Rough metallic electrodes can display anomalous frequency dependence in their electrical impedances. The impedance is here calculated perturbatively, to one-loop order, as a function of fluctuations in the height of the metallic surface. Only suitably rough surfaces display anomalous impedances. This calculation strongly constrains any relation between the Hausdorff dimension of the surface and the power law of the anomalous frequency dependence.

The energies, muon–alpha-particle sticking probabilities, and the fusion rates have been calculated for the J=0, ν=1 and the J=1, ν=1 states of the (dtμ) system. The results for the J=0, ν=1 state generally agree with previous calculations using the adiabatic representation basis. The muon–alpha-particle sticking probability is obtained for the J=1, ν=1 state for the first time. A small muon–alpha-particle sticking probability obtained for this state raises interesting possibilities for muon-catalyzed fusion.

It is pointed out that both classical Wheeler-Feynman electrodynamics and its finite quantized generalization inevitably lead to microscopic causality violation. As there is some evidence for such effects in proton Compton scattering, there is possibly reason to prefer such absorber theories of action at a distance over field theories as the more reasonable microscopic description of nature.

The homotopy theory of path integrals in two-dimensional multiply connected spaces is used to reexamine the wave function and angular momentum of a charged particle on a circle in various configurations. A topological phase factor arising from the nontrivial representation of the fundamental group leads to the fractional angular momentum quantization.

A general procedure for the extraction of directional kinetic energies and Compton profiles exclusively from total molecular electron densities has been developed within the nonlocal-density approximation. The estimation of directional kinetic energies and Compton profiles requires the computation of an average electron density ρ̃(r). However, the kinetic energy anisotropy can be evaluated easily by integrating simple functions of electron density and their partial derivatives. The procedure has been tested for the ${\mathrm{H}}_2$ molecule, where good agreement is found with the results obtained directly from the corresponding wave functions.

We give a detailed presentation of Hartree-Fock calculations of atoms and molecular chains in ${10}^{12}$ G magnetic fields, as are supposed to exist on the surface of neutron stars. These calculations are the first self-consistent ones treating exchange properly for atoms heavier than helium in high fields. We find that the isolated atom is energetically favored over molecular chains for Z>2 at fields greater than 1×${10}^{12}$G and for Z>4 at fields greater than 5×${10}^{12}$ G. These results indicate that matter on the surface of neutron stars is bound very weakly, if at all.

The modified form of the perturbing potential is used in a Brillouin-Wigner type of many-body formalism to obtain an exact equation for the critical value of the screening constant. Using lowest-order configurations and an extrapolation formula, it is shown that the critical value of the screening constant is obtained correct to two decimal places.

A description of the theoretical basis is presented for a new method to calculate widths of two-electron Feshbach resonances, which employs discretization techniques for the continuum projection of the wave function. New features of our approach are the finite-difference expressions used to evaluate the density of states and the inverse interpolation procedure needed to achieve the required discrete-continuum degeneracy. Two following papers illustrate the use of our method to calculate resonance widths for atomic and molecular systems, respectively.

We apply a method to calculate autoionization widths of doubly excited states, recently proposed by Mac̆´as and Riera [Chem. Phys. Lett. 117, 42 (1985); Europhys. Lett. 2, 351 (1986); Phys. Lett. 119A, 28 (1986)] and described in detail in the preceding article (this issue), to the lowest (nonrelativistic) He-like Feshbach resonances of ${}_{}{}^1{}_{}{}^{}$,3S, ${}_{}{}^1{}_{}{}^{}\mathrm{P}$, ${}_{}{}^1{}_{}{}^{}$,3D symmetry. Comparison with accurate data from the literature is shown to be very good. We also present the contributions to the resonance widths from configurations of a given type, or character, making up the closed-channel wave functions. An important advantage of our approach, which is its simplicity, permits us to set up a number of tests for the approximations involved and regarding the use of different discretizing basis sets.

We apply a new method to calculate widths of two-electron Feshbach resonances, which was described in detail and applied to atomic systems in preceding articles (this issue), to molecular and quasimolecular autoionizing states. For simplicity in the programming effort, we restrict our calculations to the small-R region where one-centered expansions are sufficiently accurate to describe the wave functions. As test cases, positions and widths for the ${\mathrm{H}}_2$, ${\mathrm{He}}_2$${\mathrm{}}^{2+}$, ${\mathrm{HeH}}^{+}$, and ${\mathrm{LiHe}}^{3+}$ resonances of lowest energy are computed for R<0.6 a.u. The advantage of using block-diagonalization techniques to define diabatic resonant states instead of generalizing the Feshbach formalism is pointed out.

The inelastic scattering of two structured systems—for example, an excited atom and a molecule—is considered in the case of nonreactive collisions. Explicit formulas are presented for cross sections corresponding to transitions between arbitrary eigenstates of the two isolated systems. These formulas are then used to derive cross sections for polarization transfer and multipole relaxation in one system when the other system is unpolarized. Both space-fixed and body-fixed formulations are given. Explicit matrix elements are worked out for interactions such as occur between model alkali-metal atoms and rigid-rotor diatomic molecules. An effective interaction method is also discussed and related to an adiabatic-state approach.

Close-coupling quantum-mechanical calculations have been carried out in the rigid-rotor approximation for low-energy collisions (E≲0.3 eV) of Rb(5 ${}_{}{}^2{}_{}{}^{}P_{j_1)}^{}{}_{}{}^{}$ with ${\mathrm{H}}_2$ or ${\mathrm{D}}_2$(${\mathrm{j}}_2$), the molecule lying in its ground electronic and vibrational state. The calculations use realistic adiabatic potential energy surfaces which are determined from previous pseudopotential calculations, and the main nonadiabatic coupling matrix elements involved during the collision are evaluated. The total cross sections for various transitions among the 5 ${}_{}{}^2{}_{}{}^{}P_{j_1}^{}{}_{}{}^{}$ fine-structure levels of Rb and rotational levels $j_2$=0,2,4, and $j_2$=1,3 of the molecule are determined and discussed. The results are in good agreement with crossed-beam experimental data concerning the 5 ${}_{}{}^2{}_{}{}^{}$${\mathrm{P}}_{1/2}$→5 ${}_{}{}^2{}_{}{}^{}\mathrm{P}_{3/2}^{}{}_{}{}^{}$ transition in Rb induced by collisions with ${\mathrm{H}}_2$ or ${\mathrm{D}}_2$.

A sequence of three frame transformations is used to describe the escape of a photoelectron into a uniform magnetic field. Standard elements of quantum-defect theory are combined with a Harmin-Fano-type local frame transformation from spherical to cylindrical coordinates, accounting nonperturbatively for the electron motion in both the magnetic field and the field of the atom. A dramatic dependence of the cross section on the incident light polarization is predicted whenever s waves are not present at threshold, as in ${\mathrm{H}}^{\mathrm{-}}$ photodetachment.

A renormalized solution that is based upon the exact inversion theories of Gel’fand, Levitan, and Marchenko has been developed by using a multiple-scales analysis. Our previous theory [J. Opt. Soc. Am. A 2, 1916 (1985)] for the inverse-scattering problem for inhomogeneous, continuously varying regions has been extended to include discontinuities in the dielectric permittivity. A singular perturbation method has been used to obtain a uniformly valid expression for the electric field within the dielectric region. The advantage of the multiple-scales analysis of the interior electric field is that it rigorously indicates the dielectric region over which the weak-scattering or high-frequency approximation is valid. Furthermore, it is an effective renormalization technique that is physically motivated by the requirement of energy conservation and that allows a systematic investigation of the various scales associated with the inverse problem. The singular perturbation method for the solution of the inverse problem associated with the electromagnetic reflection data from a discontinuous dielectric region utilizes the high-frequency Born approximation to determine the magnitude of the discontinuity in the neighborhood of the origin. The method used for reconstructing discontinuous profiles is also appropriate for the reconstruction of profiles with turning points. The theory is demonstrated by two examples.

Both dipole-allowed and dipole-forbidden transitions occur in slow l-change collisions of ${\mathrm{Na}}^{+}$ with Na(28d) Rydberg atoms, despite the validity of the dipole approximation. Measurements of the velocity dependence of the final-state distribution under single-collision conditions are reported. Effects of strong coupling were found, in partial agreement with recent coupled-channel calculations. Microwave-resonance techniques were used to identify the selective-field-ionization signatures of 28f, g, and h states.

A stored-ion collision technique has been used to study the charge-changing collisions of multicharged nitrogen ions with ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ target gases. The ions were produced inside a Penning trap with use of electron-impact ionization. The time constants for exponential ion loss by charge-changing collisions were measured at several target-gas densities, and from these time constants and densities the rate coefficients for electron capture were calculated. For the collision of ${\mathrm{N}}^{3+}$ with ${\mathrm{H}}_2$, for which calculations by Gargaud and McCarroll were available, the cross section for electron capture was obtained from the rate coefficient using v¯, where v¯ is the rms ion velocity. The relationships of the other measurements to available theory and to ion-beam measurements at higher energies are discussed. Rate coefficients were obtained at mean ion energies near 1.1, 1.65, and 2.3 eV for ${\mathrm{N}}^{\mathrm{q}+}$ charges q of 2, 3, and 4, respectively. The results of the rate coefficient determinations are k(${\mathrm{N}}^{2+}$,${\mathrm{H}}_2$)=[7.8(1.2)]×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$/s, k(${\mathrm{N}}^{3+}$,${\mathrm{H}}_2$)=[5.4(0.8)]×${10}^{\mathrm{-}11}$ ${\mathrm{cm}}^3$/s, k(${\mathrm{N}}^{4+}$,${\mathrm{H}}_2$)=[4.2(0.6)]×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$/s, k(${\mathrm{N}}^{2+}$,${\mathrm{N}}_2$)=[2.6(0.3)]×${10}^{\mathrm{-}9}$ ${\mathrm{cm}}^3$/s, k(${\mathrm{N}}^{3+}$,${\mathrm{N}}_2$)=[3.5(0.4)]×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$/s, and k(${\mathrm{N}}^{4+}$,${\mathrm{N}}_2$)=[2.0(0.3)]×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$/s.

We prove from quantum electrodynamics that two-photon emission in transitions between atomic inner shells can be treated in lowest-order approximation in the single-particle model. By taking many-body effects into account we show that, in the reduced single-particle model, the Pauli exclusion principle does not prohibit summing over all possible intermediate states, including core states. Some transition-rate formulas are presented that are useful for numerical calculations.

A simple recoupling frame transformation is shown to adequately describe numerous effects of the spin-orbit interaction which show up in photoionization of the calcium atom. This is accomplished after solving the nonrelativistic Schrödinger equation in LS coupling by an eigenchannel R-matrix method, ignoring all spin-orbit terms in the Hamiltonian. The calculation reproduces most features of the total cross section observed experimentally, and predicts a strong effect of the spin-orbit interaction on partial cross sections, on the photoelectron angular distributions, and on the alignment of the ionic photofragments.

Energy spectra of transmitted β rays are compared with spectra generated by a Monte Carlo procedure. Reasons for the similarities between the experimental results of β and γ interactions are explored. In addition, the energy distribution of the backscattered β rays and variation of absorbed energy as a function of absorber thicknesses are presented.

Methods developed previously for estimating the amplitude for the nonrelativistic potential scattering of a charged particle accompanied by the emission of a single low-frequency photon are extended and applied to the problem of two-photon emission. In the case where only one photon is soft, previously developed techniques, which involve asymptotic evaluation of integrals in configuration space, can be taken over with little modification. The simplest way to obtain a low-frequency approximation when both photons are soft is through analytic continuation of this latter approximation, valid when one photon is soft and the other hard, in the frequency of the hard photon. A direct examination of the relevant integral shows that this method is in fact justified. The low-frequency approximation for two-photon bremsstrahlung requires, as input, the physical (on-shell) amplitudes for radiationless scattering and for single-photon emission, and introduces an error which vanishes linearly with frequency. The result obtained here represents the nonrelativistic analog of a theorem of Brown and Goble [Phys. Rev. 173, 1505 (1968)] who based their derivation on the principles of Lorentz invariance, analyticity, and gauge invariance.