The recoil correction to the ground-state energy of hydrogenlike atoms is calculated to all orders in $\alpha Z$ in the range $Z=1\mathrm{}$–110. The nuclear size corrections to the recoil effect are partially taken into account. In the case of hydrogen, the relativistic recoil correction beyond the Salpeter contribution and the nonrelativistic nuclear size correction to the recoil effect amounts to $-7.2\left(2\right)\mathrm{}$ kHz. The total recoil correction to the ground-state energy in hydrogenlike uranium ${(}^{238}{\mathrm{U}}^{91+})$ constitutes 0.46 eV.

Lifetimes of Cs II ${5p}^{5}6p$ levels, oscillator strengths to the lower ${5p}^{5}5d$ and ${5p}^{5}6s$ levels, Landé$\hspace{0.5em}g$ factors and $\mathrm{LS}$ compositions of all these levels are presented. Results are in very good agreement with most available experiment. Large correlation effects are associated with those ${5p}^{5}5d$ and ${5p}^{5}6s$ states, which strongly interact.

We have formulated a three-dimensional fully numerical (i.e., chemical basis-set free) method and applied it to the solution of the single-particle Schrödinger equation. The numerical method combines the rapid “exponential” convergence rates of spectral methods with the geometric flexibility of finite-element methods and can be viewed as an extension of the spectral element method. Singularities associated with multicenter systems are efficiently integrated by a Duffy transformation and the discrete operator is formulated by a variational statement. The method is applicable to molecular modeling for quantum chemical calculations on polyatomic systems. The complete system is shown to be efficiently inverted by the preconditioned conjugate gradient method and exponential convergence rates in numerical approximations are demonstrated for suitable benchmark problems including the hydrogenlike orbitals of nitrogen.

We extend the differential virial theorem put forth by Holas and March [Phys. Rev. A 51, 2040 (1995)] to a statistical mixture of densities corresponding to different numbers of electrons. This allows us to derive an expression for the gradient of the exchange-correlation potential for densities that lead to noninteger numbers of electrons. We apply this to study the jump in the exchange-correlation potential as the electron number increases through an integer. We show that the difference between the gradient of the exchange-correlation potential for $N$ electrons, where $N$ is an integer, and that for $N+f$ electrons, where $f$ is a small positive number, is similar to the electric field in and around a charged metal sphere: It is zero inside, peaks at the surface, and then decays. Consequently, the corresponding potential is constant in the interior of the system and decays sharply at the surface.

Understanding high-precision photoassociative spectroscopy of laser-cooled alkali-metal atoms involves modeling an extremely dense level structure of weakly bound molecules in the region where coriolis and hyperfine interactions become comparable to electronic interactions. We describe an iterative eigenvalue solver suitable for resolving these bound states that is based on finding eigenvalues of the shifted inverse or Green-function operator. Nonlinear coordinate transformations applied to the nuclear motion are introduced to minimize the dimensionality of the discretized Hamiltonian. The formalism is applied to resolve the hyperfine structure of rovibrational levels of the $\mathrm{Na}{(}^{2}P)+\mathrm{Na}{(}^{2}S)$ dimer.

A computational method for calculating the hyperspherical adiabatic potential curves for three-electron atomic systems is presented. This method allows us to obtain accurate potential curves for any symmetries more efficiently. The potential curves for the $\mathrm{Li}{(}^2{S}^e)$ symmetry are analyzed. For the ground state, the energy calculated using the single channel adiabatic approximation is in good agreement with experiment. For doubly excited states, in the region of small and medium hyperradius the potential curves are similar to those for the doubly excited states of two-electron atoms and these curves can be classified using the same set of $K$, $T$, and $A$ quantum numbers. For triply excited states, the potential curves are used to show the different Rydberg series that converge to the doubly excited states of ${\mathrm{Li}}^{+}$. We also illustrate the rotor structure in the energies of triply excited states of Li.

It is shown that the $X\alpha$ scattered-wave method is particularly useful to simulate high-resolution x-ray-emission (XE) spectra of molecules. Calculations for both the resonant and off-resonant C $K$ XE spectra of benzene have been performed. In the off-resonant case the ability of this method to calculate the cross sections of the primary core ionization is crucial and multichannel interference effects may be significant. Furthermore, we discuss the treatment of molecular symmetry in modeling x-ray processes and the interpretation of x-ray emission as an inelastic scattering process.

Resonant $J^{\pi }{=1\mathrm{}}^{-}$ states of ${\mathrm{H}}^{\mathrm{-}}$ below the $N=2\mathrm{}$ threshold are studied in a semiempirical coupled-channel calculation, in which fine structure and QED corrections are included exactly. This leads to the termination of the dipole series of Feshbach resonances and to increasing mixing between different ${}^{2S+1}L$ states toward the end of the series. We predict a total of three resonances in the series dominantly of ${}^1{P}^o$ nature, and four resonances in the series dominantly of ${}^3{P}^o$ nature. The highest state of the latter series contains a 17% admixture of ${}^1{P}^o$ configurations, so one-photon excitation of this state from the ${}^1{S}^e$ ground state is far from forbidden.

The $f$ values for the ${\mathrm{np}}^6\to {\mathrm{np}}^5\mathrm{}(n+1\mathrm{})s$ dipole transitions of neon, argon, krypton, and xenon are studied using relativistic many-body perturbation theory. The contributions from the correlation corrections of single and pair excitations are calculated to all orders. It is hoped that the present work may help to distinguish among the considerable variety of experimental and theoretical values presently available.

The nuclear spin conversion of ${\mathrm{CH}}_3\mathrm{F}$ molecules induced by the intramolecular spin-rotation interactions is calculated and shown to be the leading process in ${}^{12}{\mathrm{CH}}_3\mathrm{F}.$ For ${}^{13}{\mathrm{CH}}_3\mathrm{F}$ molecules, it complements the spin conversion induced by spin-spin interactions. Comparison with experimental data allows a qualitative estimate of a few relaxation rates and of the transverse anisotropy of the spin-rotation tensor that cannot be obtained with usual spectroscopic methods.

We present a calculation of the two-electron Bethe logarithm, the main part of the theoretical expression for the Lamb shift of the atomic ground state. The basic method uses Hylleraas pseudostates to approximate the intermediate states in the slowly convergent sum defining the quantity of interest. Three tricks improve the convergence in our method. First, we choose the nonlinear parameters of the pseudostates by a variational method. Second, we extend the energy sum analytically, beyond the last pseudoenergy. Finally, we extrapolate the result using a physically reasonable parameter as the independent variable. The extrapolation proves to be remarkably linear. Results are given for helium and several two-electron ions and compared with previous calculations. The hydrogen system is also considered.

We propose an explicit expression of the α parameter of the $X\alpha$ theory that takes into account the nonlocal exchange effects in an average sense. For each system (and for the various configurations of the same system) the value of α is determined self-consistently within the electronic structure calculation. We have performed some exchange-only atomic calculations: the errors on the total energies and on the ionization potentials are of some parts per million and smaller than 1%, respectively. Some preliminary results for the multiplet splittings are also presented.

We present an approximation scheme for the calculation of the principal excitation energies and transition moments of finite many-body systems. The scheme is derived from a first-order approximation to the self-energy of a recently proposed extended particle-hole Green’s function. A Hermitian eigenvalue problem is encountered of the same size as the well-known random phase approximation (RPA). We find that it yields a size consistent description of the excitation properties and removes an inconsistent treatment of the ground-state correlation by the RPA. By presenting a Hermitian eigenvalue problem the new scheme avoids the instabilities of the RPA and should be well suited for large-scale numerical calculations. These and additional properties of the new approximation scheme are illuminated by a very simple exactly solvable model.

Experimental data on the temperature dependence of the ortho-para nuclear spin conversion rate of gaseous ${\mathrm{CH}}_3\mathrm{F}$ are presented. In the range 300–750 K, the ${}^{12}{\mathrm{CH}}_3\mathrm{F}$ conversion rate increases by one order of magnitude. By contrast, the conversion rate for ${}^{13}{\mathrm{CH}}_3\mathrm{F}$ decreases with increasing temperature (for $T<\mathrm{}600\mathrm{}\mathrm{K}$). These results are in qualitative agreement with a theoretical model based on mixing of states due to intramolecular spin-spin interactions between the molecular nuclei. Above 600 K, the rate in ${}^{13}{\mathrm{CH}}_3\mathrm{F}$ starts to increase again, indicating a possible additional mechanism for the conversion.

Elastic-scattering cross sections for 59.54-keV photons have been measured at an angle of 121° for 42 elements in the atomic region $12<~Z<~92.$ The measurements were performed using a ${}^{241}\mathrm{Am}$ radioisotope as the photon source and a Si (Li) detector. The measured cross sections have been compared with those based on the modified-relativistic form factors (MF’s), a combination of the MF’s and angle-independent “anomalous” scattering factors $(\mathrm{M}\mathrm{F}+\mathrm{A}\mathrm{S}\mathrm{F}),$ and the relativistic second-order $S$-matrix calculations. The MF cross sections are found to be enormously higher for the elements with $K$-shell binding energy ${(E}_K)$ close to the incident photon energy ${(E}_{\mathrm{inc}})$ of 59.54 keV. The $S$ matrix and $\mathrm{M}\mathrm{F}+\mathrm{A}\mathrm{S}\mathrm{F}$ cross sections, in general, represent the trend of the measured data over the whole atomic region under investigation. These theoretical cross sections are in good agreement with the measured data for the elements with $12<~Z<~26$ and, thereafter, deviate with increasing $Z.\mathrm{}$ The $S$ matrix and $\mathrm{M}\mathrm{F}+\mathrm{A}\mathrm{S}\mathrm{F}$ values are, on the average, higher by 17%, and 24%, respectively, for the elements with $39<~Z<~67;$ and by 10% and 19%, respectively, for the elements with $70<~Z<~92.$ In case of ${}_{68}\mathrm{Er},$ having a $K$-shell binding energy 2.1 keV lower than the incident photon energy, the $\mathrm{M}\mathrm{F}+\mathrm{A}\mathrm{S}\mathrm{F}$ value shows good agreement with the measured one, and the $S$ matrix value is lower by 12%.

The main properties of the interaction of ultralow-energy antiprotons $(E<~{10}^{-6}$ a.u.) with atomic hydrogen are established. They include the elastic and inelastic cross sections and protonium (Pn) formation spectrum. The inverse Auger process $(\mathrm{Pn}+\overrightarrow{e}\mathrm{H}+\overline{p})$ is taken into account in the framework of a unitary coupled-channel model. The annihilation cross section is found to be several times smaller than the predictions made by the black sphere absorption models. A family of $\overline{p}\mathrm{H}$ near-threshold metastable states is predicted. The dependence of protonium formation probability on the position of such near-threshold $S$-matrix singularities is analyzed. An estimation for the $\mathrm{H}\mathrm{H}¯$ annihilation cross section is obtained.

Cadmium $\mathrm{}(e,2e)\mathrm{}$ energy spectra have been measured for kinematics corresponding to a momentum transfer of 1 a.u. Two previously unknown cadmium autoinizing levels have been observed. Their energies are in excellent agreement with existing ab initio structure calculations of the ${4d}^9{5s}^{2}5p$ $J=3\mathrm{}$ levels. One level is easily seen at an ejected-electron direction along the momentum-transfer axis, but is absent for a direction 39° away from this axis. The opposite is true for the other level; it is absent in the former, but present in the latter case. This behavior is in agreement with a calculation that takes into account that the $J=3\mathrm{}$ levels can autoionize into both singlet and triplet $5sEf$ continua. The intensity of the new levels, relative to the well-known ${4d}^9{5s}^{2}5p$ $J=1\mathrm{}$ levels, agrees well with a plane-wave Born approximation calculation for the $J=3\mathrm{}$ levels. The third ${4d}^9{5s}^{2}5p$ $J=3\mathrm{}$ level is calculated to lie within the broad ${4d}^9{5s}^{2}5p{}^1{P}_1$ level and cannot be seen in the present experiments.

A systematic construction, based on a unified approach described by Gerjuoy, Rau, and Spruch [Rev. Mod. Phys. 55, 725 (1983)], of unrestricted variational principles related to the $R$-matrix theory for the Dirac equation is presented. Variational principles for eigenvalues and matrix elements of the operators ${\mathcal{R̂}}^{(\pm )}\mathrm{}\left(E\right)\mathrm{}$ and ${\mathcal{B̂}}^{(\pm )}\mathrm{}\left(E\right),$ relating values of upper and lower components of spinor wave functions on a surface S of a closed volume V inside which the functions satisfy the Dirac equation at energy $E,$ are derived. A variational principle for eigenvalues of the operators ${\mathcal{R̂}}^{\left(-\right)}\mathrm{}\left(E\right)\mathrm{}$ and ${\mathcal{B̂}}^{\mathrm{}(+)\mathrm{}}\mathrm{}\left(E\right)\mathrm{}$ has been already found before by Hamacher and Hinze [Phys. Rev. A 44, 1705 (1991)] but other variational principles are constructed in this paper.

Dielectronic recombination cross sections for ${\mathrm{U}}^{28+}$ are calculated in the distorted-wave approximation and compared with measurements obtained using an electron-ion merged beams apparatus. Although the experiment covered energies between 0 and 420 eV, the theoretical calculations were restricted to energies below 180 eV, where the most important resonance structures occur. The theoretical cross sections involving $\Delta n=0\mathrm{}$ excitations from the ${5s}^2{5p}^2$ ground configuration are found to be equally well described using either semirelativistic wave functions, as found in the AUTOSTRUCTURE codes, or fully relativistic wave functions, as found in the HULLAC codes. The main features of the experimental spectrum are well identified for the 80–180 eV energies, although complicated by the possible presence of unknown fractions of metastable levels. However, the resonance structures observed at the energies less than 80 eV, in the vicinity of a huge zero-energy peak, remain largely unexplained.

Cold-target recoil-ion-momentum spectroscopy (COLTRIMS) has been used to study single electron capture from He by ${\mathrm{Ar}}^{8+}$ ions at projectile velocities between 0.2 and 1.0 a.u. Populations of $3d$ through $7l$ states on the final ion are resolved, and angular distributions are presented for separated major final channels. As the projectile velocity is raised, the reaction window is observed to spread. Contrary to expectations based on a Landau-Zener picture of the process, higher $n$ and $l$ become favored with higher $v.\mathrm{}$ The results are in excellent agreement with coupled-channel calculations.