Nine triply excited states of lithium are calculated with the saddle-point and saddle-point complex-rotation methods. Relativistic corrections are computed with first-order perturbation theory. The widths are studied with one open channel at a time as well as fully coupled open channels. Some coupled calculations include up to ten open channels. Radiative decays of the triply excited states are also computed. The predicted Auger branching ratios are in excellent agreement with experiment. An identification is found for a weak line in the observed Auger spectra. Our predicted 2s2s2p${\mathrm{}}^2$${\mathit{P}}^{\mathit{o}}$ width is substantially smaller than the experiment of Kiernan et al. [Phys. Rev. Lett. 72, 2359 (1994)] but it agrees much better with the recent experiment of Kiernan et al. [J. Phys. B 28, L161 (1995)].

It is shown that precision lifetime measurements now available for the ns-np resonance transitions in alkali-metal-like atoms and ions and the existence of strong cancellation effects in ns-${\mathit{n}}^{\prime }$p transitions for ${\mathit{n}}^{\prime }$≳n can be combined and used to specify the electric dipole polarizabilities ${\mathrm{\alpha }}_{\mathit{d}}$ of these systems to a precision comparable to that of the lifetime measurements. The method is described and applied to ${\mathrm{Mg}}^{+}$ and ${\mathrm{Ca}}^{+}$ ions. Existing precision lifetime measurements are coupled with Coulomb approximation with Hartree-Slater core calculations, which estimate the contribution of the ${\mathit{n}}^{\prime }$≳n transitions in near cancellation, and the analysis yields to values ${\mathrm{\alpha }}_{\mathit{d}}$(${\mathrm{Mg}}^{+}$)=(34.62±0.26)${\mathit{a}}_0^3$ and ${\mathrm{\alpha }}_{\mathit{d}}$(${\mathrm{Ca}}^{+}$)=(70.89±0.15)${\mathit{a}}_0^3$.

An asymptotic-expansion method is presented for the evaluation of correlated three-electron integrals arising in Hylleraas-type variational calculations for lithium and other many-electron atoms. The method proves to be very efficient in accelerating the rate of convergence of an infinite series representation of the integrals. An analytic expression for the terms in the series is derived.

The hyperfine splitting values of the ground state of the hydrogenlike atoms ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}_{}^{5+}{}_{}{}^{}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}_{}^{6+}{}_{}{}^{}$, ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}_{}^{7+}{}_{}{}^{}$ and the lithiumlike atoms ${}_{}{}^7{}_{}{}^{}\mathrm{Li}_{}^0{}_{}{}^{}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}_{}^{4+}{}_{}{}^{}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}_{}^{6+}{}_{}{}^{}$, ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}_{}^{8+}{}_{}{}^{}$, ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}_{}^{9+}{}_{}{}^{}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}_{}^{10+}{}_{}{}^{}$, ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}_{}^{11+}{}_{}{}^{}$, ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}_{}^{14+}{}_{}{}^{}$, ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}_{}^{23+}{}_{}{}^{}$ are calculated. The calculations of the lithiumlike ions (Z≥7) are based on a combination of the 1/Z perturbation theory and the configuration interaction Hartree-Fock method. The relativistic corrections are calculated in the zeroth and first orders in 1/Z. The nuclear charge and magnetization distribution corrections and the radiative corrections are taken into account. The uncertainty of the calculations is estimated to be ∼0.02% for the hydrogenlike ions and ∼0.06% for the lithiumlike ions, except ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}_{}^{23+}{}_{}{}^{}$, for which the uncertainty is about 0.15%. The hyperfine structure constant of the ground state of Li is calculated to be A=401.5(4) MHz. The results of the calculations are compared with the theoretical values obtained with other methods and with experiment.

We report measurements of the frequency dependence of the refractive index and polarizability of cadmium vapor in the frequency range between ω=0.045 and 0.091 a.u. The quasicontinuous refractive index spectra have been measured at T≊1050 K with a high-temperature Michelson interferometer using the technique of dispersive Fourier-transform spectroscopy. The dispersion of the dipole polarizability α(ω) of Cd obtained in our experiments can be represented as α(ω)=α(0)${\mathrm{\omega }}_0^2$/(${\mathrm{\omega }}_0^2$-${\mathrm{\omega }}^2$), with a static polarizability of α(0)=(49.65±1.46±0.16) a.u. and an effective transition frequency of ${\mathrm{\omega }}_0$=(0.250 61±0.000 23) a.u. In addition, these measurements yield approximations for the dispersion interaction energy constant ${\mathit{C}}_6$=466 a.u. and the second hyperpolarizability γ(0)=1.1×${10}^5$ a.u.

Absorption spectra of atoms in magnetic fields reveal recurrences: manifestations of classical orbits (or quantum wave packets) that go out from the atom and later return. A formula from closed-orbit theory asserts that if the orbit lies on a node of the outgoing wave function, then the strength of the recurrence is zero. New quantum calculations, however, show that the recurrence strength is nonzero, though small. We derive a semiclassical formula for the recurrence strength associated with a classical orbit at a node of the quantum wave function. This formula is compared to the quantum mechanical calculation. Compared to other orbits, the recurrence is about 100 times weaker, and obeys a different classical scaling law.

In density-functional theory (DFT), Perdew, Parr, Levy, and Balduz [Phys. Rev. Lett. 49, 1691 (1982)] have shown that for all the electronic systems, the energy of the highest occupied molecular orbital (HOMO) is equal to the negative of the ionization potential. This equality is not recovered within the different approximations of the exchange-correlation functional proposed in the literature. The main reason is that the exchange-correlation potentials of various functionals used in DFT calculations decay rapidly to zero whereas they should exhibit a Coulombic asymptotic -1/r behavior. In this work we propose a gradient-corrected (GC) exchange potential with a correct asymptotic -1/r form for large values of r. The energy of the HOMO calculated with this potential is improved compared to the local-density approximation (LDA) and to the GC functionals widely used in the DFT. Our HOMO eigenvalues are compared to the optimized-potential-model eigenvalues which are the exact values for the exchange-only potential. Using the fact that the LDA satisfies the virial theorem, the exchange energy corresponding to this GC exchange potential can be calculated under a simple assumption.

High-precision variational eigenvalues for the 1${\mathit{s}}^2$2s${\mathrm{}}^2$S, 1${\mathit{s}}^2$2p${\mathrm{}}^2$P, and 1${\mathit{s}}^2$3d${\mathrm{}}^2$D states of lithium are calculated using multiple basis sets in Hylleraas coordinates. Convergence to a few parts in ${10}^{10}$–${10}^{11}$ is achieved. The nonrelativistic energies for infinite nuclear mass are -7.478 060 323 10(31) a.u. for the 1${\mathit{s}}^2$2s${\mathrm{}}^2$S state, -7.410 156 521 8(13) a.u. for the 1${\mathit{s}}^2$2p${\mathrm{}}^2$P state, and -7.335 523 541 10(43) a.u. for the 1${\mathit{s}}^2$3d${\mathrm{}}^2$D state. The corresponding specific isotope shifts due to mass polarization are also calculated with similar accuracy. The 1${\mathit{s}}^2$2s${\mathrm{}}^2$S–1${\mathit{s}}^2$2p${\mathrm{}}^2$P and 1${\mathit{s}}^2$2p${\mathrm{}}^2$P–1${\mathit{s}}^2$3d${\mathrm{}}^2$D transition energies for ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, as well as the isotope shifts, are calculated and compared with experiment. The results yield an improved ionization potential for lithium of 43 487.167(4) ${\mathrm{cm}}^{\mathrm{-}1}$. Expectation values of powers of ${\mathit{r}}_{\mathit{i}}$ and ${\mathit{r}}_{\mathit{ij}}$ and the delta functions δ(${\mathit{r}}_{\mathit{i}}$) and δ(${\mathit{r}}_{\mathit{ij}}$) are evaluated.

A detailed presentation of the modified configuration-interaction (CI) method [S. P. Goldman, Phys. Rev. Lett. 73, 2541 (1994)] is given. The standard two-electron test case is used to introduce the concepts, as well as to show a sharp increase in the convergence of the calculations. Space-ordered radial coordinates and generalized angular functions involving the addition of large numbers of spherical harmonics are used. As a result, accuracies that exceed those of the usual CI method by several orders of magnitude are obtained with small basis sets. For example, in the case of helium, energies are obtained with relative errors of 2.6×${10}^{\mathrm{-}9}$, 1.4×${10}^{\mathrm{-}8}$, and 2.0×${10}^{\mathrm{-}10}$ for the 1${\mathrm{}}^1$S, 2${\mathrm{}}^1$S, and 2${\mathrm{}}^3$S states with 420, 276, and 264 two-electron basis functions, respectively. A detailed discussion of the calculation of matrix elements and angular coefficients and of the extension to the many-electron case is presented.

By exploring the monosubstituted benzene compound aniline, we demonstrate that resonance inelastic x-ray spectroscopy of chemically shifted species is site selective. Core-excited levels with distinct, super-electron-volt shifts can be resonantly excited and their x-ray emission spectra analyzed separately. Core-excited levels referring to sites with small, sub-electron-volt, chemical shifts give resonant x-ray spectra that interfere strongly. It is demonstrated that this interference, which is manifested in the one-step model, can be used to monitor chemical shifts in the sub-electron-volt energy region. We show that in the limit when these chemical shifts go to zero some salient symmetry-selective features of the benzene resonant x-ray emission spectrum are restored in the aniline spectra.

We study the asymmetry characteristics of the low-velocity electronic emission in the bare ion-atom collision. These electrons form the so-called soft electron peak (SE peak) in the double-differential cross section. We parametrize the SE peak, expanding the double-differential cross section in Legendre polynomials. We extend previous studies determining the coefficients of the expansion by fitting available experimental data for ${\mathrm{C}}^{6+}$, ${\mathrm{O}}^{8+}$, and ${\mathrm{Ne}}^{10+}$ colliding with He at 5 MeV/amu incidence energy. We discuss the accuracy of that fitting and the convergence of the expansion and compare the fitting with predictions of the continuum distorted-wave-eikonal initial state theory. We confirm the existence of an asymmetry in the forward-backward direction in the electron distribution. We analyze these coefficients and former results as a function of projectile charge and impact energy, looking for scaling laws in these variables. We have found a law for the zeroth-order coefficients in Legendre polynomial expansion.

To calculate the behavior of metastable argon atoms in a direct-current glow discharge, a balance equation is constructed, taking into account all known production and loss processes of the metastable atoms. Density profiles and fluxes of the metastable atoms are computed. The relative importance of different production and loss processes determining the metastable density is calculated for the case of a molybdenum cathode in pure argon. Besides electron-impact excitation, fast-ion and atom-impact excitation are found to be the dominant production processes at the high voltages used here, while loss of the metastable atoms is caused predominantly by diffusion and also by electron quenching to the nearby resonant states. The role of metastable atoms in the total discharge is investigated. They are found to play a minor role in the ionization of argon atoms, but their part in the ionization of sputtered molybdenum cathode atoms appears to be rather important. Moreover, they seem to have a significant effect on the secondary electron emission at the cathode. The investigation also includes the influence of pressure, voltage, and current on the metastable densities and fluxes, on the relative importance of the different production and loss processes, and on the role of metastable atoms in the entire discharge.

The time-dependent Schrödinger equation is integrated for continuum states of two-electron atoms in the framework of the s-wave model, in which both electrons are restricted to having vanishing individual orbital angular momenta. The method is suitable for studying the time evolution of correlations in the two-electron wave functions and yields probabilities for elastic and inelastic electron scattering and for electron-impact ionization. The spin-averaged probabilities for electron-impact ionization of hydrogen in the s-wave model reproduce the shape of the experimentally observed integrated ionization cross section remarkably well for energies near and above the maximum.

The metastable $3^2$${\mathit{D}}_{3/2,5/2}$ doublet of ${\mathrm{Ca}}^{+}$ ions stored in a Paul trap was investigated in the presence of different neutral gases, in the pressure range ${10}^{\mathrm{-}9}$–${10}^{\mathrm{-}6}$ mbar. The natural lifetimes were determined to be τ(${\mathit{D}}_{3/2}$)=1111±46 ms and τ(${\mathit{D}}_{5/2}$)=994±38 ms, which agree very well with previous experiments. The estimation of the quenching rates of ${\mathrm{Ca}}^{+}$-He [${\mathrm{\Gamma }}_{\mathrm{He}}$=(1.05±0.42)×${10}^{\mathrm{-}12}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$], ${\mathrm{Ca}}^{+}$-Ne [${\mathrm{\Gamma }}_{\mathrm{}\mathrm{Ne}}$=(0.9±0.7)×${10}^{\mathrm{-}12}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$], and ${\mathrm{Ca}}^{+}$-${\mathrm{N}}_2$ [${\mathrm{\Gamma }}_{{\mathrm{N}}_2}$=(1.7±0.2)×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$] was carried out for collisions in the energy range 0.3–1.3 eV. In addition, rate constants for the mixing of the fine-structure states were measured in the presence of helium and nitrogen for the j=3/2→j=5/2 case [${\gamma }_{35}$(He)=(2.24±0.10)×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$ and ${\gamma }_{35}$(${\mathrm{N}}_2$)=(2.8±0.3)×${10}^{\mathrm{-}9}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$] and for the j=5/2→j=3/2 case [${\gamma }_{53}$(He)=(1.2±0.7)×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$ and ${\gamma }_{53}$(${\mathrm{N}}_2$)=(1.26±0.10)×${10}^{\mathrm{-}9}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$]. The measurements were carried out populating the metastable levels by direct laser excitation of the forbidden S-D transitions.

Ab initio calculations of the rate coefficients for dielectronic recombination (DR) of ten ions along the Ni i isoelectronic sequence in the ground state (${\mathrm{Mo}}^{14+}$, ${\mathrm{Ag}}^{19+}$, ${\mathrm{Xe}}^{26+}$, ${\mathrm{Pr}}^{31+}$, ${\mathrm{Gd}}^{36+}$, ${\mathrm{Dy}}^{38+}$, ${\mathrm{Ta}}^{45+}$, ${\mathrm{Au}}^{51+}$, ${\mathrm{At}}^{57+}$, and ${\mathrm{U}}^{64+}$) through the Cu-like 3${\mathit{d}}^9$4ln′l′ (n′=4,5) inner-shell excited configurations were performed using the hullac code package. Resonant and nonresonant radiative stabilizing transitions and decays to autoionizing levels followed by radiative cascades are included. Collisional transitions following electron capture are neglected. Nonresonant stabilizing transitions are found to enhance the DR rates, and may even dominate the process at low electron temperature. The remarkable difference between the isoelectronic trend of the rate coefficients for DR through 3${\mathit{d}}^9$4l4l′ and through 3${\mathit{d}}^9$4l5l′ is emphasized. The trend of DR through 3${\mathit{d}}^9$4l4l′ shows irregularities at relatively low temperature due to the progressive closing of DR channels as Z increases. Thus, the DR coefficients cannot be reproduced or interpolated by a simple analytical formula. Even for the smooth contributions of the 3${\mathit{d}}^9$4l5l′ configurations, a simplified model using configuration averaging for autoionization and radiative decays instead of level-by-level detailed computations is found to overestimate the DR rates by a factor of up to 2.

We have formulated the quantum rearrangement scattering of atom-diatomic molecules in phase space from the viewpoint of the density operators within the framework of Torres-Vega’s and Frederick’s phase-space representation of quantum mechanics [J. Chem. Phys. 98, 3103 (1993); 93, 8862 (1990)]. This formalism has a remarkable feature in that it naturally includes the on-the-energy-shell coherences of the initial system that are important for depicting actual scattering experiments. We have found that the full density operator describing the rearrangement scattering is closely related not only to the usual reactive transition operator T${\mathrm{^}}_{\mathrm{\beta }\mathrm{\alpha }}$, but also to the function F defined in the paper which is nonlocal in position vector and could reflect some fine structures of the reactive scattering in strong interaction region. The time-dependent reactive scattering in the quantum phase-space representation is also discussed.

The electron-impact excitation-rate coefficients for the 3d to 4l transitions in Ni-like tantalum were calculated using the distorted-wave and the multiconfiguration Dirac-Fock methods. As for the few-electron cases, the effects of autoionizing resonances are found to be very important for most transitions. In some transitions, resonances can enhance the rate coefficients by as much as a factor of 5. A collisional-radiative model was employed to study the effects of resonances on the laser gains. We found that the inclusions of the resonance excitation-rate coefficients in the calculations significantly reduce the gain coefficients for the two J=0→1 lasing transitions but fail to explain the large discrepancies between the predicted and measured lasing spectrum.

Electron emission cross sections differential in energy and angle of the ejected electrons were measured in collisions of 5-MeV/u ${\mathrm{C}}^{6+}$, ${\mathrm{O}}^{8+}$, and ${\mathrm{Ne}}^{10+}$ ions on He. The experimental results deviate substantially from calculations based on the plane-wave Born approximation indicating that the ejected electrons are significantly affected by the two-center field of the target and projectile ion. The two-center effects were confirmed by comparison with results from the continuum-distorted-wave–eikonal-initial-state (CDW-EIS) approximation that has recently been improved by using Hartree-Fock-Slater wave functions for the ejected electrons. It is shown for nearly complete energy and angular ranges that the improved CDW-EIS method predicts cross sections in excellent agreement with experiment.

We have measured the polarization rates of lines emitted after single-electron capture occurring during ${\mathrm{Ar}}^{8+}$-Li collisions at an impact energy of 80 keV. In order to obtain information on the final ${\mathit{m}}_{\mathit{l}}$ values which are populated in the electron-capture process, we have also calculated the polarization rates from the ${\mathit{nlm}}_{\mathit{l}}$ distributions determined by using the classical trajectory Monte Carlo (CTMC) method. The good agreement which is obtained between the experimental and the calculated polarization rates indicates the reliability of the CTMC method which predicts that ${\mathit{m}}_{\mathit{l}}$=0, ±1, and ±2 are preferentially populated by the electron-capture process.

Collisions between charged particles and highly excited Na Rydberg atoms have been measured to continue a study of the projectile-velocity dependence of collisionally induced dipole-allowed and dipole-forbidden transitions. Experiments involving ${\mathrm{H}}^{+}$, ${\mathrm{H}}_2^{+}$, ${\mathrm{He}}^{+}$, and ${\mathrm{Ne}}^{+}$ projectiles incident on Na(30s) and Na(29d) cover the projectile-velocity range from 1.6 to 10 times the mean orbital velocity of the excited electron. The ratio of the sum of the two largest dipole-allowed cross sections that depopulate an initial 30s state (30s→30p and 30s→29p) to the total depopulation cross section of 30s has been measured for reduced velocities ranging from 5 to 10. Absolute cross sections for the two dipole-allowed transitions 30s→30p and 29d→30p, where large quantum defects play a significant role, are also presented. These exhibit characteristic velocity-dependent thresholds. The experimental data are in good agreement with close-coupling calculations that use an m-averaged dipole coupling to describe both allowed and forbidden channels. The results emphasize the importance of optically forbidden transitions and have implications in the study of astrophysical and laboratory plasmas.