Magnetic-dipole and electric-quadrupole transition rates for S-like ions between ground-state terms have been calculated using multiconfiguration Dirac-Fock wave functions. Sudden changes were found in these transition rates from one element to the next where there is a change of the dominant configuration. Also, ordering of the levels changes as the nuclear charge increases, but this is not necessarily reflected as a sudden change in transition rates. Our results demonstrate the necessity of using multiconfiguration calculations in the study of the systematics of transition rates along isoelectronic sequences.

The drift velocity w of electrons has been measured in the perfluoroalkanes n-${\mathrm{C}}_{\mathrm{N}}$${\mathrm{F}}_{2\mathrm{N}+2\mathrm{}}$ (N=1–4) over the density-reduced electric field (E/N) range 0.03×${10}^{\mathrm{-}17}$ V ${\mathrm{cm}}^2$≤E/N≤500×${10}^{\mathrm{-}17}$ V ${\mathrm{cm}}^2$ using a pulsed Townsend experimental method. The present measurements of w are the first to be obtained for ${\mathrm{C}}_2$${\mathrm{F}}_6$, ${\mathrm{C}}_3$${\mathrm{F}}_8$, and n-${\mathrm{C}}_4$${\mathrm{F}}_{10}$ at low E/N values. The electron-drift-velocity measurements in ${\mathrm{C}}_3$${\mathrm{F}}_8$ and n-${\mathrm{C}}_4$${\mathrm{F}}_{10}$ are dependent on gas pressure at high E/N values, even after allowing for nonequilibrium and boundary corrections to the measured electron swarm transit time. This is the first observation of a pressure dependence in the electron drift velocity in these gases and is believed to be due to changes in the electron energy distribution function f(ɛ,E/N) with gas pressure resulting from increases in the density-normalized electron attachment coefficient η/N with gas pressure. The perfluoroalkanes ${\mathrm{CF}}_4$, ${\mathrm{C}}_2$${\mathrm{F}}_6$, and ${\mathrm{C}}_3$${\mathrm{F}}_8$ exhibit regions of pronounced negative differential conductivity (NDC) similar to but smaller in magnitude than that in ${\mathrm{CH}}_4$. Possible mechanisms leading to the observation of NDC effects in these molecular gases are discussed.

The compound-nucleus system fits into a mathematical theory of open systems in physics developed by the mathematician M. Livšic [Translations of Mathematical Monographs (American Mathematical Society, Providence, Rhode Island, 1973), Vol. 34]. In this article we review some basic concepts of the above theory and apply it to study the structure of the compound-nucleus S matrix. One of the results is a factorization of the S matrix in the form S(ω)=S +${\mathrm{iA}}_k$/(${\tau }_k$-ω)], where $A_k$ are known matrices and ${\tau }_k$ are the complex resonance energies.

A nonadiabatic variational procedure is proposed to diagonalize the Hamiltonian of the helium atom. An analysis of the wave functions of the ${}_{}{}^1{}_{}{}^{}\mathrm{S}_{}^{\mathrm{e}}{}_{}{}^{}$ states is made. The one-body densities and the shape densities (extracted from two-body densities) are investigated to obtain information on the radial-radial and radial-angular electron-electron correlations. The geometric structure of these states is studied and the K-classification scheme is recovered. Regions where strong radial-angular correlation takes place are found.

Half-dressed sources are defined as sources deprived partially or totally of the cloud of virtual quanta which surrounds them in the ground state of the total system. Two models of a half-dressed point source S are considered, the first in the framework of the theory of massive scalar fields and the second in quantum electrodynamics (QED). In both cases the detector is modeled by a second fully dressed source T of the same field, which is also bound to an oscillation center by harmonic forces. It is shown that when S at time t=0 is suddenly coupled to or decoupled from the field, the detector T, which is initially at rest, is set in motion after a time t=$R_0$/c, where $R_0$ is the S-T distance. Neglecting the reaction back on the field due to the oscillatory motion of T, the amplitude of oscillation for t=∞ is obtained as a function of $R_0$. Thus the time-varying virtual field of S is shown to be capable of exerting a force which excites the model detector. For the QED case, this force is related to the properties of the energy density of the virtual field. This energy density displays a singularity at r=ct, and the mathematical nature of this singularity is studied in detail. In this way it is shown that the energy density of the time-dependent virtual field is rather different from that of a pulse of radiation emitted by a source during energy-conserving processes. The differences are discussed in detail, as well as the limitations of the model.

We investigate the influence of additional nonlinear terms in the Dirac Lagrangian on strongly bound electron states in heavy and superheavy atoms. Upper bounds for the coupling constants are deduced by comparison with precision spectroscopy data in QED. We demonstrate that nonlinear interactions may cause significant modifications of electron binding energies in superheavy quasiatomic systems which would not be visible in ordinary atomic-physics measurements.

A new variational approach to muonic molecules is proposed. The total three-body wave function is expanded in terms of basis functions spanned over the three rearrangement channels in the Jacobian coordinate system. Energy levels of the dtμ molecule are calculated with a high accuracy and a short computation time. For the weakly bound state with J=v=1, which is a key to the muon-catalyzed d-t fusion, the calculated energy ${\varepsilon }_{11}$ is better than the literature data. With the use of the most up-to-date, 1986 CODATA–recommended [E. R. Cohen and B. N. Taylor, CODATA Bull. 63 (1986)] values of physical constants, we obtained ${\varepsilon }_{11}$=-0.660 264 eV with 2662 basis functions and ${\varepsilon }_{11}$(∞)=-0.66030±000 02 eV by extrapolation.

It is known that the square root of the electron density satisfies {-(1/2${\nabla }^2$+$v_{\theta }$([n];r) +$v_s$([n];r)}$n^{1/2}$(r) =${\varepsilon }_M$$n^{1/2}$(r), where $v_s$ is the Kohn-Sham potential and ${\varepsilon }_M$ is its highest-occupied orbital energy. The Pauli potential $v_{\theta }$ is defined as the functional derivative of the difference between the noninteracting kinetic energy $T_s$[n] and the full von Weizsäcker kinetic energy. It has already been proven that $v_{\theta }$([n];r)≥0 for all r. By starting primarily with a slightly modified version of an equation of Bartolotti and Acharya, new exact properties of $v_{\theta }$([n];r) are derived for the purpose of approximating it. The gradient expansion for $T_s$[n] gives a $v_{\theta }$([n];r) that is found to violate several of the exact conditions. For instance, $v_{\theta }$≥0 is violated unless the full von Weizsäcker term is employed. A new approximate form for $v_{\theta }$([n];r) is proposed.

The local-spin-density (LSD) generalized-exchange (GX) theory is corrected for self-interaction by splitting the single-particle Fermi hole into pure-exchange and self-interaction holes. An analysis of these components shows that the non-self-interaction-corrected GX scheme overestimates the pure exchange while underestimating the self-interaction. This self-interaction-corrected scheme is called the GX-SI scheme. Using this method of correcting for self-interaction, two other approximate self-interaction-corrected (SIC) GX schemes can be derived in which (1) the GX-LSD-SI total exchange does not include the nonlocal, self-interaction potential and (2) the GX-SIX exchange is very similar to the exchange derived by Gopinathan [Phys. Rev. A 15, 2135 (1977)]. Neither of these exchanges obeys the sum rule. The GX-SI scheme contains correction terms to the LSD GX which are smaller than the corresponding ones derived in the SIC of Perdew and Zunger [Phys. Rev. B 23, 5048 (1981)]. This shows that the LSD-GX exchange is a better approximation to the true exchange of an inhomogeneous electron gas around an atom than the LSD free-electron gas exchange.

In the formal theory of scattering, the limiting behavior of off-energy-shell scattering wave functions and T matrices as the energy shell is approached is of considerable importance in deriving an impulse approximation to the full scattering amplitudes. On-shell limits do not exist for the pure Coulomb potential, but sufficiently near the shell the off-shell wave function and T matrix are approximated by the continuum eigenstate and scattering amplitude, respectively, multiplied by certain ‘‘off-shell’’ factors. For central potentials which are Coulomb-like at large distances, but modified at smaller radii, it is shown that the on-shell limits again do not exist and the near-shell approximations mimic the pure Coulomb case with the asymptotic charge appearing in the off-shell factors. Numerical results for a realistic atomic potential covering a broad range of defects from the energy shell give a picture of the approximations involved and show that the errors arising from the use of near-shell forms are comparable in magnitude to the energy defects divided by the energy.

A calculational procedure is presented to study the effect of the configuration interaction on the fine-structure-level splittings for a quasi-two-electron atom. A detailed application is carried out to examine the anomaly in the fine-structure-level splittings of the Al ii ${}_{}{}^1{}_{}{}^{}$,3F series which are strongly affected by the presence of the 3p3d ${}_{}{}^3{}_{}{}^{}F$ perturber. Our calculated level splittings are in close agreement with the available experimental values. In particular, our study has identified a direct link between the experimentally observed fine-structure-level splittings and the probability densities of the dominating configuration in the calculated state wave functions.

Total cross sections for electron scattering by ${\mathrm{N}}_2$ molecules in the energy range 600–5000 eV have been obtained from measurements of the attenuation of a linear electron beam. The results have been compared with available experimental cross sections and with theoretical calculations based on the first Born approximation. No previous experimental data have been found in the literature for impact energies above 1600 eV.

Cross sections for the dissociative recombination of ${\mathrm{H}}_3^{+}$ ions with low internal energy have been obtained using the merged-beam technique. Dissociative-excitation measurements have confirmed that only the v=0 and 1 states were present in the ion beam. The resulting cross sections can be expressed in the form (2.17×${10}^{\mathrm{-}16}$)${\mathrm{E}}_{\mathrm{c}.\mathrm{m}.\mathrm{}}^{\mathrm{-}0.57}$ (${\mathrm{cm}}^2$) for $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}$ below 0.03 eV and (3.23×${10}^{\mathrm{-}17}$)${\mathrm{E}}_{\mathrm{c}.\mathrm{m}.\mathrm{}}^{\mathrm{-}1.15}$ (${\mathrm{cm}}^2$) above.

Differential cross sections for the electron-impact excitation of ions are calculated and compared along the He-like isoelectronic sequence. With the use of a distorted-wave method, cross sections are obtained for the transitions 1 ${}_{}{}^1{}_{}{}^{}2$ ${}_{}{}^3{}_{}{}^{}S$,2 ${}_{}{}^3{}_{}{}^{}P$ in ${\mathrm{Li}}^{+}$, ${\mathrm{O}}^{6+}$, and ${\mathrm{Si}}^{12+}$. A comparison is also made to the cases of neutral He and the limit Z→∞ (Z being the nuclear charge). When scaled by multiplication by $Z^4$ and compared at the same energy in threshold units, the resulting cross sections are quite similar both in magnitude and in angular distribution all along the isoelectronic sequence. The Coulomb-wave approximation is also used to calculate the differential cross section to test its validity.

Based on the hyperspherical approach, we have calculated the generalized oscillator strengths and the electron-impact-excitation Born cross sections from the initial ${}_{}{}^1{}_{}{}^{}\mathrm{S}_{}^{\mathrm{e}}{}_{}{}^{}$ high-lying doubly excited states to the final ${}_{}{}^1{}_{}{}^{}\mathrm{P}_{}^{\mathrm{o}}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}\mathrm{D}_{}^{\mathrm{e}}{}_{}{}^{}$ high-lying doubly excited ones. Together with the previous results on the ${}_{}{}^1{}_{}{}^{}\mathrm{S}_{}^{\mathrm{e}}{}_{}{}^{}$${\mathrm{-}}^1$${\mathrm{S}}^{\mathrm{e}}$ excitation processes, we have found a simple propensity rule that the excitation processes with Δ$n_2$=0 are most likely to take place within each manifold, i.e., the S-S, S-P, or S-D excitation process where $n_2$ is the radial bending quantum number, i.e., the number of the nodes of the bending vibrational wave functions on the body fixed frame based on the rovibrator model of the doubly excited states. In addition to the propensity rule, Δ$n_2$=0, we have also found a set of propensity rules, i.e., Δv=ΔT=0 for angular correlation and ΔA=0 for radial correlation according to the rovibrational model where v is the bending vibrational quantum number, T is the vibrational angular momentum, and A is the radial correlation quantum number.

This may be interpreted as a result of isomorphism of the surface density plot of the squared channel functions between the initial and final states. The radial propensity rule ΔA=0 seems to dominate over the angular one, i.e., Δv=ΔT=0 and modifies the latter in the ${}_{}{}^1{}_{}{}^{}\mathrm{S}_{}^{\mathrm{e}}{}_{}{}^{}$${\mathrm{-}}^1$${\mathrm{P}}^{\mathrm{o}}$ excitation processes where both types of the propensity rules are incompatible with one another because of the Pauli exclusion principle for two atomic electrons. This leads to the angular propensity rule Δv=ΔT=1 for the ${}_{}{}^1{}_{}{}^{}\mathrm{S}_{}^{\mathrm{e}}{}_{}{}^{}$${\mathrm{-}}^1$${\mathrm{P}}^{\mathrm{o}}$ excitation processes, though the propensity rule Δ$n_2$=0 and ΔA=0 remains unchanged. The propensity rule for the S-P excitation is equivalent to the selection rule for photoabsorption by He, as is expected. These propensity rules theoretically demonstrate that the two atomic electrons show remarkable collective behaviors as the result of strongly correlated motion between them, while an incident electron interacts with an atom in the high-lying doubly excited state perturbatively. It has been found that the propensity rule obtained here, i.e., Δv=ΔT=1 for the S-P excitation is not in agreement with the selection rule observed in the threshold excitation spectra of He by electron impact [P. J. M. van der Burgt et al., J. Phys. B 19, 2015 (1986)] and with the selection rule for the infrared photon absorption by a linear triatomic molecule. The reason for these discrepancies is also discussed.

Absolute differential cross sections for vibrational excitation of water-vapor molecules are measured by use of a crossed-beam method. The energy and angular range were from 2.2 to 20 eV and from 30° to 150°, respectively. Vibrational-excitation cross sections were measured for the bending (010) and stretching (100) and (001) modes of the electronic ground state. A broad resonance for the stretching modes near 6-eV impact energy was observed. The present results generally agree in angular distribution with the measurements by G. Seng and F. Linder [J. Phys. B. 9, 2539 (1976)], except below 30° scattering angle. However, the integral cross sections agree within experimental uncertainty. The theoretical results of A. Jain and D. G. Thompson [J. Phys. B 16, L347 (1983)] for the bending mode are in good agreement with the present results. These new results have implications for theoretical modeling of cometary ionospheres.

The time spent by a quantum particle in a scattering event or a tunneling process (the traversal time) through a rectangular barrier is calculated from the viewpoint of the stochastic formulation of quantum mechanics. Comparison with previous results is also provided.

The decay possibilities of atoms with two K-shell vacancies have been studied by bombarding a thin (465 μg/${\mathrm{cm}}^2$) Al target with electrons of $E_0$=20 keV. In addition to the more common probability involving a sequential decay [which leads to a $K^{\mathrm{-}2}$→$K^{\mathrm{-}1}$$L^{\mathrm{-}1}$ transition with the emission of a Kα hypersatellite x ray, called the one-electron–one-photon transition (OEOP)], we have also investigated the weakly correlated two-electron–one-photon transition (TEOP) by spectroscopy of the emitted x rays using a high-resolution crystal spectrometer. The two transitions were recorded with different crystals always relative to the intensity of the Kα line, which originates from a single-K-shell vacancy. The branching ratio $R_B$=$I_{\mathrm{TEOP}/I_{\mathrm{OEOP}}}$ was found to be $R_B$=(2.2±0.8)×${10}^{\mathrm{-}3}$, which is in good agreement with theoretical predictions, that include the electron correlation approximately and is close to previous heavy-ion induced investigations.

A new ab initio method for computing Auger transition rates in molecules is proposed; it is based on the use of orthogonalized plane waves for the free electron and of Hartree-Fock many-center orbitals for the bound electrons. Transition rates and energies are calculated for the case of the LiF molecule ionized in its deepest shell, and the results are compared with the experimental spectrum. Various levels of approximation are tested for evaluating the partial transition rates of various decay channels, and a consistent improvement in the agreement with experiment is obtained when the plane waves are orthogonalized to the relaxed orbitals of the doubly ionized molecular ion.

We follow up on our previous analysis of the two-photon exchange potential in the scattering of a light point-charged particle by a neutral system (electron-atom scattering) by examining all the time-ordered Feynman diagrams involved. In a close parallel with the work of J. F. Babb and L. Spruch [Phys. Rev. A 36, 456 (1987)] on Rydberg states of helium, the present analysis on scattering is valid for all distances larger than the atomic radius (R>a). In the dipole approximation, we reproduce the potential obtained by G. Feinberg and J. Sucher [Phys. Rev. A 27, 1958 (1983)] using a more powerful covariant field-dispersion-theory technique. We give simple expressions for the additional nonadiabatic and multipole corrections in the two-Coulomb-photon exchange channel and also give the lowest nonadiabatic and energy-dependent corrections to the retardation potentials. These potentials are valid for all R>a. The implication of these additional correction potentials in the study of heliumlike Rydberg states is briefly discussed.