We examine expectation values of ${\mathrm{p}}_1$⋅${\mathrm{p}}_2$ in ground states of He and ${\mathrm{H}}^{\mathrm{-}}$, the singly and doubly excited states of He, and the ground and low-lying valence states of the alkaline-earth-metal atoms. A simple commutator relation derived by Froese Fischer and Smentek-Mielczarek [J. Phys. B 16, 3479 (1983)] can be used to explain the sign and relative magnitudes of 〈${\mathrm{p}}_1$⋅${\mathrm{p}}_2$〉 in the ground states of He and ${\mathrm{H}}^{\mathrm{-}}$ and singly excited states of He. In the doubly excited states of He and in the ground and low-lying valence states of the alkaline-earth metals, the molecular model, which treats the electron–core-electron system as a floppy, linear triatomic ‘‘molecule,’’ correctly predicts signs and general trends for 〈${\mathrm{p}}_1$⋅${\mathrm{p}}_2$〉. These results represent an important test of the molecular model. The ability of this model to make intuitive predictions about quantities like 〈${\mathrm{p}}_1$⋅${\mathrm{p}}_2$〉 is a strong confirmation of its validity and utility.

For the case of particle-number-conserving systems, the Clifford algebra unitary-group approach (CAUGA) is reformulated from the U($2^n$)↓U(n) subduction viewpoint, providing a more direct physical insight into the structure of this formalism. This enables us to exploit a general system partitioning in the many-electron correlation problem for atomic and molecular systems within the CAUGA formalism. Several methods are given for the the CAUGA representation of both Gel’fand-Tsetlin and U(${\mathit{n}}_1$+${\mathrm{n}}_2$)⊃U(${\mathrm{n}}_1$)⊗U(${\mathrm{n}}_2$) adapted partitioned bases, namely the permutation-orthogonalization method, the U(n) Clebsch-Gordan coefficient method, and the linear algebraic equation method. The flexibility offered by a general system partitioning for a physically meaningful configuration-interaction (CI) truncation and for a more efficient CI matrix element evaluation is illustrated on several examples.

The recently introduced technique of constructing finite basis sets from B-splines for use in atomic-physics calculations is applied to the alkali-metal atoms Li, Na, K, Rb, and Cs. Valence energies are calculated within the framework of many-body perturbation theory to second order, and corrections to hyperfine splitting and transition matrix elements to third order in the approximation that a dominant subset of the terms in this order, associated with Brueckner orbitals, is evaluated. Agreement with experiment at the 1% level is found for all of the atoms considered. Comparisons are made with other calculations, and a short discussion of the systematic extension of this work is given.

The energies and oscillator strengths for the spin-allowed 6$s^2$ ${}^1$$S_0$–6s6p ${}^1$$P_1$ and spin-forbidden 6$s^2$ ${\mathrm{}}^1$$S_0$–6s6p ${\mathrm{}}^3$$P_1$ transitions in neutral barium have been determined in relativistic multiconfiguration Dirac-Fock calculations, where restricted relativistic configuration mixing to represent intravalence correlation is combined with a polarization model to account for valence-core electron correlation. The relativistic and correlation effects—as can be seen from this study—are not additive but must be calculated simultaneously. The contributions of different configurations to intravalence correlation in both initial and final states are studied in detail. The present results demonstrate that although inclusion of intravalence correlation considerably decreases the discrepancies between the computed quantities and experimental data, it is nevertheless not sufficient: To achieve good agreement, particularly for oscillator strengths, one must also include core-valence correlation. The core-polarization model used in this study to represent this type of correlation again proves to be quite a satisfactory approximation.

An algorithm developed earlier for generating ground-state electron densities and energies from one-body external potentials and trial densities of first-order density matrices (one-matrices) is tested for noninteracting systems. For these tests, two end-point systems A and B are known while densities and energies for potentials between $v_A$ and $v_B$ are generated. The end-point external potentials $v_A$ and $v_B$ are chosen to be ${\mathrm{Li}}^{\mathrm{-}}$ and Be Coulomb potentials, respectively, while the intermediate external potentials are Yukawa-like potentials. Densities for these Yukawa-like potentials are generated by starting with reasonably good first approximations to the Yukawa densities and using the algorithm to improve upon these densities. Typical improvements in energies of densities adjusted to conform to the algorithm are anywhere from a factor of 2 to a factor of 8 better than the original guesses. Within exchange-only density-functional theory, this algorithm also provides for a means of computing implicitly the noninteracting kinetic energy $T_s$[ρ], from one or more known end points, by using just densities and one-body potentials. It is suggested that the algorithm might also be used to generate excited-state energies as an illustration of a Theophilou-type calculation, and a simple noninteracting example is presented. It is shown that the exact interacting exchange-only energy for the ground state may be written explicitly [Eq. (34)] in terms of the density, the effective potential, and the external potential. Finally, it is shown that it is possible for an approximation to the universal Hohenberg-Kohn density functional to yield exact ground-state energies and densities for a range of various external potentials, even if the approximate functional yields incorrect energies for all other external potentials.

The decay curves for 2p-1s and 3p-1s transitions in 32-MeV H-like oxygen projectiles excited by a thin carbon foil have been measured and compared with the results of a cascade computer program which calculates the intensities of these transitions for an assumed initial distribution of excited states as a function of decay time. The measured decay curves agreed best with those predicted by the cascade program using an l-independent population probability proportional to $n^{\mathrm{-}4}$ for each state.

A first-order relativistic theory of electron capture satisfying Coulomb boundary conditions in entrance and exit channels is formulated and evaluated. In this way, the asymptotic time dependence caused by the long-range, properly Lorentz-transformed Coulomb interaction is eliminated from initial and final electron wave functions, and a short-range perturbation is obtained in the transition amplitude. Within this theory, the post and prior forms of the transition amplitude are shown to be equivalent. Numerically calculated cross sections are in good agreement with experimental data. They are slightly larger than those derived from the relativistic eikonal approximation.

Absolute cross-section measurements are reported for electron-impact ionization of iron ions with initial charges 11+, 13+, and 15+. The data extend from below the ionization thresholds to 1500 eV for ${\mathrm{Fe}}^{11+}$ and to 1400 eV for ${\mathrm{Fe}}^{13+}$, while the ${\mathrm{Fe}}^{15+}$ data cover the energy range from 630 to 1000 eV. Good agreement is found in each case between the measurements and detailed calculations which include the contributions due to the mechanism of inner-shell excitation-autoionization, but predicted significant enhancements of the ${\mathrm{Fe}}^{15+}$ cross section due to resonant-excitation double autoionization are not observed. Ionization rate coefficients and fitting parameters are presented based on the data.

Data for simultaneous capture and ionization in helium by ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{2+}$, and ${\mathrm{Li}}^{3+}$ are compiled and analyzed in terms of direct and rearrangement mechanisms at high projectile velocity. Some new data for ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{2+}$ are presented and a similarity in the ratio of cross section for capture and ionization to single capture plus capture and ionization for projectiles of charges Z=2 and 8 is noted.

The possibility of a microscopic Penning trap [suggested by C. W. Clark, E. Korevaar, and M. G. Littman, Phys. Rev. Lett. 54, 320 (1985)] formed by the magnetic-field-induced stabilization of saddle-point motion of an atomic electron moving in the presence of combined internal Coulomb and externally applied electric and magnetic potentials is investigated using time-dependent methods. Photoeffect spectra are calculated as the Fourier transform of the dipole correlation function for propitiously chosen initial conditions, and these indeed show oscillations as predicted by Clark et al. However, it is shown that maximal trapping occurs for the case in which only the magnetic field is present (giving the usual Landau confined states for electrons with zero average mechanical momenta) and that the Stark-Coulomb saddle point simply destabilizes this simpler motion. Both the relationship of the calculated spectra to the propagation of wave packets in the combined fields and their relationship to the periodic classical orbits ‘‘quantized’’ by Clark et al. are discussed. The more difficult problem of predicting what might be observed in a photoeffect spectrum of an atomic ground state in the presence of crossed external fields is also discussed from the time-dependent perspective.

In the framework of the kinetic theory of stopping it is possible to relate the stopping power of a substance to the velocity distribution of the scatterers, which can be obtained from the Compton profile. This relation is explored, and is used to determine values of the mean excitation energy for Al solid and vapor and gaseous Ar, He, ${\mathrm{N}}_2$, and ${\mathrm{CH}}_4$. The mean excitation energy is determined as the value which within the kinetic theory gives the best fit to measured or calculated stopping cross sections.

The nature of the absorption spectrum of a system of two strongly coupled autoionizing states each of which can decay to its own continuum is discussed. The interference minimum in the spectrum is found to be quite sensitive to the relative magnitude of the autoionization rates of the uncoupled states. The general considerations also yield the results for the laser-induced autoionization with two exit channels.

Angular distributions of product Ne ions have been measured for ${\mathrm{Ne}}^{+\mathrm{q}}$ (q=3–6) capturing electrons from He at laboratory incident energies between 172 and 1200 eV. For q=4 the distributions are strongly peaked in the forward direction, while for q=3, 5, and 6 the reaction products are concentrated at larger scattering angles. Oscillatory structure is seen for q=4 and 6. The distributions are interpreted in terms of classical defelction functions calculated using model potentials. The oscillatory structure is identified as due to Stueckelberg oscillations. On the basis of the experiment and model results, it is argued that the forward peaking for q=4 may be expected to be a general characteristic of capture by multiply charged, but not bare, projectiles which lead to the population of s orbits on the projectile core.

The positron-annihilation spectra and decay rate in neon gas have been simulated via the Boltzmann time-dependent equation in the presence of electric and magnetic fields at room temperature using the positron-atom interaction model of McEachran, Ryman, and Stauffer [J. Phys. B 3, 551 (1978)]. The electric and magnetic fields are varied over the ranges 0–10 V${\mathrm{?}}^{\mathrm{-}1}$ and 0–10 kG, respectively. Equilibrium is reached at about 18?0 ns after the initial introduction of a positron swarm when there are no electric and magnetic fields present. The equilibrium value of the annihilation decay rate is 6.97 at zero electric and magnetic fields. The time for attaining equilibrium decreases with the increase in electric field. Its values are 6000, 3600, and 2400 ns for E=2, 5, and 10 V ${\mathrm{cm}}^{\mathrm{-}1}$, respectively. The effect of magnetic field is to delay the approach to the equilibrium of the positron distribution.

The structure of the ground state of the Hamiltonian of a two-level system linearly coupled to a single mode of a radiation Bose-like field is studied for arbitrary values of the coupling constant including the counter-rotating terms. First of all the Hamiltonian is canonically transformed, introducing a new set of unitary operators in such a way that the eigenstates of the transformed Hamiltonian are exactly factorizable into eigenstates of the new pseudospin (1/2) and of the new field. The ground state is then found by a variational procedure. The validity of the results obtained by this approach is shown introducing a suitable class of canonical transformations by which it is possible to see that this variational ground state differs from the exact one only for perturbative contributions for which we give explicit expressions. Furthermore, we present investigations on the properties of this system in its ground state based on the calculation of the covariance of suitable pairs of operators. In this way we succeed in obtaining, among other things, a physically transparent meaning for the mathematical variational condition which determines the ground state.

The structures above the Kr K edge are reported and for the first time interpreted as due to multielectron transitions involving K, M, and N electrons. The cross section of the 1s3d multielectron transition is analyzed and an onset more rapid than the one expected according to the ‘‘shake’’ model is observed. This behavior is quite well described by a model proposed by Stöhr, Jaeger, and Rehr [Phys. Rev. Lett. 51, 821 (1983)] based on the exchange interaction.

We have measured the Stark spectra of 5$d_{3/2}$8l autoionizing states in barium. Because of the anisotropic 5d ion core, the Stark manifolds at higher fields are considerably more complex than those for the analogous 6snl bound states. The electrostatic coupling of the Rydberg electron with the anisotropic core gives rise to relatively large fine-structure splittings. For nonpenetrating orbitals ($l_{\mathrm{Ry}>l_{\mathrm{core}}}$), jK coupling is a useful representation and the number of fine-structure components due to this interaction with the core increases the number of eigenstates (2$j_{\mathrm{core}+1\mathrm{}}$)-fold. We present a theoretical model for the calculation of Stark spectra in jK coupling. Results for barium are in quantitative agreement with the experimental observations for both π and σ polarizations up to fields where there is extensive overlap between adjacent n manifolds. These fine-structure effects occur for any states with nonisotropic cores ($j_{\mathrm{core}>(1/2)\mathrm{}}$), i.e., the states of most atoms except for bound singly excited states of alkali-metal and alkaline-earth-metal atoms.

Photodissociation cross sections for both ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ above the H(n=1)+H(n=2) threshold are presented. The partial cross sections into H(1s)+H(2s) and H(1s)+H(2p), obtained by full numerical integration of coupled Schrödinger equations, show pronounced oscillations as a function of the excitation energy. These oscillations are the result of a quantum interference effect between two dissociation paths leading to the same final state. The condition for this interference to occur is the existence in the Franck-Condon region of two dissociative states (B and B’ in the case considered in this work) which can be excited at the same energy and which are coupled to each other by some nonadiabatic or other electronic interactions. The relationship between the full numerical calculation and the ‘‘half-collision’’ approximation is analyzed in detail. In addition, the predissociation of the D state, which occurs in the same spectral region, has also been studied. The line shapes obtained by solving the appropriate coupled Schrödinger equations are compared with those calculated by the use of perturbation theory. It is shown that, in order to have good agreement with the exact results, it is important to take into account contributions which are usually neglected, namely the contributions from the discrete spectrum of the final dissociative channel. Finally, the branching ratio Ω=σ(${\mathit{H}}_2$→H(1s)+H(2)σ(${\mathrm{H}}_2$p→H(1s)+H(2s) in the case of predissociation has been calculated and compared with other published calculations.

The main atomic ionization energies of Ca (Z=20) are calculated by the g-Hartree method. The agreement between theory and experiment is excellent. A detailed comparison of present method with other approximation schemes is made.

Absorption properties of a system consisting of two autoionizing states coupled strongly either by internal interactions or by external fields are investigated. The autoionizing states may themselves correspond to those induced by laser fields as in resonant multiphoton ionization. The analysis is based on the density matrices and incoherent processes like spontaneous emission and radiative recombination are included. Optical susceptibilities exist in a number of special cases for autoionizing transitions. Exact results for such optical susceptibilities are obtained. Explicit numerical results for susceptibilities, corresponding traditionally to strong-field inverse Raman effect, are given with a view to recent work on dc-field-coupled autoionizing states and on laser-induced autoionization. The behavior of both absorptive and dispersive parts is discussed for a range of parameters.