The electron-diffraction pattern for two slits with magnetic flux confined to an inaccessible region between them is calculated. The Aharonov-Bohm effect gives a diffraction pattern that is asymmetric but has a symmetric envelope. In general, both the expected displacement and the kinetic momentum of the electron are nonzero as a consequence of the asymmetry. Nevertheless, Ehrenfest’s theorems and the conservation of momentum are satisfied.

Lifetimes of the 2${\mathit{p}}^5$3s ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ and ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ levels in Svii and Clviii have been measured using the beam-foil technique. The results are 17.4±0.5 (13±1) and 52±2 (27±1) ps for Svii (Clviii). Many theoretical results, obtained by a variety of methods, are available for these lifetimes. A summary of the theoretical lifetimes reveals a significant scatter of the results, and none of the calculations agrees with all the present experimental data.

We have found a long-lived metastable state of stopped ${\mathrm{\pi }}^{\mathrm{-}}$ in liquid helium by measuring the time spectra of two different delayed products: (i) protons emitted after ${\mathrm{\pi }}^{\mathrm{-}}$ absorption by ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ nuclei and (ii) 70-MeV electrons originating from free ${\mathrm{\pi }}^{\mathrm{-}}$→${\mathit{e}}^{\mathrm{-}}$${\nu }_{\mathit{e}}$¯ decay. The lifetime and fraction of delayed ${\mathrm{\pi }}^{\mathrm{-}}$ absorption obtained by using the emitted protons are 7.26±0.12 nsec and 1.66±0.05%, respectively. The free-decay fraction of a pion in liquid helium was obtained to be 0.64±0.03% from this result, which is consistent with the observed free-${\mathrm{\pi }}^{\mathrm{-}}$ decay fraction. These results imply that 2.30±0.07% of stopped ${\mathrm{\pi }}^{\mathrm{-}}$ are trapped in the metastable state which have an overall lifetime of 10.1±0.2 nsec. The same experimental and analysis were performed for stopped ${\mathrm{\pi }}^{\mathrm{-}}$ in liquid neon, where no evidence for trapping was found.

Calculations on the ground state of HT and ${\mathrm{CH}}_3$T and the excited states of ${\mathrm{HHe}}^{+}$ and ${\mathrm{CH}}_3$${\mathrm{He}}^{+}$ have been carried out within the sudden approximation to test alternative approaches to existing problems, with the ultimate aim of studying the effects of a molecular environment on the detailed energetics of tritium β decay. By using an appropriate projection operator most of the transition probability has been accounted for. Commonly used sum rules are shown to have limited utility. The inaccuracies introduced by describing an excited state by a single spin-adapted configuration are discussed. The problem of determining transition probabilities from configuration-interaction wave functions is highlighted and some solutions are proposed.

The configuration of an N-body system can be entirely represented by N-1 relative position vectors after separation of the center-of-mass motion. Many of the sets of coordinates that are commonly used for describing molecular configurations can be viewed as spherical coordinates, for the various vectors, collected together. The spherical angles are local; i.e., they are defined for frames that change from one vector to another. Each particular set of coordinates of that nature (polyspherical coordinates) consists of three Euler angles for the overall rotation of the body-fixed frame and 3N-6 internal coordinates: the N-1 vector lengths, N-2 planar angles between pairs of vectors, and N-3 dihedral angles between two vectors around a third one. This article aims at developing an example of this type of parametrization, where the body-fixed-frame z axis is parallel to one vector. The quantum-mechanical kinetic-energy operator for the system so described is derived. The operator action on the angular part of the functional basis set is studied (Wigner rotation matrix elements for the Euler angles and spherical harmonics for the internal angles), and the structure of the matrix representing the kinetic-energy operator is described in detail. The advantages and drawbacks of the present vector parametrization and the polyspherical coordinates are discussed. The principal advantage is in numerically calculating the matrix elements of the kinetic-energy operator: The integration over all angles turns out to be analytically achieved, so that the numerical effort is to be concentrated only on the N-1 radial coordinates. Radial basis functions are to be selected according to the physical context (collisonal or vibrational, or any other). Thus the angular basis set proposed constitutes an adequate finite-basis representation for the kinetic-energy operator and, combined with a discrete-variable representation for the potential energy, is likely to provide an efficient collocation framework for the dynamical study of more-than-three particle systems.

The existence of bound states and the discrete-spectrum classification in the three-body Coulomb nonrelativistic system with unit charges is considered. It is shown that in such systems the bound states exist not at arbitrary, but instead only at definite values of the mass ratios, which must lie in a ‘‘stable region.’’ The position of this ‘‘stable region’’ is studied for the bound ground S states.

We have measured the hyperfine structure (hfs) of 12 levels in the configurations 3d4s, 3${\mathit{d}}^2$, and 3d4p in singly ionized scandium by collinear fast-ion-beam–laser spectroscopy. The hfs of the four levels in the configuration 3d4s has to our knowledge not been measured before. From these levels the ions were excited to levels in the 3d4p configuration by the frequency-doubled output of a ring dye laser with an intracavity mounted ${\mathrm{LiIO}}_3$ crystal. Levels in the 3${\mathit{d}}^2$ configuration were excited to levels in the 3d4p configuration with visible laser light. The resulting magnetic dipole (A) and electric quadrupole (B) hfs constants are analyzed in Sandars-Beck effective-operator formalism. The multiconfiguration Dirac-Fock method has been used to calculate the hfs constants for levels in the configurations 3d4s, 3d5s, 3d6s, 3${\mathit{d}}^2$, and 3d4p. Within the framework of the configuration-interaction method, an approach is presented for the calculation of the core polarization, which uses a virtual basis set localized inside the core. For all levels, this approach gives better results compared to previously published calculations.

We examine the ability of one- and two-point Gauss-Laguerre quadratures in correctly describing the asymptotic behavior of Fourier transforms. We illustrate the effectiveness of this method with the example of the neon atomic form factor and compare it to the results obtained from the familiar expansion in terms of inverse powers of the independent variable and the derivatives of the charge density at the origin.

A family of equations for the (square root of the) electronic density is constructed and analyzed within the context of density-functional theory.

In the calculation of the dynamic polarizability including electronic correlation and ensuring gauge invariance, contributions of spectroscopic states and quasispectral series are analyzed. An improvement of our original electric-field variant ket approach is proposed and illustrated by application to H and LiH systems.

Doubly excited ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{e}}$ resonant states in ${\mathrm{Ps}}^{\mathrm{-}}$ are calculated using a method of complex-coordinate rotation. Resonance parameters (both resonance positions and widths) for doubly excited states associated with the n=2, 3, 4, 5, and 6 thresholds of positronium atoms are evaluated using elaborate Hylleraas-type functions. In addition to ten Feshbach-type resonances lying below various Ps thresholds, we have identified three shape resonances, one each lying above the n=2, 4, and 6 Ps thresholds. It is further noted that the energy levels for the present ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{e}}$ states are nearly degenerate with respect to the previously calculated ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ states. Such a symmetric character suggests that the highly and doubly excited ${\mathrm{Ps}}^{\mathrm{-}}$, similar to its counterpart in ${\mathrm{H}}^{\mathrm{-}}$, would exhibit rovibrational behaviors analogous to those of XYX triatomic molecules.

A theoretical procedure for calculating magnetic susceptibility and nuclear magnetic shieldings in molecules in the presence of a spatially uniform time-independent magnetic field, within the Landau gauge for the vector potential, is described. Sum rules for charge and current conservation and gauge invariance have been derived. A computational scheme based on the random-phase approximation has been used to calculate magnetic susceptibility and shielding tensors in the water molecule, adopting fairly flexible Gaussian basis sets of large size. The results show that very accurate molecular wave functions are needed to obtain paramagnetic contributions to the magnetic susceptibility of the same quality as those obtainable within the Coulomb gauge for the vector potential. The theoretical nuclear magnetic shielding tensors in the Landau gauge are characterized by the same quality as those in the Coulomb gauge.

The effect on the β spectrum of exchange between bound and continuum electrons is discussed for decay of a many-electron atom. Results of calculations of the exchange distortion of the β spectrum are presented using both a screened hydrogenic and a Hartree-Fock approximation for the electron wave functions. The results of the two approaches agree well and show that the inclusion of exchange leads to an enhancement of the β spectrum, particularly at low electron energy. This corrects an error in a previous calculation that found that exchange decreased the β intensity. For the low-energy ${\mathrm{\beta }}^{\mathrm{-}}$ emitters ${}_{}{}^{106}{}_{}{}^{}\mathrm{Ru}$ and ${}_{}{}^{241}{}_{}{}^{}\mathrm{Pu}$, the present calculation indicates that the enhancement due to exchange is of the order of several percent over much of the spectrum, becoming larger at very low electron energy. Exchange with 1s electrons dominates in the high-energy part of the spectrum, but exchange with ns (n≥2) electrons becomes significant in the low-energy region. The inclusion of exchange leads to an increase in the phase-space integral by 6.4% for ${}_{}{}^{106}{}_{}{}^{}\mathrm{Ru}$ and 7.5% for ${}_{}{}^{241}{}_{}{}^{}\mathrm{Pu}$. Results are presented for exchange effects in other β spectra, including those of ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{35}{}_{}{}^{}\mathrm{S}$, in which experimentally measured distortions have been interpreted as evidence for a heavy antineutrino of mass 17 keV. The distortions due to exchange are found to be significantly smaller than the measured distortions.

We discuss a nonperturbative treatment of lepton-pair production caused by the strong and sharply pulsed electromagnetic fields generated in peripheral relativistic heavy-ion collisions with an emphasis on the capture process into the atomic K shell. We calculate, in a field-theoretical framework, impact-parameter-dependent probabilities and cross sections for such processes by solving the time-dependent Dirac equation on a three-dimensional Cartesian lattice using the basis-spline collocation method. We give a full discussion of the stationary states used in computing S-matrix elements. Use of the axial gauge for the electromagnetic potentials produces an interaction easier to implement on the lattice than the Lorentz gauge. Preliminary calculations are given for muon-pair production with capture into the K shell in collisions of ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$${+}^{197}$Au at collider energies per nucleon of 2 and 100 GeV.

Charge-exchange differential cross sections are calculated by the second Born approximations without a recourse to any further approximation. The exact second Born approximation cross sections show satisfactory agreement with the experimental data for proton-helium collisions at all the energies of 2.82, 5.42, and 7.4 MeV while they are considerably smaller than the existing experimental cross sections in the Thomas peak region for proton-hydrogen collisions at 2.8 MeV. Discussions are given on how to choose the interactions for two-electron systems in order to satisfy the boundary condition of neutral-atom collisions.

A mechanism of unphysical structures in photoionization cross sections calculated in the independent-particle approximation (IPA) has been identified, in a study of the nature of near-threshold structures in the energy dependence of the krypton 3p photoionization, generated in the Hartree-Fock-Slater-Latter approximation. We find that overscreening of the IPA potential due to the incomplete cancellation of the electron self-Coulombic interaction and the electron self-exchange interaction in the IPA can lead to a spurious positive barrier in the effective central potential ${\mathit{V}}_{\mathit{e}\mathit{f}\mathit{f}}$=V+l(l+1)/2${\mathit{r}}^2$ for a continuum electron and a consequent spurious shape-resonance-like structure, such as the structure at about 8 eV above the threshold seen in the Kr 3p photoionization cross section.

Theoretical studies of low-energy electron-silane scattering are reported in which target polarization is included by using an ab initio optical potential. These calculations employ the complex Kohn scattering method and were undertaken both at the static-exchange level and with target polarization. A polarized virtual-orbital method, which was introduced in our earlier study of electron-methane scattering, was also employed in this study to generate a compact description of the closed channels included in the optical potential. Differential, integral, and momentum-transfer cross sections are reported at incident energies ranging from 0.2 to 20 eV. The computed total cross section shows a Ramsauer-Townsend minimum at 0.3 eV and a broad d-wave shape resonance at 3.0 eV. Excellent agreement is found between our polarized Kohn results and the recent experimental results of Wan, Moore, and Tossell [J. Chem. Phys. 91, 7340 (1989)].

Absolute measurements and calculations of the rate coefficient 〈νσ〉 for dielectronic recombination associated with Li-like ions of nitrogen, fluorine, and silicon are reported. The measurements were performed with a single-pass merged-beam technique. The excitation associated with the dielectronic recombination reaction is 2s→2p. With the present energy resolution, we are able to distinguish between capture into low-lying resonances, which are insensitive to perturbing fields, and capture into the high Rydberg states, which are perturbed by small electric fields present in the experiment. The experimental data are compared with distorted-wave calculations that include the influence of static electric fields in the interaction region.

Photoionization cross sections, branching ratios, and photoelectron angular distributions have been calculated for Ra (Z=88) 7s, 6p, 6s, 5d, and 5p, and Rn (Z=86) 6p, 6s, 5d, and 5p subshells within the framework of the relativistic random-phase approximation, including coupling between all of the relativistic channels arising from these subshells, in an effort to elucidate the interplay between relativistic and interchannel interactions at high Z where no experiments are extant. The results show that, aside from inducing structure in subshell cross sections, relativistic plus interchannel effects dominate the photoelectron angular-distribution asymmetry parameter and the branching ratio between spin-orbit doublets largely through the relativistic splitting of Cooper minima. This qualitatively confirms effects predicted by simple central-field calculations. Detailed explanations of the reasons for each of the structures are presented.

We have reformulated the Dirac R-matrix method for low-energy electron scattering by (effectively) one-electron, alkali-metal-like systems and developed an independent computer program for this special purpose. A highly accurate and relativistic representation of the target was used to perform a multichannel close-coupling calculation of cross sections for electron scattering. Our results include the negative-ion affinity and elastic, inelastic, and total cross sections for incident electrons with 0 to 2.8 eV kinetic energy. We find that core-polarization and relativistic effects lead to multiplets of very narrow ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{\mathit{J}}$, J=0,1,2 shape resonances: the effect of the induced core polarization on the electron-electron correlation leads to 6s6${\mathit{p}}^3$${\mathit{P}}_{\mathit{J}}^{\mathit{o}}$ resonances in contrast to previously predicted bound states of ${\mathrm{Cs}}^{\mathrm{-}}$, and relativistic interactions are responsible for the autoionizing decay of 6${\mathit{p}}^2$ ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{\mathit{J}}$ states below the first excitation threshold.