Rigorous bounds are derived for the momentum-transfer squared, ${\mathit{K}}^2$, and used to construct a universal formula to extrapolate the generalized oscillator strength through the unphysical region to the optical oscillator strength. Results of the universal function are compared with those obtained from experimental small-angle differential cross sections to determine the range of its applicability.

Previously, we presented an alternative relativistic formalism for nonrelativistic two-body bound-state systems [T. Zhang, L. Xiao, and R. Koniuk, Can. J. Phys. 70, 670 (1992)]. The kernel of the integral equation for the bound-state systems is generated by summing Feynman scattering amplitudes and multiplying by a bound-state amplitude. In this paper, we present our calculations of two-loop contributions to hyperfine splitting of positronium to order ${\mathrm{\alpha }}^6$ coming from vacuum-polarization corrections to two-exchange-photon interactions.

The X (1 ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$), A (1 ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }$), B (2 ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$), and (1) ${}_{}{}^2{}_{}{}^{}\mathrm{\Delta }$ electronic states of SrH are calculated. A small-core Hartree-Fock pseudopotential for the Sr atom is used together with a large molecular basis set, and extensive valence and core configuration interactions are done. The existence of a double-potential well for the B state, due to an avoided crossing between neutral and ionic configurations, is clearly shown. The dipole moment of this state as a function of the internuclear distance varies greatly, and the vibrational energy levels show an irregular progression. The Einstein coefficients for stimulated absorption for vibronic transitions among these four states are also calculated. This predicts irregular band intensities involving the B state. Spectroscopic data for the (1) ${}_{}{}^2{}_{}{}^{}\mathrm{\Delta }$ state are found, too.

In this work we analyze the properties of the exchange-correlation potential in the Kohn-Sham form of density-functional theory, which leads to requirements for approximate potentials. Fulfilment of these requirements is checked for existing gradient-corrected potentials. In order to examine the behavior of approximate potentials over all space we compare these potentials with exact Kohn-Sham potentials calculated from correlated densities using a newly developed iterative procedure. The main failures in the existing gradient-corrected potentials arise in the asymptotic region of the atom where these potentials decay too fast and at the atomic nucleus where the potentials exhibit a Coulomb-like singular behavior. We show that the main errors can be corrected by a simple potential in terms of the density and its gradients leading to considerably improved one-electron energies compared to the local-density approximation. For Be and Ne it is shown that the electron density is improved in the outer region.

We present an efficient analytic approach for the evaluation of two-photon transition rates in a hydrogen atom. The method is a variation of the Dalgarno and Lewis method [Proc. R. Soc. London Ser. A 233, 70 (1955)] for the evaluation of the second-order Stark effect in a hydrogen atom.

Based on field theory, we use a Green’s-function formalism to derive an order-by-order approximation to the transition probability of many-electron atoms. The nth-order approximation is obtained by cutting the kernel in the Dyson equation at the nth order of the electron-electron interaction. From the perturbative point of view, each order of approximation is equivalent to the sum of an infinite subset of Feynmann diagrams. The transition probability in each order of approximation is shown analytically to be gauge invariant. Numerical calculations have been done for several atoms. The results of the second-order approximation are, in addition to being gauge invariant, in good agreement with experiment.

An exact quantum Monte Carlo method is used to calculate the H-He interaction potential under the Born-Oppenheimer approximation. The method used is exact in that it requires no mathematical or physical approximations beyond the Schrödinger equation. As in most Monte Carlo methods there is a statistical error which is readily estimated. For the equilibrium internuclear distance of 7.0 bohr the calculated electronic energy is -3.403 7459±0.000 0016 hartrees and the corresponding well depth (ε/k) is 6.8±0.5 K. The calculated potential is consistent with low-energy scattering cross-section measurements [J. P. Toennies, W. Welz, and G. Wolf, Chem. Phys. Lett. 44, 5 (1976)] and with low-temperature diffusion measurements [Hardy et al., Phys. Rev. Lett. 45, 453 (1980)].

The spectra of Cu, Mg, and V, produced by a hollow cathode with Ar and Ne as carrier gases, have been registered in the infrared region (1800–9000 ${\mathrm{cm}}^{\mathrm{-}1}$) with the Fourier-transform spectrometer at the National Solar Observatory on Kitt Peak. These spectra reveal the presence of three groups of lines around 1.8, 3.1, and 2.9 μm. Many of these emission lines have been identified as 3${\mathit{p}}^4$${(}^3$P)5f-6g, 5g-6h, 6g-7h, 6h-7i, and 6f-7g transitions in Ar ii. From these observations, it has been possible to extend the term system of this ion and to determine the energies of approximately 70 new levels. More precisely, the 3${\mathit{p}}^4$${(}^3$P)6h, 7h, and 7i configurations have been analyzed.

Eighty-one microwave resonances in Na Rydberg states n=21–35 between d, f, g, and h states have been accurately measured. Among them 43 transitions are first-time measurements, and 38 transitions have been improved, primarily by the elimination of stray electric and magnetic fields, compared with previous measurements. For the d-f transitions, the measured intervals and d-state fine-structure splittings are a factor of 10 more precise; for d-g and d-h series, the measured intervals are a factor of 3 more precise than before. The nf-state fine-structure splittings in Na for n=21–29 have also been accurately measured, and the conclusion that the Na f-state fine-structure splitting ${\mathit{nf}}_{5/2}$-${\mathit{nf}}_{7/5}$ is about 5% smaller than the hydrogen f-state fine-structure interval is confirmed through n=29.

Fluorescence-excitation spectroscopy near ∼84 nm has been used to measure the threshold for the dissociation of ${\mathrm{H}}_2$(B’ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{+}{}_{}{}^{}$)=H(1s)+H(2s) at 118 377.06±0.04 ${\mathrm{cm}}^{\mathrm{-}1}$ and the corresponding limit for ${\mathrm{D}}_2$ at 119 029.72±0.04 ${\mathrm{cm}}^{\mathrm{-}1}$. The onset of dissociation was observed clearly, free from overlapping molecular lines, by the use of delayed quenching of 2s atoms produced by the photoexcitation pulse. These measurements have yielded the values ${\mathit{D}}_0$(${\mathrm{H}}_2$)=36 118.11±0.08 ${\mathrm{cm}}^{\mathrm{-}1}$ and ${\mathit{D}}_0$(${\mathrm{D}}_2$)=36 748.38±0.07 ${\mathrm{cm}}^{\mathrm{-}1}$ for the dissociation energies of the ground electronic states X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$, in agreement with the latest ab initio calculations, which include nonadiabatic, relativistic, and radiative corrections. From the present values and recently determined ionization energies of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$, the dissociation energies of the respective ions were found to be ${\mathit{D}}_0$(${\mathrm{H}}_2^{+}$)=21 379.37±0.08 ${\mathrm{cm}}^{\mathrm{-}1}$ and ${\mathit{D}}_0$(${\mathrm{D}}_2^{+}$)=21 711.64±0.07 ${\mathrm{cm}}^{\mathrm{-}1}$, also in agreement with recent ab initio calculations.

Mandelshtam, Ravuri, and Taylor [Phys. Rev. Lett. 70, 1932 (1993)] have recently proposed a novel approach for the calculation of resonance states in one- and two-channel problems. We show that a modification of this approach, suitable for stabilization calculations, can yield both the resonance position and width for doubly excited states in two-electron systems. This provides a simple and numerically efficient method to calculate the spectral density of states. In the region of overlapping ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}^{\mathit{e}}$ Rydberg manifolds, we find very narrow resonances associated with the symmetric excitation of both electrons. The mechanism for the occurrence of such resonances is discussed.

Even if all constituents move slowly, the interaction between a pair of systems predicted by nonrelativistic theory can differ drastically at large separations of the systems from the true interaction, that which takes into account the finite speed of the virtual electromagnetic waves (generated by vacuum fluctuations) responsible for the interaction at large separations. We here adapt, improve, and generalize a rough physical picture presented previously, and arrive at exact results for the asymptotic interaction, V(r). One need use neither the Schrödinger equation nor the Dirac equation; all that need be known of either system is its electric-dipole polarizability. [For a neutral system, one needs the static scalar α(ω=0) for a spherically symmetric system and the static tensor ${\mathrm{\alpha }}_{\mathit{i}\mathit{j}}$(ω=0) for a nonspherically symmetric system; the α(ω) for an electron is -${\mathit{e}}^2$/m${\mathrm{\omega }}^2$.] Apart from its simplicity and the insights it leads to, the approach provides a uniform derivation for a number of known results, and one result not previously given, the asymptotic interaction of a distant electron and a cylindrically symmetric core, a Rydberg ${\mathrm{H}}_2$ molecule and a Rydberg carbon atom, with their cores in their ground states, being prototypes.

The relativistic correlation-potential method was used to calculate binding energies and fine-structure intervals for Pd, Ba, and Yb negative ions and to investigate low-energy electron scattering by Yb, Hg, and Ra atoms. The results for the binding energies are the following: 540 meV for the 5s state of ${\mathrm{Pd}}^{\mathrm{-}}$, 190 and 133 meV for the 6${\mathit{p}}_{1/2}$ and 6${\mathit{p}}_{3/2}$ states of ${\mathrm{Ba}}^{\mathrm{-}}$, and 36 meV for the 6${\mathit{p}}_{1/2}$ state of the ${\mathrm{Yb}}^{\mathrm{-}}$. A number of prominent p and d resonances are revealed in the scattering phase-shift calculations. These p or d resonances lead to a phenomenon of 100% polarization of the scattered electron beam at appropriate electron energy and scattering angle. A criterion is proposed to measure the strength of the nonlocal correlation potential and to evaluate its ability to create a bound state: FG(r’,r)Σ(r,r’)dr dr’>1 is the necessary condition for the formation of a bound state. Here Σ is the correlation potential and G is the electron Green’s function at zero energy.

The dynamic dipole polarizabilities at real and imaginary frequencies have been determined for the ground 2 ${}_{}{}^2{}_{}{}^{}$S and excited 2 ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ states of Li using our time-dependent gauge-invariant method. Accurate ${\mathit{C}}_6$ dispersion energy coefficients for the Li(2 ${}_{}{}^2{}_{}{}^{}$S)–${\mathrm{H}}_2$ and Li(2 ${}_{}{}^4{}_{}{}^{}\mathrm{P}_{}^{\mathrm{o}}{}_{}{}^{}$)–${\mathrm{H}}_2$ systems and their dependence on the intramolecular H-H distance are reported.

We have performed a time-resolved study of the behavior of Rb atoms in electric fields (0.1–3 kV/cm) at energies close to and above the field-ionization threshold. This is done using a pair of picosecond laser pulses that creates an electronic wave packet and monitors its evolution in terms of the time-autocorrelation function. In the discussion of the results, emphasis is put on the relation with the classical picture of field ionization, viz. the escape of an electron over the saddle point in the potential energy. This picture is found to be capable of qualitatively explaining the observed dependences on excitation energy and light polarization. Furthermore, the observed dynamics as a function of field strength is shown to be in agreement with the general scaling properties of the Hamiltonian of hydrogen, which also accounts for the measured time periods quantitatively. The relation between time- and frequency-domain measurements is shortly addressed, as is the question of why a hydrogenic approximation explains the observed dominant features adequately.

We present a model of the line shape of a Doppler-free two-photon transition in a metastable neon beam. This model considers the ac Stark effect, the Gaussian profile of the laser beam, and the depletion, or bleaching, of the metastable state as the atoms cross the laser. The model fit the experimental data well and was recently used to verify the time-dilation effect at an accuracy of a few ppm.

Absolute values for the total, one-, two-, and three-electron-transfer cross sections for ${\mathrm{Ar}}^{\mathit{q}+}$ ions (8≤q≤16) colliding with argon at 2.3q keV laboratory energy were measured by the growth-rate method. The ${\mathrm{Ar}}^{\mathit{q}+}$ ions were produced by the Cornell superconducting solenoid, cryogenic electron-beam ion source (CEBIS) and extracted at 2.3 kV. Selected charge states traversed a gas cell, after which they were detected and charge-state analyzed by the energy-retardation method and by a π/ √2 cylindrical electrostatic analyzer. The target gas pressure in the cell was measured directly by the orifice flow method used for absolute pressure-gauge calibration. The overall error in the ${\mathrm{Ar}}^{\mathit{q}+}$ on Ar cross-section measurements is ±10%.

The Kα and Kβ x-ray spectra of palladium and lanthanum bombarded by 5.5-MeV/amu ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ions were measured with a high-resolution transmission crystal spectrometer. The observed complex structure of the Kα${\mathit{L}}^0$ and K${\mathrm{\beta }}_{1,3}$${\mathit{L}}^0$ lines consisting of many M satellites was analyzed by means of theoretical line profiles based on multiconfiguration Dirac-Fock calculations. The average M-shell and M-subshell ionization probabilities in near-central collisions are determined. The experimental results are compared to the predictions of the semiclassical-approximation theory. The agreement is much improved by using Dirac-Hartree-Fock (DHF) wave functions instead of screened relativistic hydrogenic wave functions. The importance of DHF wave functions in the calculation of the M-shell ionization probabilities is illustrated with other examples.

We report on studies of resonant inelastic scattering of quasifree electrons on ${\mathrm{C}}^{5+}$. The resolution of the electron spectrometer is sufficient to resolve the energy structure of electrons emitted as a result of decay of doubly excited 3l3l’ configurations in ${\mathrm{C}}^{4+}$. The line energies compare well with theoretical calculations, using the truncated-diagonalization method. Theoretical calculations based on the Hartree-Fock atomic model for the differential cross sections are also presented. The relative strength of these states within the 3l3l’ manifold is measured as a function of scattering angle and compared with theory. The agreement is good for several states, but the 3s3d ${}_{}{}^3{}_{}{}^{}$D and 3p3d ${}_{}{}^1{}_{}{}^{}$F states show large deviations from the Hartree-Fock-model calculations. Good agreement is found between theory and experimental data for the ${}_{}{}^1{}_{}{}^{}$F state when the autoionization rate to the ground state calculated with the truncated-diagonalization method is used in the calculations. It is likely that strong correlation effects for the ${}_{}{}^3{}_{}{}^{}$D state are not as well treated in the Hartree-Fock model as by the truncated-diagonalization method.

Nonradiative and radiative electron captures in collisions of ${\mathrm{He}}^{+}$ ions with carbon atoms at energies below 1 keV are studied theoretically by using a molecular-orbital expansion method to calculate the adiabatic potential-energy curves and the nonadiabatic coupling matrix elements of ${\mathrm{CHe}}^{+}$. The corresponding scattering equations are solved. For nonradiative transitions, electron capture into channels separating to He+${\mathrm{C}}^{+}$${(}^2$D) are found to be dominant below 10 eV. However, as the energy increases, the channels separating to He+${\mathrm{C}}^{+}$${(}^2$P) take over because of the positive asymptotic energy defect. At 100 eV, the nonradiative capture cross section is 5×${10}^{\mathrm{-}17}$ ${\mathrm{cm}}^2$. The radiative electron-capture cross section is found to be very small, with a magnitude nowhere greater than ${10}^{\mathrm{-}22}$ ${\mathrm{cm}}^2$.