Two resonance structures, conventionally labeled b and c, appear between the first and second excitation thresholds in the electron-impact-excitation cross section of neon, and it has been suggested that spectroscopic assignments for these resonances should be based upon the ‘‘grandparent model’’ rather than on the ‘‘parent’’ model. Supportive evidence comes from both experimental and theoretical studies. In this model, it is assumed that two outer electrons participate in the formation of the resonance state relatively independently of the core electrons. This structure is reflected in the angular momentum coupling used to describe the resonance states. In this work, we validate the grandparent model of these resonances using complex dilated double-configuration Hartree-Fock calculations to determine the resonance eigenstates in the competing coupling schemes. For the b resonance, we also examine the isolation of the core from the two outer electrons as well as the effect of core relaxation. We reveal the roles played by exchange and orthogonality in the b resonance through graphical analysis by making use of special properties of the dilated eigenfunctions. Comparison with the lowest shape resonance in electron-sodium scattering is presented.

The ionization potentials of the 1${\mathit{s}}^2$2s states are calculated for Z=3 to 10 with a method of full core plus correlation using multiconfiguration interaction wave functions. Relativistic and mass polarization effects are included using first-order perturbation theory. The QED contributions to the ionization potential are calculated using effective nucleus charges. The results of this work generally agree with those of experiments. For example, our predicted ionization potentials for Li i and Be ii are 43 487.15(9) and 146 883.03(18) ${\mathrm{cm}}^{\mathrm{-}1}$ in comparison with the experimental results of 43 487.15 and 146 882.86 ${\mathrm{cm}}^{\mathrm{-}1}$, respectively. The predicted nonrelativistic energies in this work agree with those of King [Phys. Rev. A 40, 1735 (1989); 38, 6017 (1988)]. Our results show that the higher-order relativistic perturbation tends to reduce the ionization potential. It becomes appreciable for Z≥7, increases from less than 1 ${\mathrm{cm}}^{\mathrm{-}1}$ for carbon to about 14 ${\mathrm{cm}}^{\mathrm{-}1}$ for Ne. Although the agreement between our predictions and experiments is good for most systems, there is a clear discrepancy of more than 1 ${\mathrm{cm}}^{\mathrm{-}1}$ in the case of boron. The reason for this discrepancy is not understood at this time.

The Thomas-Fermi (TF) and Thomas-Fermi-Dirac (TFD) statistical models are extended by the electron-spin interaction with an external uniform magnetic field B. The statistical atom, which is spherical, is then described with the aid of two distributions: the electron density n(r) and the relative magnetization ζ(r). In the TF atom the magnetic field polarizes the electron spins totally (ζ=1) in a region near the atomic boundary, while the rest of the TF atom is only partially polarized; however, ζ(r) and n(r) are continuous. A convenient description of this atom is done with the aid of a suitably defined reduced potential f(x) to which n(r) and ζ(r) are related. At B>0 the neutral TF atom remains infinite. Its magnetic moment shows unphysical ${\mathit{B}}^{3/4}$ proportionality for small B. The inclusion of the exchange in the TFD model for B>0 results in two possible types of atom: the atom of the type I—which exists only for B≤1.3×${10}^7$ G—has continuous n(r) and ζ(r); in the type-II atom there is a discontinuity in both n(r) and ζ(r) that makes this atom unusable in physical applications. The type-I atoms have finite radii and are assumed to represent approximately the crystal atomic cells. The appropriate differential equation and boundary conditions for ζ(r), together with the relationship between ζ(r) and n(r), have been derived for this atom. The solutions of the equations and the atomic radii have been obtained for a wide range of atomic numbers and magnetic fields. On the basis of these solutions, the coefficients for the volume magnetostriction, the spin susceptibilities, and the ionization energies have been calculated for elements of the whole periodic table. Qualitatively, the experimental tendencies are found to be represented well by the type-I TFD atoms. A modified virial theorem for the spin-polarized TF and TFD atoms has been proved.

The principal result of this paper is a general expression for the second-order dipole polarization energy of a Rydberg electron resulting from the term -${\mathrm{\alpha }}_1$/${\mathit{r}}^4$ in the asymptotic potential, where ${\mathrm{\alpha }}_1$ is the core polarizability. It is shown that the second-order term contributes even as well as odd powers of 1/n in a 1/n expansion of the energies for Rydberg states. The results are used to extend the interpretation of the terms in a quantum-defect expansion. It is shown that the Ritz expansion for the quantum defect, which contains only even inverse powers of the effective quantum number ${\mathit{n}}^{\mathrm{*}}$, provides a powerful method for deducing the even-order terms in the second-order energy. Least-squares fits to high-precision variational calculations for the Rydberg states of helium, using 1/n and quantum-defect expansions, are presented. The results reveal well-defined ‘‘Ritz defects,’’ which represent the degree to which the data cannot be represented by a Ritz expansion for the quantum defect. The implications for extrapolations of quantum defects are discussed. Finally, it is shown that the second-order polarization energy plays a significant role in understanding the quantum defects for the alkali metals.

Potential-energy curves of various electronic states of ${\mathrm{CO}}^{2+}$ and ${\mathrm{CO}}^{+}$ are computed using all-electron ab initio molecular-orbital methods. Configuration-interaction effects are treated by perturbative techniques (using Möller-Plesset perturbation theory to fourth order) and by variational methods (using the coupled-cluster approach). In the case of ${\mathrm{CO}}^{2+}$, calculations indicate that the lowest-energy ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }$ and ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ states are nearly degenerate in the Franck-Condon region but that only the latter is likely to be metastable; the former is expected to predissociate rapidly due to a curve crossing with a purely repulsive ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{}^{\mathrm{-}}{}_{}{}^{}$ state. Experimental measurements have been carried out on the kinetic energy released when metastable ${\mathrm{CO}}^{2+}$ ions dissociate by a tunneling mechanism, using an ion-translational-energy spectrometer. The kinetic-energy spectra are measured of fragment ions produced when ${\mathrm{CO}}^{2+}$ dissociates via an intermediate highly excited (dissociative) ${\mathrm{CO}}^{+\mathrm{*}}$ state populated in an electron-capture reaction in collision with He. The experimental results remain difficult to interpret within the framework of the computed potential-energy curves.

The adiabatic channel wave functions of Coulombic three-body systems are investigated in mass-weighted hyperspherical coordinates. We consider the ABA Coulombic systems, where two of the particles are identical, and examine the density distribution functions at fixed hyperradii R for different systems as the mass ratio λ=${\mathit{m}}_{\mathit{A}}$/${\mathit{m}}_{\mathit{B}}$ varies from the atomic limit (λ→0, as in ${\mathrm{H}}^{\mathrm{-}}$) to the molecular limit (λ→∞, as in ${\mathrm{H}}_2^{+}$). The bonding and antibonding as well as the rovibrational characters of the three-body systems are illustrated by these density plots.

The dipole-dipole-quadrupole (B) and second dipole (γ) hyperpolarizabilities and the dipole (${\mathrm{\alpha }}_1$) and quadrupole (${\mathrm{\alpha }}_2$) polarizabilities are calculated for the ground states of the magnesium and calcium atoms and the aluminum cation. The results are based on finite-field fourth-order many-body perturbation theory using a finite-field self-consistent-field wave function as the zeroth-order wave function. Our fourth-order results are ${\mathrm{\alpha }}_1$=71.7${\mathit{e}}^2$${\mathit{a}}_0^2$${\mathit{E}}_{\mathit{H}}^{\mathrm{-}1}$, ${\mathrm{\alpha }}_2$=809${\mathit{e}}^2$${\mathit{a}}_0^4$${\mathit{E}}_{\mathit{H}}^{\mathrm{-}1}$, B=(-7.75×${10}^3$)${\mathit{e}}^3$${\mathit{a}}_0^4$${\mathit{E}}_{\mathit{H}}^{\mathrm{-}2}$, and γ =(1.02×${10}^5$)${\mathit{e}}^4$${\mathit{a}}_0^4$${\mathit{E}}_{\mathit{H}}^{\mathrm{-}3}$ for Mg; ${\mathrm{\alpha }}_1$=24.2${\mathit{e}}^2$${\mathit{a}}_0^2$${\mathit{E}}_{\mathit{H}}^{\mathrm{-}1}$, ${\mathrm{\alpha }}_2$=124${\mathit{e}}^2$${\mathit{a}}_0^4$${\mathit{E}}_{\mathit{H}}^{\mathrm{-}1}$, B=-642${\mathit{e}}^3$${\mathit{a}}_0^4$${\mathit{E}}_{\mathit{H}}^{\mathrm{-}2}$, and γ=(2.37 ×${10}^3$)${\mathit{e}}^4$${\mathit{a}}_0^4$${\mathit{E}}_{\mathit{H}}^{\mathrm{-}3}$ for ${\mathrm{Al}}^{+}$; and ${\mathrm{\alpha }}_1$=157${\mathit{e}}^2$${\mathit{a}}_0^2$${\mathit{E}}_{\mathit{H}}^{\mathrm{-}1}$, ${\mathrm{\alpha }}_2$=(3.02×${10}^3$)${\mathit{e}}^2$${\mathit{a}}_0^4$${\mathit{E}}_{\mathit{H}}^{\mathrm{-}1}$, B=(-3.29×${10}^4$)${\mathit{e}}^3$${\mathit{a}}_0^4$${\mathit{E}}_{\mathit{H}}^{\mathrm{-}2}$, and γ=(3.83×${10}^5$)${\mathit{e}}^4$${\mathit{a}}_0^4$${\mathit{E}}_{\mathit{H}}^{\mathrm{-}3}$ for Ca.

The best-known nonrelativistic energy of the term 1s2s2p ${}_{}{}^4{}_{}{}^{}$P° of neutral lithium is improved to an accuracy of less than 1 ${\mathrm{cm}}^{\mathrm{-}1}$ by using the Rayleigh-Ritz variational method with Slater-type basis functions. The relativistic, mass-polarization, and Lamb-shift effects are calculated perturbatively as first-order corrections to the nonrelativistic energy. Combined with best-known data from experiment, we attain the ionization potential 56 460.0(2) ${\mathrm{cm}}^{\mathrm{-}1}$ for the term 1s2s2p ${}_{}{}^4{}_{}{}^{}$P° of neutral lithium, compared to the experimental value of 56 473(5) ${\mathrm{cm}}^{\mathrm{-}1}$ by Mannervik and Cederquist [Phys. Scr. 27, 175 (1983)]. The discrepancy between theory and experiment is discussed. The relative term value of 1s2s2p ${}_{}{}^4{}_{}{}^{}$P° for neutral lithium is calculated to be 463 062.4(3.3) ${\mathrm{cm}}^{\mathrm{-}1}$ above the lithium ground state, compared with 463 039(122) ${\mathrm{cm}}^{\mathrm{-}1}$ by Rassi et al. [J. Phys. B 10, 3535 (1977)] from the ejected-electron spectrum. We have also extended the calculation to Li-like ions up to Z=9, where no experimental values are available.

The three-electron atomic correlation integral with Slater-type wave functions is evaluated in closed analytic form. The result is expressed in terms of rational functions, logarithms and dilogarithms of simple arguments, whose precise and fast numerical evaluation is straightforward.

The perturbed ladder-operator method is applied to the solution of the Coulomb eigenequation perturbed by an anharmonic potential, i.e., with a total potential U(x)=-m(m+1)/${\mathit{x}}^2$-2q/x +${\mathit{b}}_1$x+${\mathit{b}}_2$${\mathit{x}}^2$+${\mathit{b}}_3$${\mathit{x}}^3$+... . This method is an extension of the Schrödinger-Infeld-Hull factorization method within the perturbative scheme. The introduction of specific basis functions for the finite-difference solution of the factorazibility condition, together with the use of the symmetry properties of the Bernoulli polynomials, allows a straightforward determination of analytical expressions of the perturbed Coulomb ladder functions and eigenvalues. Some illustrative examples showing the capabilities of the method are given; particularly, analytical expressions of the linear, quadratic, and cubic Stark shifts are quickly derived.

The Kohn-Sham (KS) one-electron Schrödinger equations assume the existence of a one-body effective potential ${\mathit{v}}_{\mathrm{eff}}$(x), defined to generate the correct electron density ρ(x) of the ground state. This paper returns to the electron-density description of an N-fermion system. It is best thought of as starting from a given ρ(x), ideally to be obtained from diffraction experiments. A method is then set up that focuses predominantly on the way the ‘‘correct’’ ${\mathit{v}}_{\mathrm{eff}}$(x) can be ‘‘recovered,’’ if it exists, from such an experimental density. Certainly the method has associated with it one practical disadvantage in common with the KS procedure; an order of N Euler equations have to be solved, with input information ρ(x), though the ‘‘unknown’’ potential ${\mathit{v}}_{\mathrm{eff}}$(x) does not now appear. In this program, we have found it most helpful to work with the Pauli potential and energy, which enable the N-fermion problem to be converted to a boson problem for the density amplitude [ρ(x)${]}^{1/2}$. The way the above-mentioned Euler equations determine the Pauli potential and energy is worked out explicitly. Examples that embrace the important area of atomic central-field calculations are presented to illustrate the method. As a by-product, the theory developed can afford a direct test as to whether a given electron density is, in fact, representable via a one-body potential ${\mathit{v}}_{\mathrm{eff}}$(x).

We have examined the recent solution of the Fock expansion through O(${\mathit{r}}^2$) for the ground state of the helium atom and have verified that it correctly treats the discontinuity in the local energy characteristic of the triple-collision point. We have also developed an exponential representation of the Fock expansion that satisfies Kato’s cusp conditions for two-particle collisions even when the expansion is truncated at a finite order.

A series of high-level correlated (many-body-perturbation-theory and coupled-cluster) calculations on the dipole polarizability of Ca, Sr, and Ba has been carried out. The relativistic effects have been incorporated in calculations at both the Hartree-Fock and correlated levels of approximation. Calculated values of the dipole polarizability of Ca, Sr, and Ba are 152, 190, and 273 a.u., respectively, and in agreement with experimental data from electric-deflection measurements. The relativistic effect on the dipole polarizability is very small (-2 a.u.) for Ca, amounts to about -11 a.u. for Sr, and becomes comparable with the electron-correlation contribution for Ba (-37 a.u.). An optimized Gaussian basis set has been generated for Ba, the details of which are included in the paper.

Valence-orbital ionization potentials (VOIP’s) for 5d transition elements have been derived by performing fully relativistic self-consistent numerical local-density atomic calculations. The von Barth–Hedin–Lundqvist local exchange and correlation potential was employed. In order to evaluate the accuracy of the calculated VOIP’s, theoretical ionization potentials were compared with experimental results obtained from data on the atomic spectra of neutral and of singly, doubly, and triply charged 5d transition elements, for the few atomic configurations for which measurements are available. Good agreement was obtained between experimentally derived and theoretical ionization potentials, the latter calculated by a ‘‘transition-state’’ procedure. Comparison was also made with results obtained by performing nonrelativistic local-density calculations. The use of the Kohn-Sham local exchange-only potential was also investigated, in order to assess the effect of correlation corrections included in the von Barth–Hedin–Lundqvist potential. Moment-polarized relativistic local-density calculations were also performed and compared with the available experimental results.

The problem of calculating the cross section for bound-electron–positron pair creation in very-high-energy heavy-ion colliders (100 GeV/u or higher, an effective γ≳2×${10}^4$) is addressed. The multipole decomposition of the basic time-varying interaction is explicitly written in terms of simple and compact forms that display the energy (γ) dependence directly. Then, specific gauge transforms remove the γ dependence for smaller impact parameters, up to negligible terms of higher order in 1/γ. For larger impact parameters b, the interaction is shown to weaken as 1/b, where the known perturbative results apply. Only at small impact parameters are strong-coupling calculations necessary, but the gauge choices show that the contributions from these regions are γ independent. Putting these results together leads to a simple form for the cross section, A lnγ+B, where A and B are energy independent and A is known from the perturbative calculations. This form and its weak dependence on energy makes extrapolation from lower-energy results reliable and indicates the usefulness of a possible experiment at comparatively low energies (γ∼200).

A six-state coupled-channel optical potential for electron-atom scattering is applied to electron-hydrogen scattering at energies of 13.87, 16.46, 19.58, 35, 40, 54.4, 100, and 200 eV. The n=1, 2, and 3 channels are coupled explicitly, whereas the rest of the excited states of the atom including the continuum are taken into account via the ab initio complex nonlocal polarization potential. The differential and integrated cross sections, as well as the exchange asymmetries for n=1 and 2 channels, the total cross section, and the λ, R, and I parameters for the 2p excitation, are presented at each energy. The ratio of differential cross sections for n=1 to 2, and for 2s to 2p, and the 2s+2p differential cross sections are found to be in good agreement with experiment. There are still some discrepancies between experiment and theory for the 2p angular correlation parameters λ, R, and I.

Measurements of absolute differential cross sections for ${\mathrm{H}}^{+}$-${\mathrm{H}}_2$ direct, single-, and double-charge-transfer scattering at 0.5, 1.5, and 5.0 keV are reported at laboratory scattering angles less than 1° with an angular resolution of approximately 0.02°. The cross sections exhibit deep interference oscillations in single-charge-transfer scattering, but no such oscillations are present in direct and double-charge-transfer scattering. Theoretical cross sections derived using the diatoms-in-molecules method to describe the molecular states in a semiclassical molecular-orbital three-state close-coupling model within a semiclassical framework agree satisfactorily with the experimental results.

For the case of one-electron collisional systems and the straight-line nuclear trajectories, we study the limits of separated and united atoms of dynamical adiabatic states compatible with physical boundary conditions. The limit of separated atoms is similar to the problem of hydrogen atom in crossed, orthogonal electric and magnetic fields, and analytic results are obtained by utilizing the O(4) symmetry of bound states in a Coulomb field. In the united-atom limit the overlapping manifolds of dynamical potential-energy curves are predicted and analyzed.

We have calculated the binding-energy–distance curves for several diatomic molecules in an excited electronic state based on the method developed in the previous work [Phys. Rev. A 42, 6497 (1990)]. We also compared the result with experimental curves.

A determination of the alignment of ${\mathrm{He}}^{+}$(2p) between the n=2 and 3 levels was carried out by measuring the angular distribution of the 304-Å fluorescence that follows photoionization with synchrotron radiation. The alignment ${\mathit{A}}_{\mathit{c}}^0$ is related to the cross-section ratio ζ=${\mathrm{\sigma }}_{2\mathit{p}\mathit{k}\mathit{d}}$/${\mathrm{\sigma }}_{2\mathit{p}}$ and thus provides a means of separating the kd and ks partial-wave contributions to the 2p ion production. The partial-cross-section ratio R=${\mathrm{\sigma }}_{2\mathit{p}}$/${\mathrm{\sigma }}_{2\mathit{s}}$ was also determined by measuring the fluorescence signal at the magic angle with and without an external electric field that quenches the 2s ions. With these data a partition of the n=2 cross section into the partial cross sections ${\mathrm{\sigma }}_{2\mathit{s}\mathit{k}\mathit{p}}$, ${\mathrm{\sigma }}_{2\mathit{p}\mathit{k}\mathit{s}}$, and ${\mathrm{\sigma }}_{2\mathit{p}\mathit{k}\mathit{d}}$ was carried out. The effect of the broad $1_3$ autoionizing resonance in these partial cross sections was determined. A comparison with the results of a many-body-perturbation-theory calculation shows good agreement for the alignment, as well as for R, ${\mathrm{\sigma }}_{2\mathit{s}\mathit{k}\mathit{p}}$, and ${\mathrm{\sigma }}_{2\mathit{p}\mathit{k}\mathit{s}}$, but somewhat of a discrepancy for ${\mathrm{\sigma }}_{2\mathit{p}\mathit{k}\mathit{d}}$.