The $J=0\mathrm{}\leftarrow 1$ fine-structure transition in the atomic ion ${\mathrm{F}}^{+}$ in its ground ${}^{3}P$ state has been detected in the laboratory by far-infrared laser magnetic resonance. The fine-structure interval has been measured accurately as $4453253.2\pm 1.6\mathrm{MHz}$ $(148.544\mathrm{}537\pm 0.000053{\mathrm{cm}}^{\mathrm{-}1})$ which corresponds to a wavelength of $67.319877\pm 0.000015\mu \mathrm{m}.$ The hyperfine splitting for the ${}^{19}\mathrm{F}$ nucleus was also observed and its measured value is in fair agreement with predictions based on ab initio wave functions.

Theory for Doppler effects in resonant x-ray Raman scattering (RXS) is presented. It is shown that the “electron” Doppler effect is important in nonradiative RXS for decay transitions between continuum nuclear states lying above the dissociation threshold, and that the averaging of the RXS cross section over molecular orientations can lead to strong non-Lorentzian broadenings of the atomiclike resonances. The Doppler effect is found to give a unique possibility to distinguish dissociating identical atoms, because different peaks correspond to atoms with opposite Doppler shifts. Spectral features of the atomiclike profile are predicted and analyzed. Strong oscillations of the RXS cross section will occur as a consequence of the interference of the Auger electrons. Due to the Doppler effect and the interference, the atomiclike profile can be associated with supernarrow spectral features, the width of which goes below the lifetime broadening and is practically independent of the spectral distribution of the incident radiation. As another consequence of the oscillations and strong anisotropy caused by the interference, we predict parity selection rules for Auger decay transitions in both bound and dissociative systems. The corresponding experiments can be realized by measurements of resonant Auger of surface adsorbed molecules and for molecules by the electron-ion coincidence technique.

According to Hohenberg-Kohn-Sham density-functional theory (DFT), and its constrained search formulation, the Schrödinger ground-state wave function Ψ is a functional of the ground-state electronic density ρ(r). But the explicit functional dependence of Ψ on ρ is unknown. It is, however, possible to describe Kohn-Sham (KS) DFT and its electron-interaction energy functional and functional derivative rigorously in terms of the wave function Ψ. This description involves a conservative field which is a sum of two fields, the first representative of electron correlations due to the Pauli exclusion principle and Coulomb repulsion, and the second of correlation-kinetic effects. The sources of these fields are expectations of Hermitian operators with respect to Ψ. The energy functional is expressed in integral virial form in terms of these fields, whereas the functional derivative is the work done to move an electron in the conservative field of their sum. In this paper we illustrate the physics of transformation from Schrödinger to KS theory by application of this description to a ground state of the exactly solvable Hooke’s atom. As such we determine properties such as the pair-correlation density, the Fermi and Coulomb holes, the Schrödinger and KS kinetic-energy-density tensors and kinetic fields, and the electron-interaction and correlation-kinetic fields, potentials, and energies, the majority of these constituent properties of the transformation being obtained analytically. In this manner we demonstrate the separate contributions and significance of each type of electron correlation to the KS electron-interaction energy and its functional derivative. Based on this study and previous work, it is proposed that in the construction of approximate energy functionals and their derivatives for application to more complex systems, it is the fields that be directly approximated.

The molecular beam electric resonance technique has been used to examine the hyperfine spectrum of ${}^6{\mathrm{Li}}^{19}\mathrm{F}$ for the purpose of obtaining an improved value of the ratio of the electric quadrupole moments of the two lithium nuclei. A total of 29 transitions in vibrational states 0-2 and rotational states 1-4 have been included in a fit to determine the Li nuclear quadrupole interaction along with the magnetic spin-rotation and spin-spin interactions. The magnetic interactions are consistent with values calculated from the previously reported ${}^7{\mathrm{Li}}^{19}\mathrm{F}$ values, but those have been refitted to take advantage of the new information from ${}^6{\mathrm{Li}}^{19}\mathrm{F}$. The electric quadrupole moment ratio of the two lithium isotopes determined from measurements on the two forms of LiF is ${Q(}^6\mathrm{Li}{)/Q(}^7\mathrm{Li})=0.020161\mathrm{}\pm 0.000013$ (one standard deviation estimate).

We propose a method for measuring directly the Wigner function of a molecular vibrational state. Our method does not involve the calculation of integral transforms, as in tomographic proposals, and is applicable to a large class of molecular states.

The stability of the bound excited states of both the hydrogen and helium anions in an environment represented by the statically screened Coulomb potential have been studied. Energies have been calculated at the full configuration interaction level of theory, as a function of the screening parameter. Our calculations demonstrate that the bound excited states of both ${\mathrm{H}}^{-}$ and ${\mathrm{He}}^{-}$ survive only under mild screening conditions. Stronger screening will yield a sequential electron detachment process. Finally, the applicability of the present calculations to model real plasmas is discussed.

Response calculations in the framework of time-dependent density-functional theory (TDDFT) have by now been shown to surpass time-dependent Hartree-Fock (TDHF) calculations in both accuracy and efficiency. This makes TDDFT an important tool for the calculation of frequency-dependent (hyper)polarizabilities, excitation energies, and related properties of medium-sized and large molecules. Two separate approximations are made in the linear DFT response calculations. The first approximation concerns the exchange-correlation (xc) potential, which determines the form of the Kohn-Sham orbitals and their one-electron energies, while the second approximation involves the so-called xc kernel $f_{\mathrm{xc}},$ which determines the xc contribution to the frequency-dependent screening. By performing calculations on small systems with accurate xc potentials, constructed from ab initio densities, we can test the relative importance of the two approximations for different properties and systems, thus showing what kind of improvement can be expected from future, more refined, approximations to these xc functionals. We find that in most, but not all, cases, improvements to $v_{\mathrm{xc}}$ seem more desirable than improvements to $f_{\mathrm{xc}}.$

We present results of numerical experiments that are the one-dimensional analog of positron-hydrogen scattering. The obtained wave functions are exact, within model restrictions.

$K$-shell fluorescence yields were measured for Cs, Sm, Eu, Ho, Ta, W, Hg, and Pb using a Ge(Li) detector employing the reflection geometry. The target atoms were excited by using γ rays from ${}^{57}\mathrm{Co}$ radioactive sources of strength 100 mCi. Recently determined values of $w_K$ for Ba, Ce, Nd, Gd, Dy, Er, and Yb are also tabulated. The experimental results are compared with the literature experimental values, theoretical predictions, and the semiempirical fits.

We present calculations of the differential, integrated elastic, and total cross sections for positrons scattered from alkali-metal atoms. The energy of the positrons ranges from 10 eV to 1000 eV. In the calculations we use parameter-free model potentials for the correlation-polarization and absorption interactions. The absorption potential used for positron scattering is based on a quasifree model that we recently proposed and tested for the noble-gas targets. For positron–alkali-metal scattering the model potentials have produced reliable scattering cross sections over the extended range of impact energies when compared against the available experimental data.

We calculate the helium double photoionization and ionization with excitation cross sections using the convergent close-coupling formalism. We investigate the effect of the ground-state correlations by employing various highly correlated ground-state wave functions: 6-, 10-, and 14-parameter Hylleraas and 7-, 15-, and 18-term multiconfiguration Hartree Fock. As a test of the quality of our calculation, we compare the double to single photoionization cross-section ratio calculated in the three different gauges: length, velocity, and acceleration. We also calculate the partial photoionization cross sections up to $n<~6$ ion excited states and compare them with the latest experimental data. Using the 14-parameter Hylleraas ground state, we obtain almost identical results for the three gauges from the double ionization threshold to 1 keV, and have good agreement with the recent measurements.

We develop a method for calculation of dissociative electron attachment cross sections based on the Fano-Feshbach projection-operator approach. The coupling between the diabatic state and electron continuum is calculated with the inclusion of orthogonality scattering and long-range electron-molecule interaction. The dynamics of nuclear motion in the nonlocal complex potential is treated by semiclassical theory. We apply the theory to the calculation of dissociative attachment to the ${\mathrm{H}}_2$ and HF molecules. Our results for attachment to ground-state hydrogen molecules and the near-threshold vibrational enhancement of ${\mathrm{H}}_2$ are essentially the same as previous nonlocal results. However, the shape of the energy dependence of the cross section for attachment to vibrationally excited states of ${\mathrm{H}}_2$ is slightly different. The calculated value for the total attachment cross section to the ground state of HF is consistent with the little experimental data available; more definite conclusions are difficult because of the approximate nature of the experimental results. The results for the vibrational enhancement are in very good agreement with experiment.

Time-of-flight mass spectroscopy was used to study the relaxation dynamics of HCl following photoexcitation in the vicinity of the Cl $K$ edge $\left(\sim 2.8\mathrm{keV}\right)$ using monochromatic synchrotron radiation. At the lowest resonant excitation to the $6{\sigma }^{*}$ antibonding orbital, almost half of the excited molecules decay by emission of a neutral H atom, mostly in coincidence with a highly charged ${\mathrm{Cl}}^{n+}$ ion. The present work demonstrates that neutral-atom emission can be a significant decay channel for excited states with very short lifetimes (1 fs).

We solve the Holstein equation of radiation trapping in an atomic vapor cell by the geometric quantization technique (GQT). In the GQT, the rate equation for the excited-state density is transformed into an “equivalent” Schrödinger equation for an associated quasiparticle. The problem of finding the complete set of radiation escape factors is thus reduced to searching quantized energy values for the quasiparticle locked into the vapor cell. We combine already known solutions for the trapping factors at high opacities with new results for the phase jump at the vapor cell boundary to arrive, within the framework of the GQT technique, at solutions that are valid at all opacities. The phase factors are independent of geometry, and we derive an explicit representation for them by the Wiener-Hopf technique in the most simple geometry, a half-space. Our approach enables an analytical computation of the trapping factors in all practically occurring line shapes (including Voigt lines and hyperfine-split lines), all opacities, and all modes in one-dimensional (1D), 2D, and 3D geometries allowing for variable separation. We present results obtained in 1D geometries at all opacities that show discrepancies within 5% for the lowest-order trapping factor and even less (at the level of approximately 0.1%) for higher-order modes, in agreement with the predictions of the GQT theory that has been developed.

The electron nuclear dynamics theory is applied to the study of proton collisions with ground-state oxygen atoms at collision energies of 0.5, 1.0, and 1.5 keV. Total electron transfer cross sections are calculated in reasonable agreement with recent experiments. In addition, differential cross sections are calculated for this system with comparisons to recent experimental measurements.

We present third-order many-body perturbation theory calculations of the Lennard-Jones $C_3$ coefficient for the alkali-metal atoms lithium, sodium, potassium, rubidium, cesium, and francium. All-order singles-doubles calculations of $C_3$ are also presented for lithium, sodium, and potassium. For lithium and sodium the present values of $C_3$ are compared with other theoretical and semiempirical values.

A refined measurement of a binary, collision-induced, depolarized Raman spectrum of mercury vapor is analyzed in terms of recent interatomic potential and interaction-induced pair polarizability models, using quantum line-shape computations. The comparison of the computed spectra with a measurement at the temperature of 1070 K permits improvements, especially of the existing anisotropy model of the pair polarizability. The main result of this paper is that for highly polarizable atoms (such as Hg), especially at elevated temperatures, the long-range contribution to the pair polarizability needs to be suppressed at short interatomic distances. This is done with the help of damping functions, known from interatomic potential models.

Relativistic calculations of photoionization cross sections using the Breit-Pauli $R$-matrix method in the close-coupling approximation and the fully relativistic distorted-wave method are reported. Both methods give fine-structure results; the former produces extensive resonance structures in the low-energy region, and the latter, as a complement to the former, gives accurate results for high energies. Radiation damping of autoionizing resonances, important for He-like and Li-like ions, is included in the $R$-matrix calculations. In the present work, the Breit-Pauli $R$-matrix method is employed to calculate photoionization cross sections for photoelectron energies up to 50 Ry in C-like Fe XXI and up to 630 Ry (with radiation damping included) in Li-like Fe XXIV, and the relativistic distorted-wave method is used to calculate high-energy cross sections for He-like through Mg-like ions. The combined relativistic $R$-matrix and distorted-wave results are expected to provide accurate relativistic photoionization cross sections for highly charged ions throughout the energy range of importance, for practical applications such as photoionization in x-ray astronomy. The Breit-Pauli $R$-matrix results can also be employed for obtaining photorecombination (subsuming both the direct radiative and the dielectronic recombination) cross sections using the Milne relation. The relativistic distorted-wave results, including inner-shell ionization, for high photon energies may be merged with the low-energy cross sections computed by the Opacity Project using the nonrelativistic $R$-matrix method.

The rate coefficients for excitation autoionization (EA) from the levels of the ground and first excited configuration in nearly all argon ions (Li-like Ar${}^{15+}$ to S-like Ar${}^{2+})$ have been computed. Collisional excitation cross sections are computed in the distorted-wave approximation and integrated over a Maxwellian distribution of free-electron energies. Radiative and autoionizing transition probabilities are computed using the fully relativistic, intermediate coupling code RELAC. For each ion, the rates of EA are compared to semi-empirical calculations of the direct ionization rate. For charge states with few $M$-shell electrons in the ground configuration (Na-, Mg-, and Al-like), EA can significantly enhance the direct ionization rate coefficients. In the first excited configuration of each ion considered, the EA rate coefficient enhances the direct ionization rate coefficient only at low temperatures.

A general two-state exponential potential model is solved with use of the Bessel transformation and the WKB (Wentzel-Kramers-Brillouin) type semiclassical approximation. Accurate expressions are obtained for the nonadiabatic transition probability for one passage of the transition point and for the two dynamical phases. Functionalities of these quantities in terms of two basic parameters are the same as those obtained before by Nikitin. The two basic parameters are, however, expressed in more general and accurate forms. Accuracies of these expressions are numerically confirmed. The three quantities, the nonadiabatic transition probability and the two dynamical phases, constitute the nonadiabatic transition matrix and can be used to describe various (spectroscopic as well as scattering) processes not only for a two-state but also for a multichannel system. A possible generalization of the present theory is also briefly discussed to formulate a unified theory that can cover both Landau-Zener-Stueckelberg and Rosen-Zener-Demkov cases within the adiabatic state representation.