Several expressions are derived that allow one to evaluate any local property at nuclear cusps in atoms and molecules. Applications of the formulas to the Hartree-Fock density and its derivatives for first- and second-row atoms show agreement with Kato’s cusp condition. Applications to the exact exchange-only and exchange-correlation energy potential for neutral atoms are given. It is shown that for an atom, the values of ${\mathit{V}}_{\mathrm{x}}$(0) and ${\mathit{V}}_{\mathrm{xc}}$(0) are both close to the negative of the charge of the nucleus.

High-resolution inverse Raman spectroscopy has been used to obtain the line shifting and line broadening coefficients of ${\mathrm{H}}_2$ perturbed by He. Measurements have been made for the $Q$-branch transitions ($J=0\mathrm{} \mathrm{to} 5$) in a density range of 10 to 20 amagat and from 296 to 995 K. Up to 795 K we have directly deduced from the experimental broadening coefficients the inelastic rotational state-to-state and vibrational dephasing rates. At higher temperatures, owing to the larger number of channels of relaxation which occur, the results have been analyzed using a scaling law. The line shift and broadening coefficients exhibit a square root and a linear dependence on temperature, respectively, and a significant $J$ dependence. Semiclassical calculations based on an accurate ab initio potential lead to line-shape parameters consistent with experiment. They allow a clear understanding of their observed temperature dependence.

We have measured the hydrogen and deuterium 1S Lamb shift by direct optical frequency comparison of the 1S-2S and 2S-4S/4D two-photon transitions. Our result of 8172.874(60) MHz for the 1S Lamb shift in hydrogen is in agreement with the theoretical value of 8172.802(40) MHz. For the 1S Lamb shift in deuterium, we obtain a value of 8183.807(78) MHz, from which we derive a deuteron matter radium of 1.945(28) fm. The precision of our value for the 1S Lamb shift has surpassed that of radio frequency measurements of the 2S-2P Lamb shift. By comparison with a recent absolute measurement of the hydrogen 1S-2S transition frequency, we deduce a value for the Rydberg constant ${\mathit{R}}_{\mathrm{\infty }}$=109 737.315 684 9(30) ${\mathrm{cm}}^{\mathrm{-}1}$.

Using Doppler-free frequency-modulation spectroscopy, we have measured most of the hyperfine components and the centers of gravity of the ${\mathit{D}}_1$ line of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ and the ${\mathit{D}}_2$ line of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$. By using previously measured fine- and hyperfine-structure splittings, we have also determined centers of gravity for the ${\mathit{D}}_2$ line of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ and the ${\mathit{D}}_1$ line of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$. Our present results are more accurate than previously reported values by a factor of more than 100. The wave numbers are ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ ${\mathit{D}}_2$: 14 903.983 468 (14) ${\mathrm{cm}}^{\mathrm{-}1}$; ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ ${\mathit{D}}_1$: 14 903.648 130 (14) ${\mathrm{cm}}^{\mathrm{-}1}$; ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ${\mathit{D}}_2$: 14 903.632 116(18) ${\mathrm{cm}}^{\mathrm{-}1}$; ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ${\mathit{D}}_1$: 14 903.296 792 (23) ${\mathrm{cm}}^{\mathrm{-}1}$. Values for the isotope shifts of the resonance lines of 0.351 338 (21) ${\mathrm{cm}}^{\mathrm{-}1}$ for the ${\mathit{D}}_1$ line and 0.351 352 (15) ${\mathrm{cm}}^{\mathrm{-}1}$ for the ${\mathit{D}}_2$ line have been derived. All uncertainties represent a 95% level of confidence.

High-precision measurements are presented of line pairs that are candidates for resonant spoiling of x-ray lasing transitions in the nickel-like tungsten ${\mathrm{W}}^{46+}$ x-ray laser. Our measurements were carried out with a high-resolution crystal spectrometer, and a typical precision of 20-50 ppm was achieved. This precision is a factor of 15 better than a previous measurement of the W $4p_{\frac{1}{2}}\to 3d_{\frac{3}{2}}$ line. Most resonances appear insufficient for effective spoiling. The closest overlap is found for the $4p_{\frac{1}{2}}\to 3d_{\frac{3}{2}}$ transition in nickel-like ${\mathrm{W}}^{46+}$ with the $2p_{\frac{3}{2}}\to 1s_{\frac{1}{2}}$ transition in hydrogenic ${\mathrm{Al}}^{12+}$, which differ by 2.4±0.3 mÅ or 335 ppm, providing a marginal overlap. However, because the W line lies between the two finestructure components of the Al Ly-$\alpha$ line, any relative Doppler shift between the two ion species due to bulk ion motion will improve the overlap and satisfy the resonance condition.

We report the measurement of thirteen 2${\mathit{s}}_{1/2}$-2${\mathit{p}}_{3/2}$ dipole-allowed transitions in the highly ionized thorium ions ${\mathrm{Th}}^{80+}$ through ${\mathrm{Th}}^{87+}$. The transitions have been measured with a high-resolution crystal spectrometer on the Livermore electron beam ion trap in which highly charged thorium ions were produced and excited in the interaction with a 100-keV electron beam. The observed 2${\mathit{s}}_{1/2}$-2${\mathit{p}}_{3/2}$ transitions are readily identified from a qualitative analysis of the dipole-allowed radiative decay channels. The identifications are confirmed by detailed modeling calculations of the line excitation processes, which account for all radiative processes, including radiative cascades among levels in the n=2 and n=3 shells, and all electron-impact excitation processes. The transition energies have been determined with an overall accuracy of 35 ppm. A detailed discussion of the measurement uncertainties is given, including the effects of beam-induced polarization on the hydrogenic reference transitions used for calibration. Measurements of the 1${\mathit{s}}^2$-1snp (n≤10) transitions in heliumlike ${\mathrm{Ar}}^{16+}$, which fall into the same wavelength region as the 2${\mathit{s}}_{1/2}$-2${\mathit{p}}_{3/2}$ transitions in thorium, are presented that validate the estimate of our experimental uncertainties. These measurements achieved twice the accuracy of previous measurements of the ${\mathrm{Ar}}^{16+}$ lines. A value of 4025.23±0.14 eV is found for the 2${\mathit{s}}_{1/2}$-2${\mathit{p}}_{3/2}$ transition in lithiumlike ${\mathrm{Th}}^{87+}$.

The value is sensitive to the effect of nuclear polarization and tests predictions of the 36-eV contribution from quantum electrodynamics to within 0.39%. A similar test of quantum electrodynamics calculations is given by the twelve 2${\mathit{s}}_{1/2}$-2${\mathit{p}}_{3/2}$ transitions measured in the neighboring charge states. A comparison of the measured energies of the 2${\mathit{s}}_{1/2}$-2${\mathit{p}}_{3/2}$ transitions in berylliumlike ${\mathrm{Th}}^{86+}$ through neonlike ${\mathrm{Th}}^{80+}$ with theoretical predictions from multiconfiguration Dirac-Fock calculations demonstrates the need for a better treatment of the electron-correlation terms in these highly charged multielectron ions. The measurements thus provide benchmarks for the development of theoretical approaches, such as relativistic many-body perturbation theory and large-scale configuration-interaction calculations, that attempt to account for electron correlations in very highly charged ions.

The excitation and emission spectra of alkali-metal atoms (Cs and Rb) in liquid helium are studied. The helium pressure is changed from the saturated vapor pressure to about 25 atm at 1.6 K, under which conditions the liquid helium is in a superfluid state. The pressure shift and broadening of the observed spectra corresponding to the D lines are explained qualitatively by a theoretical calculation based on the spherical atomic bubble model. The Cs ${\mathit{D}}_2$ excitation spectra are found to have double peaks, indicating the existence of anisotropic oscillations of the bubble surface. The disappearance of the ${\mathit{D}}_2$ emission lines and the pressure-dependent quenching of the Rb ${\mathit{D}}_1$ emission lines are also discussed.

Transitions into the lowest ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{+}{}_{}{}^{}$ valence state of ${\mathrm{O}}_2$, which we shall name f′${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$, are observed. A total of nine weak absorption bands is found from the system f′${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$←X${\mathrm{}}^3$${\mathrm{\Sigma }}_{\mathit{g}}^{\mathrm{-}}$ for the isotopes ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}_2^{}{}_{}{}^{}$ and ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}_2^{}{}_{}{}^{}$. The observed band origins and rotational constants are found to be significantly perturbed due to an electrostatic interaction between the valence state f′${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$ and the Rydberg states 3p${\mathrm{\pi }}_{\mathit{u}}$ f${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$ and 4p${\mathrm{\pi }}_{\mathit{u}}$ j${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$. In addition, rotational perturbations observed in certain vibrational levels of the Rydberg states f${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$ and j${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$ are found to be caused by the f′${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$ state through the same valence-Rydberg interaction. The f′←X bands are found to be predissociating resonances that exhibit Beutler-Fano line shapes of widely varying asymmetry. In particular, the (13,0) band of ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}_2^{}{}_{}{}^{}$ is an example of a window resonance in molecular dissociation.

The spectroscopic constants of the singly charged diatomic transition-metal–(Fe, Co, Ni, Cu, Zn) argon adduct ions are calculated within the relativistic Dirac-Fock-Slater (DFS) self-consistent-field method. Numerical solutions of the atomic Dirac-Fock-Slater equations are taken as basis functions. A variationally consistent potential approximation has been used to obtain potential-energy curves. The comparison of our results and other theoretical results with experimental values shows that the DFS method is quite suitable for calculations on such systems.

The photodetachment cross sections for ${\mathrm{H}}^{\mathrm{-}}$ and ${\mathrm{Li}}^{\mathrm{-}}$ in the vicinity of the H(n=2-4) and Li(n=3-4) thresholds are calculated. A discrete numerical basis set, combined with the method of complex rotation, is used to construct highly correlated descriptions of both initial and final states. The energies and widths of the doubly excited states are calculated directly and compared with results from experiments and other calculations when available. Other resonance parameters for photoexcitation from the ground state to the autodetaching states, describing the shape and the strength of the resonances, are also calculated. Mass polarization was considered for the doubly excited states of ${\mathrm{H}}^{\mathrm{-}}$, but was found to be much smaller than the present experimental accuracy. The possibility of describing a photodetachment resonance with a Fano profile, i.e., with a few resonance parameters connected to properties of a specific autodetaching state, is investigated and it is concluded that most resonances in ${\mathrm{Li}}^{\mathrm{-}}$ in the region studied, where overlapping resonances are common, cannot be meaningfully analyzed in this way.

Relativistic corrections to the exchange-correlation energy functional of density functional theory are examined within the no-sea approximation to the full relativistic Kohn-Sham equations. We apply the relativistic optimized-potential model to spherical atoms in order to establish a comparative standard in the longitudinal exchange-only limit and use the results for an analysis of the corresponding relativistic local- and weighted-density approximations. In addition, we investigate transverse exchange and correlation contributions. A local-density approximation for the correlation energy functional is constructed from the relativistic high-density and the nonrelativistic limits and analyzed by comparison with quantum chemical data.

The relativistic coupled-cluster method is used to calculate ionization potentials and excitation energies of Hg and element 112, as well as their mono- and dications. Large basis sets are used, with l up to 5, the Dirac-Fock or Dirac-Fock-Breit orbitals found, and the external 34 electrons of each atom are correlated by the coupled-cluster method with single and double excitations. Very good agreement with experiment is obtained for the Hg transition energies, with the exception of the high (≳12 eV) excitation energies of the dication. As in the case of element 111 [Eliav et al., Phys. Rev. Lett. 73, 3203 (1994)], relativistic stabilization of the 7s orbital leads to the ground state of ${112}^{+}$ being 6${\mathit{d}}^9$7${\mathit{s}}^2$, rather than the ${\mathit{d}}^{10}$s ground states of the lighter group 12 elements. The ${112}^{2+}$ ion shows very strong mixing of the ${\mathit{d}}^8$${\mathit{s}}^2$, ${\mathit{d}}^9$s, and ${\mathit{d}}^{10}$ configurations. The lowest state of the dication is 6${\mathit{d}}^8$7${\mathit{s}}^2$ J=4, with a very close (0.05 eV) J=2 state with strong ${\mathit{d}}^8$${\mathit{s}}^2$ and ${\mathit{d}}^9$s mixing. No bound states were found for the anions of the two atoms.

We have developed a relativistic multichannel theory that can be used to calculate the multichannel quantum-defect theory parameters (${\mu }_{\alpha }, U_{i\alpha }$) directly from first principles. With the parameters we can calculate the energy levels and Landé $g$ factors of Rydberg series based on the multichannel quantum-defect theory. We have performed calculations of excited states for the Ne atom with major configuration $1s^{2}2s^{2}2p^5\mathrm{np}$ in $J^{\pi }=0^{+}, 1^{+}, 2^{+}, \mathrm{and} 3^{+}$ symmetry. The results are in good agreement with the experimental data. We have also found that the coupling scheme is dependent on the total angular momentum $J$. The $\mathrm{jl}$-coupling scheme is more suitable than the $\mathrm{jj}$-coupling scheme in describing $J^{\pi }=1^{+}$ symmetry, whereas the $\mathrm{jj}$-coupling scheme is more suitable than the $\mathrm{jl}$-coupling scheme for $J^{\pi }=2^{+}$ symmetry.

A change of variables is proposed with the following property: given a preselected density, when a uniform grid in the new coordinates is mapped into Cartesian coordinates, the resulting grid points are distributed according to the preselected density. The preselected density is chosen so that the grid points are concentrated in the atomic-core regions. The grids generated in this way are useful for fully numerical or basis-set-free electronic-structure calculations, in particular those using plane-wave expansions: they give a good treatment of the nuclear cusps (because of the high density of grid points in the core regions) and the fast Fourier transform can be used for numerical interpolation (because the grids are uniform in the new coordinates). When compared with uniform or flat grids in Cartesian coordinates, the present scheme is clearly superior: it gives numerical integration errors that are typically two orders of magnitude smaller, and it very accurately interpolates atomic and molecular densities, even for atoms like uranium, which have a very high core density.

A spectrum-generating algebra for a unified description of rotations and vibrations in polyatomic molecules is introduced. An application to nonlinear ${\mathit{X}}_3$ molecules shows that this model (i) incorporates exactly the relevant point group, (ii) provides a complete classification of oblate top states, and (iii) treats properly both degenerate and nondegenerate vibrations.

$K{\beta }_2$ x-ray spectra of Zr, Mo, and Pd induced by photons and 16-, 25-, and 45-MeV protons were measured with a transmission bent crystal spectrometer. The average $M$-shell ionization probabilities were determined with the assumption that the yields in the $K{\beta }_2$ satellite region are due only to the $M$-shell ionization accompanying the removal of the $K$-shell electron. In the case of photoionization, these yields were found to exceed significantly those calculated with the sudden-approximation model for the shakeoff plus shakeup. Likewise, the corresponding yields for collisions with protons exceed those expected for the combined effect of the direct Coulomb ionization and the shake mechanism. The solid-state effects, as well as the direct knockout of the $M$-shell electron by the photoelectron (or the $\delta$ electron), are discussed in view of their possible effect on the line intensity in the satellite region. The direct Coulomb ionization probabilities in near central collisions with protons are determined from the difference of the relative yields of $\mathrm{K}{\beta }_2$ satellites in the proton-and photon-induced ionization. The underlying assumption is that the shake and solid-state effects are independent of the ionizing agent and that the secondary-electron ionization is similar in the two processes. The results are compared with the semiclassical approximation calculations exploiting relativistic hydrogenic and Dirac-Hartree-Fock wave functions.

The description of a non-Markovian process is presented and the asymptotic solution of the generalized master equation is obtained for a two-level atom pumped externally by a monochromatic time-dependent electric field. We give the explicit expression for the absorption line-shape function and discuss its features as a function of the temperature and the memory parameter. We verified the following interesting results: (a) At a critical temperature the line shape undergoes a phase transition, the single-bump profile splits into two bumps; (b) for small values of the memory parameter k the linewidths broaden, becoming larger than the ones calculated under the Markovian approximation, and after reaching some maximum value they narrow monotonically with increasing values of k, this behavior being standard for any finite temperature.

The hyperfine structure of highly charged lithiumlike ions is considered within QED using the $\frac{1}{Z}$ perturbation theory ($Z$ is the nuclear charge). The interelectronic interaction contribution of the order of $\frac{1}{Z}$ to the hyperfine splitting of the ground state is calculated in the range $Z=5-100\mathrm{}$. The hyperfine splitting values are found for the ground state of ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}_{}^{23+}{}_{}{}^{}$ and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}_{}^{80+}{}_{}{}^{}$.

In this paper, we report a study of circular dichroism in angular correlation between photoelectrons and Auger electrons emitted sequentially from a free, gaseous, linear molecule whose rotational motion has also been taken into account. The outgoing electrons are observed without their spins. The photonpropagation and electron-detection configurations, along with other conditions, have been specified wherein dichroic effects do not necessarily vanish in one-photon, two-step, double ionization of rotating linear molecules. The analysis is presented in terms of both the state multipoles and the photoionization matrix elements. It is completely general and is independent of any particular dynamical description of the photoabsorption as well as Auger emission processes.

The effect of Compton scattering on the ratio of double-to-single ionization from photon impact in helium has been measured for 2.1≤hν≤5.5 keV using a time-of-flight ion spectrometer with a high relative collection efficiency for Compton ions. Single ionization from Compton scattering is found to contribute measurably to a reduction in the ionization ratio for hν≳3.5 keV. Our measurements are compared with predictions based on recent calculations of the single and double ionization cross sections for photoabsorption and Compton scattering by Hino et al. [Phys. Rev. A 48, 1271 (1993), Phys. Rev. Lett. 72, 1620 (1994)], Andersson et al. [Phys. Rev. Lett. 71, 50 (1993)], and Surić et al. [Phys. Rev. Lett. 73, 790 (1994)].