We have calculated a correction of order $m{\alpha }^7{\ln }^2\alpha$ to energy levels of the general two-body system of spin-$\frac{1}{2}$ particles with arbitrary masses. The result allows for the improved theoretical predictions of the $1S-2S$ and $2S-2P$ intervals in positronium. Further implications to the hydrogen-deuterium $1S-2S$ isotope shift are discussed also.

Single and double electron transfer have been studied for the collision system ${\mathrm{Ar}}^{8+}{+\mathrm{H}}_2$ at low velocities $(v<\mathrm{}1\mathrm{}\mathrm{a}.\mathrm{u}.\mathrm{}).\mathrm{}$ X-ray ultraviolet and Auger spectroscopies complemented by translational energy gain and time-of-flight spectroscopies reveal details on the transfer mechanisms: in contrast to the other two-electron target system (He target), a channel is opened where electron capture takes place with further dissociation of ${\mathrm{H}}_2^{+}.$ We consider the target fragment dynamics and discuss possible molecule dissociation mechanisms.

A relativistic multireference many-body perturbation theory for quasidegenerate systems with multiple open valence shells is developed and implemented with analytic basis sets of Gaussian spinors. The theory employs a general class of multiconfigurational Dirac-Fock self-consistent-field wave functions as reference functions, and thus is applicable to open-shell systems with near degeneracy of a manifold of strongly interacting configurations. A procedure is described by which to perform multireference second-order Møller-Plesset perturbation calculations for a general class of reference functions constructed from one-particle Dirac spinors. Multireference perturbation calculations are reported for the ground and low-lying excited states of oxygen and oxygenlike ions with up to a nuclear charge of $Z=60\mathrm{}$ in which the near degeneracy of a manifold of strongly interacting configurations mandates a multireference treatment.

Static dipole polarizabilities ${\alpha }_D$ of the first main group elements from Li down to superheavy element 119 were calculated using a relativistic Douglas-Kroll Hamiltonian within an open-shell coupled-cluster theory. Spin-orbit effects were investigated using a fully relativistic four-component Dirac-Hartree-Fock scheme. Our final recommended values for the dipole polarizabilities from Li to Cs should be more accurate than currently available experimental data. Relativistic effects in ${\alpha }_D$ are roughly $\sim Z^2$ and we establish a clear relationship for relativistic and electron correlation effects between the dipole polarizability and the ionization potential of the neutral atom. Spin-orbit effects become non-negligible for Fr and element 119. For the latter, relativistic effects clearly dominate over electron correlation resulting in a very small ${\alpha }_D$ value comparable to that of sodium.

The ${}^2{F}_{7/2}\mathrm{}(F=3\mathrm{})\mathrm{}{–}^2{D}_{5/2}\mathrm{}(F=2\mathrm{})\mathrm{}$ 3.43-μm transition in ${}^{171}{\mathrm{Yb}}^{+}$ has been measured to be 87 366 282 258(91) kHz. This transition is of interest as an infrared frequency standard. A subsidiary measurement of the 3.43-μm ${(F=4-F}^{\prime }=3)$ transition yields a frequency of 87 362 471 500(800) kHz. Taken with a previous measurement of the ${}^2{D}_{5/2}$ level hyperfine splitting, a ${}^2{F}_{7/2}$ level hyperfine splitting of 3620(2) MHz and an A factor of 905.0(0.5) MHz are deduced. In addition, a 3.43-μm transition isotope shift of $v_{171}–v_{172}=+4048\mathrm{}\left(4\right)\mathrm{}\mathrm{MHz}$ is obtained from these experiments and a known value for the transition in the 172 isotope. These measurements taken with previous work give a value for the ${}^2{S}_{1/2}\mathrm{}(F=0\mathrm{})\mathrm{}{–}^2{F}_{7/2}\mathrm{}(F=3\mathrm{})\mathrm{}$ electric octupole transition of 642 121 497 308(178) kHz, which will be used as a starting point in the search for this extremely weak transition.

Various geometrical and energetical (bound-state) properties of the positronium negative ion $({\mathrm{Ps}}^{-}$ or $e^{-}{e}^{+}{e}^{-})$ are determined by using highly accurate variational wave functions. These wave functions have been constructed by applying the advanced two-stage strategy proposed by Frolov [Phys. Rev. A 57, 2436 (1998)]. The determined total energy of the ground state $E=-0.2620050702329757\mathrm{a}.\mathrm{u}.\mathrm{}$ is the lowest and most accurate value obtained for this system to date (the corresponding binding energy equals $-0.326674721317821\mathrm{eV}).\mathrm{}$ The computation of the second-order relativistic corrections $\left(\simeq {\alpha }^2\right)$ to the total energy is discussed also. The general form of the Breit-Pauli Hamiltonian in the relative coordinates for the ${\mathrm{Ps}}^{-}$ ion is presented.

We introduce a scheme for the optimization of Gaussian basis sets for use in density-functional calculations. It is applicable to both all-electron and pseudopotential methodologies. In contrast to earlier approaches, the number of primitive Gaussians (exponents) used to define the basis functions is not fixed but adjusted, based on a total-energy criterion. Furthermore, all basis functions share the same set of exponents. The numerical results for the scaling of the shortest-range Gaussian exponent as a function of the nuclear charge are explained by analytical derivations. We have generated all-electron basis sets for H, B through F, Al, Si, Mn, and Cu. Our results show that they efficiently and accurately reproduce structural properties and binding energies for a variety of clusters and molecules for both local and gradient-corrected density functionals.

In a previous publication [Can. J. Phys. 75, 11 (1997)] we calculated the generalized polarizabilities up to multipole order 3 as well as certain higher-order hyperpolarizabilities for two-electron atoms and ions of $Z=2\mathrm{}–6$ and 10. In this paper we apply some of these results to calculate excited-state energies in three times ionized (lithiumlike) carbon. For states with angular momentum $L>\mathrm{}3\mathrm{}$ accurate results are obtained using an asymptotic polarizability expansion that includes nonadiabatic effects. Comparison is made with recent optical measurements, and a critical discussion of the correct form of the expansion is given. In addition, the possibility of very accurate measurements of the fine-structure splitting encourages us to present a table of such splittings to very high accuracy. An appendix contains similar results for lithiumlike oxygen and neon ions.

By combining the variational principle and the Hellmann-Feynman theorem, various forms of virial equations are obtained: for a many-electron system in arbitrary scalar and vector potential fields, for a neutral or charged molecule in an arbitrary vector potential field, for a molecule and an atom in a homogeneous magnetic field. These virial equations and their integrals represent exact results for the field-dependence of the ground-state and excited-state energies of the considered systems. Their validity is demonstrated not only for the exact eigenenergies, but also for a wide class of approximate energies, including the Hartree-Fock approximation and the intense-field limit of the statistical Thomas-Fermi model.

Spectroscopy of the 411-nm transition in ${}^{171}{\mathrm{Yb}}^{+}$ has been performed and the feasibility of its use as an optical frequency standard has been demonstrated. The ${}^2{S}_{1/2}(F=0,\hspace{0.5em}{m}_F=0){–}^2{D}_{5/2}(F=2,\hspace{0.5em}{m}_F=0)$ frequency, at zero-magnetic field, has been measured to be 729 487 779 566(153) kHz. This transition is free from the first-order Zeeman shift and has a measured second-order shift of +0.38(8) Hz/(μ${\mathrm{T})}^2$. In addition, the hyperfine structure of the ${}^2{D}_{5/2}$ level has been deduced by driving the other hyperfine components of the 411-nm transition, showing it to be inverted. The ${}^2{D}_{5/2}$ hyperfine splitting, measured to be -191(2) MHz, implies an A factor of -63.6(7) MHz. These data taken in conjunction with previous work yield an isotope shift of ${\nu }_{171}-{\nu }_{172}=+1317.1\mathrm{}\left(1.3\right)\mathrm{}\mathrm{MHz}$ for this transition between the 171 and 172 isotopes.

An improved nonlocal resonance model for electron-HCl collisions is constructed. The model takes account of the dependence of the dipole-modified threshold exponent on the internuclear distance. The long-range part of the ${\mathrm{HCl}}^{-}$ potential-energy function has been determined from the most accurate ab initio calculations which are available. Only the s-wave component of the electronic continuum wave function is taken into account. Cross sections for vibrational excitation, dissociative attachment, and associative detachment have been calculated. For all three collision processes, the cross sections calculated with this model are in better agreement with experiment than previous calculations. The calculations reproduce very well even fine details of the threshold structures in the vibrational excitation cross sections of HCl.

Electron collisions with negative ions (${\mathrm{B}}_2^{\mathrm{-}},$ ${\mathrm{C}}_2^{\mathrm{-}},$ ${\mathrm{O}}_2^{\mathrm{-}},$ ${\mathrm{BN}}^{\mathrm{-}},$ and OH) have been performed in a merged- beams experiment at the heavy-ion storage ring ASTRID (Aarhus Storage Ring, Denmark). Absolute cross sections for detachment ${(e}^{-}{+AB}^{-}\to {\mathrm{AB}}^0{+2e}^{-})$ and detachment plus dissociation ${(e}^{-}{+AB}^{-}\to A^0{+B}^0{+2e}^{-})$ are reported for energies below 40 eV. For the homonuclear ions, $X_2^{-}$ $(X=\mathrm{B},\mathrm{}\mathrm{C},\mathrm{}\mathrm{O}),$ cross sections are also presented for dissociative reactions leading to an $X^{-}$ particle in the final state. The detachment process is dominant for all investigated systems. The detachment cross section is characterized by an effective threshold larger than the electron binding energy. The shapes of the detachment cross sections are similar for the studied anions pointing to a common nonresonant mechanism for detachment. Also, the cross section for detachment plus dissociation and pure dissociation show regularities pointing to a general nonresonant mechanism. Structures are observed in the detachment cross section of ${\mathrm{C}}_2^{\mathrm{-}}$ and ${\mathrm{BN}}^{\mathrm{-}}$ and in the dissociation cross section of ${\mathrm{B}}_2^{\mathrm{-}}$ and ${\mathrm{C}}_2^{\mathrm{-}}.$ The structures are attributed to short-lived dianions (resonances) formed during the collision process. The results are supported by ab initio calculations, and it is inferred that electronic excitations are important in the resonant reactions.

High-symmetric systems of a large number of scatterers located at a sphere of radius R (the R sphere) are considered. A method of constructing such systems with point symmetries of crystalline lattices which is based on the projection of atomic shells onto the R sphere is proposed. In this way one can obtain the R sphere with the number of scatterers tending to infinity. By choosing potentials of separate centers one finds that such a system is closest to a spherically symmetric one. In this case the solution of scattering is uniquely characterized by a certain value of the orbital quantum number l. Specific shape resonances, geometric resonances, which can exist in many-center systems only in narrow energetic intervals and are destroyed as a potential becomes stronger, are examined.

Cross sections, differential in translational energy gain and projectile scattering angle, for single- and double-electron capture processes in collisions of ${\mathrm{C}}^{5+}$ ions with He at laboratory energies between 0.5 and 50 keV/u, have been studied experimentally by means of a high-resolution cold-target recoil-ion momentum spectroscopy. The translational energy spectra for single-electron capture show that capture into the ${\mathrm{C}}^{4+}$ $\mathrm{}(n=3\mathrm{})\mathrm{}$ state is the dominant reaction channel observed over the entire collision energy region studied, in agreement with close-coupling calculations. However, capture into $n=2\mathrm{}$ and $n>~4$ states is only significant at $E>~4\hspace{0.5em}\mathrm{k}\mathrm{e}\mathrm{V}/\mathrm{u}.$ Transfer excitation processes contribute only very weakly to the total cross sections for single-electron capture (2–4 %). This contribution is considerably smaller than the close-coupling prediction. The autoionizing double-electron-capture (transfer ionization) spectrum clearly shows that ${\mathrm{C}}^{3+}$ ${(2l,2l}^{\prime })$ states are populated at the lowest impact energy, whereas contributions from capture into ${\mathrm{C}}^{3+}$ ${(2l,n}^{\prime }{l}^{\prime })$ states with $n^{\prime }>~3$ increase as the impact energy is increased and become the dominant process at $E=35\mathrm{}\hspace{0.5em}\mathrm{k}\mathrm{e}\mathrm{V}/\mathrm{u}.$ State-selective and differential cross sections have also been measured and compared with the close-coupling and multichannel Landau-Zener calculations.

Single- and double-electron transfer from He to the ${\mathrm{Ne}}^{8+}{(1s}^2{)S}_0^1$ ion has been studied at 80 keV by extreme ultraviolet (EUV) spectroscopy and zero-degree electron spectroscopy. Signals originating from the stabilization after two-electron capture are identified in the photon data. This gives information on the stabilization of two electrons on the projectile. Single-electron capture signals originating from $n=9\mathrm{}$ states are observed, and the absolute emission cross section is determined. The presented experimental data have unprecedented resolution. The analysis is supported by extensive theoretical calculations of the (3,3), (3,4), and (4,4) doubly excited states in Be-like neon. Decay from triplet states due to spin exchange is observed in the spectra.

By using the Zwanzig-Mori theory, the rotational relaxation Γ matrix of the sudden approximation is corrected for rotational adiabaticity, off-energy shell scattering, and initial bath-molecule correlations. Expressions derived for the case of a linear rotator perturbed by fast binary collisions are shown to satisfy all known fundamental relations; in addition, the Γ matrix is symmetric and positive definite in line space. The general case of non-Markovian relaxation of an arbitrary molecular $r\mathrm{th}$ rank tensor is treated, which substantially expands the scopes of the impact scalar $\mathrm{}(r=0\mathrm{})\mathrm{}$ relaxation. A model of Γ is developed compatible with the known data on the $N_2-N_2$ potential and is shown to fit well a variety of different relaxation characteristics $\mathrm{}(r=0,1,2\mathrm{})\mathrm{}$ measured in compressed room-temperature nitrogen.

The cross sections for double ionization and the ratios of double to single ionization, including Ps formation for Ne, Ar, Kr, and Xe are presented from threshold to 100 eV. Within the energy region 6.8 eV below the second ionization potential, i.e., the second Ore gap, we find Ne to have a double-ionization cross section indistinguishable from zero, which is consistent with prior measurements. However, the total double-ionization cross sections for Ar, Kr, and Xe just below the thresholds for direct double ionization are around 7–24 % of the maximum cross-section value for each atom, all of which are of the order of ${10}^{-21}{\mathrm{m}}^2$ and occur around 70–90 eV. In contrast to what has previously been found for He and Ne, this is direct evidence of a significant amount of transfer ionization for the three heavier noble gases in the second Ore gap, which is consistent with previous measurements for Ar and Xe.

An experimental investigation is performed to determine the initial- and final-state alignment effects in the energy-pooling process $\mathrm{Ca}\left(4s4p{}^3{P}_1\right)+\mathrm{Ca}\left(4s4p{}^3{P}_1\right)\to \mathrm{Ca}\left(4s4p{}^1{P}_1\right)+\mathrm{Ca}{(4s}^2).\mathrm{}$ This paper represents a type of four-vector correlation experiment, where two aligned atoms collide and the alignment of the final excited state is observed. The initial $\mathrm{Ca}\left(4s4p{}^3{P}_1\right)$ state polarization is controlled with polarized lasers and magnetic fields, and the final-state alignment is partially resolved by observing the polarization of the fluorescence from the $\mathrm{Ca}\left(4s4p{}^1{P}_1\right)\to \mathrm{Ca}{(4s}^2)$ emission. The mathematics are developed in this paper to provide a full quantitative description of the four-vector alignment cross sections observed here. Relative values that describe 18 of the 39 total independent parameters are obtained, thus defining the results of this collision process at an unprecedented level of detail. The final-state Ca polarization is found to be only weakly dependent on the initial-state alignment, with final-state fluorescence predominately polarized along the relative velocity vector of the collision.

The dependence of Cu (target atom) K-shell vacancy production cross sections on projectile atomic number was investigated in collision systems for which the ratio of projectile-to-target atomic numbers ${(Z}_1{/Z}_2)$ ranged from 0.34 to 2.86. A combination of energy and wavelength dispersive x-ray spectrometry was used to measure Cu K x-ray production cross sections and to determine the appropriate fluorescence yields for converting them to K-vacancy production cross sections. The high-resolution spectra also revealed the presence of sizable contributions from predominately single-ionization mechanisms not directly associated with ion-atom interactions. The role of electron capture to the projectile was examined by observing the dependence of the cross sections on target thickness. The Cu K-vacancy production cross sections determined for equilibrated projectiles display a plateau centered in the region of symmetric collisions ${(Z}_1{/Z}_2\sim 1)$ and they become essentially constant beyond $Z_1=54.\mathrm{}$ The cross sections for $Z_1>24\mathrm{}$ fall far below a $Z_1^2$ scaling law and are greatly overestimated by the perturbed stationary-state theory with energy loss, Coulomb deflection, and relativistic corrections.

Dissociative recombination and excitation of ${\mathrm{H}}_2{\mathrm{O}}^{+}$ and ${\mathrm{HDO}}^{+}$ in the vibrational ground state have been studied at the heavy-ion storage ring ASTRID. Absolute cross sections have been measured in the energy range from $\sim 0.1$ meV to $\sim 50$ eV. The total cross sections for dissociative recombination are essentially the same for the two molecular ions. Complete branching ratios for all possible product channels in dissociative recombination at $E=0\mathrm{}$ have been determined. Three-particle breakup accounts for $\sim 60\%$ of the recombination events. With ${\mathrm{HDO}}^{+},$ recombination into OD+H is twice as probable as recombination into OH+D. An isotope effect is also evident in the cross sections for dissociative excitation of ${\mathrm{HDO}}^{+},$ where ${\mathrm{H}}^{+}$ production is more likely than ${\mathrm{D}}^{+}$ production.