}1}$${\mathit{E}}_{\mathrm{xc}}$[${\mathit{n}}_{\lambda }$] and Fn(r’)‖r-r’${\mathrm{\Vert }}^{\mathrm{-}1}$${\mathit{d}}^3$r’ +${\lambda }^{\mathrm{-}1}$δ${\mathit{E}}_{\mathrm{xc}}$[${\mathit{n}}_{\lambda }$]/δn(r)≥0, where ${\mathit{n}}_{\lambda }$(x,y,z)=${\lambda }^3$n(λx,λy,λz). The local-density approximation satisfies the former inequality but violates the latter one. Moreover, with respect to the Fermi level, it is shown that the exact correlation potential δ${\mathit{E}}_{\mathit{c}}$[n]/δn(r) satisfies ${\mathit{E}}_{\mathit{c}}$[n]-${\mathit{E}}_{\mathit{c}}$[n-Δ${\mathit{n}}_{\mathit{F}}$]≤Fδ${\mathit{E}}_{\mathit{c}}$[n]/ δn(r)Δ${\mathit{n}}_{\mathit{F}}$(r)${\mathit{d}}^3$r, where Δ${\mathit{n}}_{\mathit{F}}$ is the density of the highest-occupied Kohn-Sham orbital of n. The corresponding inequality for the exact exchange potential δ${\mathit{E}}_{\mathit{x}}$[n]/δn(r) is in the opposite direction: ${\mathit{E}}_{\mathit{x}}$[n]-${\mathit{E}}_{\mathit{x}}$[n-Δ${\mathit{n}}_{\mathit{F}}$]≥Fδ${\mathit{E}}_{\mathit{x}}$[n]/ δn(r)Δ${\mathit{n}}_{\mathit{F}}$(r)${\mathit{d}}^3$r. It is a difficult challenge for an approximate exchange-correlation functional to simultaneously satisfy both inequalities. For instance, the local-density approximation does not.

Simple upper bounds for the spherical average of the atomic electronic density ρ(r) in terms of different negative powers of r, and depending on some average quantities, such as either radial expectation values or other relevant functionals of ρ(r), are obtained. The procedure used to get these results also enables us to find bounds for other atomic relevant functions, such as the number of electrons inside a sphere of radius r, i.e., Q(r), the isotropic atomic form factor F(q), the spherically averaged momentum density γ(p), and the atomic Compton profile J(q).

Precision measurements of Rydberg Stark levels of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ atoms are used to determine the 3 ${}_{}{}^2{}_{}{}^{}$S hyperfine separation, Δ${\mathit{E}}_{\mathit{h}\mathit{f}}$(3 ${}_{}{}^2{}_{}{}^{}$S). Three diode lasers at λ=671 nm, 813 nm, and 633 nm excite ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ atoms to n=15 sublevels in the presence of an electric field. Photoionization resonances at fields below the saddle point are used in conjunction with matrix diagonalization calculations to determine the binding energy of levels excited from each 3 ${}_{}{}^2{}_{}{}^{}$S hyperfine sublevel. The difference between the two fitted binding energies excited from 3 ${}_{}{}^2{}_{}{}^{}$S (F=1) and 3 ${}_{}{}^2{}_{}{}^{}$S (F=2) yields 189.36(43) MHz for Δ${\mathit{E}}_{\mathit{h}\mathit{f}}$(3 ${}_{}{}^2{}_{}{}^{}$S${;}^7$Li).

Systematic studies of the phase and density dependence of the delayed annihilation time spectra of antiprotons (DATS) in gaseous, liquid, and solid helium have been performed using the low energy antiproton ring at CERN. The results show a small but significant dependence of DATS on the phase and density of the helium medium. The average lifetime of antiprotons (${\mathit{T}}_{\mathit{a}\mathit{v}}$) in gas at 10–30 K was found to be 4.03±0.02 μs. In liquid helium ${\mathit{T}}_{\mathit{a}\mathit{v}}$ decreases with density from 3.0 μs at 1 bar to 2.5 μs at 60 bars, while in solid helium its value is 2.14±0.03 μs, 20% shorter than that in liquid helium of the same density. There is no change of DATS betweeen normal 1-bar liquid and superfluid helium. An isotope effect between ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ similar to the one previously observed in the gas phase has also been found for liquid helium. All the data can be fitted fairly well with a simple three-level chain decay model with describes the general structure of DATS, characterized by downaward curving behavior on a logarithmic scale at later times and by the presence of a short-lived component. No delayed annihilation was observed in lithium.

Epithermal effects in muonic molecular formation were observed during experiments in a low-density deuterium-tritium gas target carried out at the Paul Scherrer Institute. The high molecular formation rate of ‘‘epithermal’’ (not yet thermalized) muonic tritium atoms was reflected by a strong fast component in the fusion neutron time spectra followed by a smaller ‘‘steady-state’’ component where molecular formation occurs mostly from thermalized (‘‘cold’’) tμ atoms. Further experimental evidence for high epithermal dtμ molecular formation rates has been derived from measurements in triple H-D-T mixtures. First, theoretical calculations predicted strong resonances at high tμ kinetic energies and showed qualitative agreement with the observed experimental data, but yielded molecular formation rates that differed substantially from the observed values. At present, refined calculations are being carried out which may improve the agreement with experiment. Further experiments are being planned to clarify open questions.

We study the dynamics of a system of atoms undergoing laser cooling in a microtrap. Using a simple model, we show that the stationary state of the system can be different from the standard Bose-Einstein distribution. In particular, it can exhibit infinite sequences of phase transitions as a function of laser detuning, as well as multistable behavior. This is due to the combination of quantum statistical phenomena and other effects related to the laser-cooling process.

The gauge invariant contribution of the six radiatively corrected light-by-light scattering processes to the decay rate of orthopositronium into three photons is calculated. The infrared-safe Yennie gauge is used for the loop photons. The relative order of ${\mathrm{\alpha }}^2$ part of our result, 9.0074(9)(${\mathrm{\alpha }}^2$/${\mathrm{\pi }}^2$)${\mathrm{\Gamma }}_{\mathrm{LO}}$, makes a 0.000350 μ${\mathrm{s}}^{\mathrm{-}1}$ contribution to the decay rate, thus reducing slightly the apparent discrepancy between the theoretical and experimental results. ${\mathrm{\Gamma }}_{\mathrm{LO}}$ is the lowest-order decay rate. The analytically obtained relative order ${\mathrm{\alpha }}^2$ln α part of our result, -${\mathrm{\alpha }}^2$ln(1/α)${\mathrm{\Gamma }}_{\mathrm{LO}}$, is in agreement with earlier evaluations.

The n=10 G-to-H and H-to-I intervals in lithium atoms have been measured to an accuracy of approximately 10 parts per million. The experiment utilizes a beam of Rydberg lithium atoms produced via a resonant charge-exchange technique and the measurements were performed using precision rf spectroscopy coupled with a laser-excitation and Stark-ionization detection technique. The results are compared with recently published polarization-model calculations of the fine structure of lithium and with a hydrogenic model of its spin structure. With the availability of more precise theory, further tests of relativistic and QED effects in this simple three-electron atom will be possible. Such tests could shed light on the discrepancies found between similar high-precision measurement and theory in helium. The measured values are 338.4778(33), 341.4027(35), 108.4819(51), and 110.1566(54) MHz for the intervals 10${\mathit{G}}_{9/2}$ to 10${\mathit{H}}_{11/2}$, 10${\mathit{G}}_{7/2}$ to 10${\mathit{H}}_{9/2}$, 10${\mathit{H}}_{11/2}$ to 10${\mathit{I}}_{13/2}$, and 10${\mathit{H}}_{9/2}$ to 10${\mathit{I}}_{11/2}$, respectively.

The electrostatic fine structure for singly excited lithium is accurately calculated using an effective potential method that has proven to be very useful for helium. Relevant properties of the two-electron ${\mathrm{Li}}^{+}$ ionic core with finite nuclear mass are determined from variational wave functions. From these, non- relativistic level shifts are obtained analytically, and the leading relativistic correction is applied. A comparison with recent experimental results is made.

The energy spectrum of a hydrogenic atom (or an exciton) in crossed strong electric and magnetic fields is investigated. The effects of the Coulomb interaction and the center-of-mass motion on the relative motion of the system in the plane perpendicular to the magnetic field are especially discussed. The softening of the proton (hole) cyclotron mode is studied numerically by using the Bohr-Sommerfeld quantization rule and the result is compared with the classical one of Dzyaloshinskii [Phys. Lett. A 165, 69 (1992)]. Different softening behavior is found in the quasiclassical calculation in contrast to that of the classical analysis.

The individual charge state and total ion yields resulting from the photoionization of argon gas have been measured as a function of photon energy through the K edge using synchrotron radiation and time-of-flight spectroscopy. We have formulated a model for the mean ion charge q¯(hν) observed at nominal photon energy hν, and have determined the mean ion charge q¯ resulting from the decay of the atom following [1s]4p, [1s]5p, and [1s]ɛp photoabsorption. We have also characterized the energy-dependent photoelectron recapture probability due to postcollision interaction. In contrast with the recent analysis by Doppelfeld et al. [J. Phys. B 26, 445 (1993)], we find that the gradual increase in q¯(hν) that begins approximately 20 eV below the argon K edge can be attributed to lifetime energy broadening of the K-hole state and the finite energy width of the x-ray source.

Using data gathered by the metastable atom time-of-flight technique, evidence is presented for the first time that some of the direct products of dissociative recombination (DR) in ${\mathrm{Ne}}_2^{+}$ and ${\mathrm{Ar}}_2^{+}$ are purely ground-state atoms. These results are very surprising because there are no evident curve crossings between the initial molecular-ion potentials and those of the repulsive ground states. Such curve crossings have been thought to be necessary for DR to occur. Using a laser-based atom beam deflection technique, it is shown that at least some of the fast ground-state atoms produced by DR are reexcited to metastable states that are easily detected.

We present a study of characteristics of autoionization spectra for the Mg 3pns Rydberg series. The calculations were performed using multichannel quantum-defect theory combined with two versions of K matrices. The systematic investigation of states from the lower- to higher-lying members of the Mg 3pns Rydberg series allows one to reach a deeper understanding of physical manifestations involved. The calculations permit a detailed interpretation of recent experimental measurements in atomic magnesium. Energy levels are identified and assigned to the Mg 3pns autoionizing states for n greater than 6. A comparison with available experiments is provided.

The excitation of arsenic-atom spectral lines in the collisions of slow electrons with ${\mathrm{As}}_4$ molecules has been investigated. We used the extended-crossing-beams method and recorded the optical signal from the intersection region. The recorded lines are in the 213–550 nm spectral region. We also measured the optical excitation functions (OEF) in the range of electron energies 0–100 eV. The largest excitation cross sections belong to transitions from the 5s ${}_{}{}^2{}_{}{}^{}$P and 5s ${}_{}{}^4{}_{}{}^{}$P levels. A complex structure of the OEF indicated that the contribution of different excitation channels varies with the increase of electron energy. The measured onset energies show that in the near-threshold region there occurs a reaction e+${\mathrm{As}}_4$=${\mathrm{As}}^{\mathrm{*}}$+${\mathrm{As}}_3$+e.

Total cross sections for electron transfer, target excitation, and ionization processes are reported for the ${\mathrm{H}}^{+}$+Na(3s) and ${\mathrm{H}}^{+}$+Na(3p) systems at 1–100 keV impact energies. We have employed a two-center coupled-Sturmian-pseudostate approach that has recently been developed and applied to several quasi-one-electron systems by Winter [Phys. Rev. A 48, 3706 (1993)]. The Sturmian basis set, together with an analytic Hartree-Fock potential, are chosen carefully so that all three channels (transfer, excitation, and ionization) are represented properly. We also discuss briefly the effects of the binding-energy correction on the calculated cross sections. We find that our various cross sections (${\mathrm{\sigma }}_{\mathrm{cap}}^{\mathrm{tot}}$, ${\mathrm{\sigma }}_{\mathrm{cap}}^{\mathrm{H}(\mathrm{n}=2\mathrm{})\mathrm{}}$, ${\mathrm{\sigma }}_{\mathrm{cap}}^{\mathrm{H}\left(2\mathrm{}\mathit{s}\right)}$, ${\mathrm{\sigma }}_{\mathrm{cap}}^{\mathrm{H}\left(2\mathrm{}\mathit{p}\right)}$, ${\mathrm{\sigma }}_{\mathrm{exc}}^{\mathrm{N}\mathrm{a}(3\mathrm{}\mathit{s}\to 3\mathit{p})}$, ${\mathrm{\sigma }}_{\mathrm{exc}}^{\mathrm{N}\mathrm{a}(3\mathrm{}\mathit{s}\to 3\mathit{d})}$, ${\mathrm{\sigma }}_{\mathrm{ion}}^{\mathrm{tot}}$) and the ${\mathit{A}}_{20}$ alignment parameter for Na(3s→3p) compare very well with most of the available experimental data, as well as with previous theoretical results.

For all the above quantities, when a comparison is made between theory and measurement, our results are equally good or better than the earlier calculations employing different theoretical approaches. We still find a persistent discrepancy between theory (present as well as previous calculations) and measurements for the electron transfer cross sections into the metastable state of the H atom (${\mathrm{\sigma }}_{\mathrm{cap}}^{\mathrm{H}\left(2\mathrm{}\mathit{s}\right)}$). Our results for the orientation and alignment effects in the electron transfer process of ${\mathrm{H}}^{+}$+Na(3p) collisions are in good qualitative accord with recent observations and previous theoretical studies. In particular, we see a strong enhancement for the H(n≥3) capture cross sections in the ${\mathrm{H}}^{+}$+Na(3p) collisions. The H(n=2) production cross sections in the ${\mathrm{H}}^{+}$+Na(3p) collisons follow a roughly similar trend, as observed experimentally when plotted against the impact energy.