Recent microscopic studies have underscored the relevance of classical percolation ideas to electron mobility in simple fluids. We show that Wigner phase-space averaging can be used to construct a semiclassical potential on which these concepts can be defined rigorously. The conduction-band threshold energy ${\mathit{V}}_0$ is then determined by solving a well-defined classical continuum percolation problem. Application of our model predicts the density dependence of ${\mathit{V}}_0$ quantitatively for the noble-gas fluids.

We investigate why the two-phase boundary between the string and liquid phases is always oriented in a specific direction in non- equilibrium molecular-dynamics simulations of shear flow. We start simulations from a configuration of the two-phase boundary that is rotated 90° around the flow direction. It is confirmed that the original orientation found in simulations is more stable than the rotated orientation. In addition, a change from the rotated to the stable orientation is observed in one of our simulations.

The critical exponents of model ionic fluid mixtures exhibiting liquid-liquid phase separation are calculated analytically through the mean-spherical approximation. Classical exponents β and γ are found in agreement with the available experimental data for ionic fluids. The phase diagram of molten tetra-n-butylammonium picrate–1-chloroheptane is also well reproduced through the same theoretical approach, showing excellent agreement of the calculated exponent β with the experimental value. Possible applications to other multicomponent fluids are briefly discussed.

We present a quantitative treatment of the interplay between underlying anisotropy and the inherent degree of randomness (noise) in growth processes. Using a renormalization procedure, we show how the noise and anisotropy of diffusion-limited aggregates evolve with cluster size. The fixed point associated with isotropically growing clusters is stable with respect to noise, but at a value 2 orders of magnitude below the ‘‘bare’’ value in simple diffusion-limited aggregation. This fixed point is unstable with respect to any anisotropy in the growing conditions amplifying itself in the growing cluster, causing flow to (in our case one of two) absolutely stable fixed points associated with strongly anisotropic growth. The location and exponents of the isotropic fixed point explain why clusters of order ${10}^4$ particles are required to see sensitivity to lattice anisotropy in the Witten-Sander model.

The quantum theory of a damped harmonic oscillator is developed by considering an exactly solvable model, previously discussed by Unruh and Zurek [Phys. Rev. D 40, 1071 (1989)]. A one-dimensional harmonic oscillator is coupled to a scalar field. The field is assumed to be initially in thermal equilibrium. The Heisenberg equations of motion are solved without approximation, and the first and second moments, 〈q(t)〉, 〈p(t)〉, 〈${\mathit{q}}^2$(t)〉, 〈${\mathit{p}}^2$(t)〉, and 〈q(t)p(t)+p(t)q(t)〉 of the coordinate and momentum of the oscillator are calculated. The high-temperature, zero-temperature, free-particle, and weak-damping limits are discussed. A Wigner function of Gaussian form is constructed. The density-matrix equation derived by Louisell $[—Quantum Statistical Properties of Radiation (Wiley, New York, 1973)] is examined and shown to have a solution in agreement with our weak-damping limit.

In the phenomenon of diffraction of an electromagnetic wave in a lattice, the phase relations between the transmitted wave and the diffracted wave are fundamental. A vector can be written that describes the quantum state of the radiation in the above-mentioned case, and the photoelectric absorption cross section can be computed. It will be proved that the way the dynamical theory of x-ray diffraction deals with absorption is not correct because it does not consider the interference between the α and β rays; this phenomenon causes the failure of the dynamical theory in the explication of the Borrmann effect, which will be explained by means of a theory proposed herein. In addition, a new phenomenon is described that is not expected by the dynamical theory, the coherent scattering of photons from the β ray to the α ray; such a phenomenon is the real origin of the β-ray extinction in the crystal and a quite anomalous expression for the extinction depth is found that is inversely proportional to the incident intensity.

The interaction of an atomic system with an unquantized electromagnetic field is studied by means of the Heisenberg-operator equations of motion. The electromagnetic fields created by the atom are taken into account by assuming that the charge and probability current densities are the actual charge and current source terms in Maxwell’s equation. When Ehrenfest’s theorem is written to order (1/c${)}^2$, the equations of motion are found to have a constant of motion that can be interpreted as stating that the sum of the atomic energy, energy of interaction, and energy stored in the electromagnetic field is constant. This constant of integration can be expressed as an expectation of a new semiclassical Hamiltonian that now includes the effects of the atomic self-fields to order 1/${\mathit{c}}^2$. This Hamiltonian is related to the classical Darwin Lagrangian. Since the new approximate Hamiltonian is the sum of an atomic and a field Hamiltonian, it provides a formulation of semiclassical radiation theory that is formally close to the usual formulation of quantum electrodynamics. A Schrödinger equation can be derived by applying the variational principle to the expectation of the new Hamiltonian. The result is a nonlinear integro-differential equation, in Ψ, which is somewhat similar to Hartree’s self-consistent equation for a multielectron atom.

When the Heisenberg equations are written to include the next-higher-order terms, 1/${\mathit{c}}^3$, it is found that the total energy of the atom and the electromagnetic field in the vicinity of the atom decreases at a rate that is given by the Larmor power formula (2${\mathit{e}}^2$/3${\mathit{c}}^3$)(d〈v〉/dt${)}^2$, where 〈v〉 is the quantum-mechanical expectation of the electron’s velocity operator. This approximate formulation of semiclassical radiation theory is applied to semiclassical calculations of atomic radiative shifts. It is then shown that, if some retardation effects are included to all orders of 1/c in the vector potential, the semiclassical analysis provides a formula for radiative energy-level shifts that are time dependent and that contain coefficients similar to the starting point of the Bethe calculation of the Lamb shift. The incorporation of mass renormalization in semiclassical theory is then discussed.

An exact Hamiltonian formulation of nonrelativistic quantum mechanics that simplifies to ordinary classical mechanics as ħ→0 is presented. The theory allows one to treat a quantum system as the corresponding classical system mechanically connected to an infinite number of additional classical degrees of freedom. The onset of quantum effects such as tunneling and interference results from the mechanical interactions between the different parts of the overall infinite system. The formalism is applied to the one-dimensional motion of a particle in a symmetric double well. It is shown that the tunneling in that system involves multidimensional classical motion that circumvents the barrier.

Here we discuss the limits of the recognizability of neutron interference patterns either observed in low-contrast measurements or when collecting very few neutrons only. Low contrast can be caused by a strong beam attenuation or by a large phase shift applied to one beam path. Stochastic and deterministic cases have different influences on the interference pattern, which can be interpreted as a different wavelike or particlelike behavior of the system. Measurements of interference patterns with very few neutrons only are related to the phase–particle-number uncertainty relation, which is discussed on the basis of stochastic and quantum theory arguments. Analogies between coherent-state behavior known in atomic physics and the behavior of neutrons in an interferometer are discussed also.

A functional P[γ] is defined on the space of histories for a quantum particle, and its meaning as a quasiprobability is discussed. The method of obtaining the Wigner and the Margenau-Hill phase-space distributions is shown as particular path integrals over P[γ].

The probability amplitude for a spin-1/2 particle in a precessing magnetic field to be in an energy eigenstate is calculated exactly. The probability for the particle to be in a given energy eigenstate and the corresponding phase of the amplitude are obtained. In the adiabatic limit there are no transitions, and the phase is the sum of the dynamical phase and the Berry phase. When a unitary transformation is made, the Hamiltonian and the energy operator transform differently. The energy eigenvalues, Berry phases, and probability amplitudes calculated in a frame rotating with the magnetic field are the same as in the laboratory frame. If the energy operator is incorrectly taken to be the Hamiltonian in the rotating frame, incorrect energy eigenvalues, Berry phases, and probability amplitudes are obtained. Nevertheless, in the adiabatic limit the correct total phase results.

A detailed breakdown of many-body perturbation theory contributions through third order is presented for the ground-state removal energies of cesium and thallium, with the aim of identifying which Goldstone diagrams are numerically dominant. A comparison of these diagrams with Feynman graphs is made. A discussion of the issues involved in carrying out ab initio calculations of properties of these atoms accurate at the few tenths of a percent level is presented.

The local scaling transformation is used to generate a wave function ${\mathrm{\Psi }}_{\mathrm{\rho }}$({${\mathbf{r}}_{\mathit{k}}$}) from a reference function ${\mathrm{\Psi }}_0$({${\mathbf{r}}_{\mathit{k}}$}) in such a manner that the generated function ${\mathrm{\Psi }}_{\mathrm{\rho }}$({${\mathbf{r}}_{\mathit{k}}$}) has exactly the same one-electron density as a given density ρ(r). The method enables us to perform a variational determination of the density ρ(r) through the minimization of the energy E[ρ] associated with the wave function ${\mathrm{\Psi }}_{\mathrm{\rho }}$({${\mathbf{r}}_{\mathit{k}}$}). Using the single-ζ wave function as a reference, we apply this procedure to the ground-state Li and Be atoms within the Hartree-Fock approximation. Comparison of the densities themselves as well as the associated position 〈${\mathit{r}}^{\mathit{n}}$〉 and momentum 〈${\mathit{p}}^{\mathit{n}}$〉 moments shows that the present density compares well with the near-Hartree-Fock density.

The positions and widths of the J=0 energy levels of the tdμ molecular ion have been computed including the effects of strong nuclear interaction on the tdμ wave function. The applied formalism incorporates the strong force into the nonadiabatic treatment of tdμ by means of a nuclear surface boundary condition derived from the latest R-matrix parametrization of nuclear scattering data. Accurate basis-set expansions of the tdμ wave functions have been used, including basis functions containing inverse powers of the t-d distance. Relative to the results of adiabatic calculations employing the same nuclear input, the computed energy shifts and widths are reduced by 4% and 8% for the ground and excited states, respectively. Our results are qualitatively consistent with the results of recent nonadiabatic optical potential calculations. The fusion rates derived from our calculations, 1.25×${10}^{12}$ and 1.05×${10}^{12}$ ${\mathrm{s}}^{\mathrm{-}1}$ for the ground and excited states, respectively, are about 15% larger than those given by the standard formula that factorizes the nuclear and molecular effects.

Matrix elements of two-body potentials and correlation functions between three- and four-body hyperspherical states, including their velocity-dependent parts, are calculated analytically for any value of the total orbital angular momentum. The resulting formulas contain explicitly written functions of the radial variable, and the Raynal-Revai coefficients. The latter are expressible through finite sums of 3-j and 9-j symbols. The formulas allow precise and fast evaluation of matrix elements of the effective potential in the correlation-function hyperspherical-harmonic method for atomic, molecular, and nuclear three- and four-body problems. The generalization to any number of particles is straightforward.

First-order perturbation theory has been applied to calculate the relativistic corrections to the binding energies and the hyperfine splittings of muonic hydrogen molecular ions xyμ (x,y=p,d,t). The calculations include small-distance corrections to the potential due to the finite size of the nuclei and vacuum polarization. The numerical accuracy of the results is ≊0.1 meV. The zeroth-order wave function employed was previously determined by Alexander and Monkhorst [Phys. Rev. A 38, 26 (1988)].

The radiation emitted by an ion collisionally excited by an electron beam is anisotropic. We discuss two schemes, one for use with LS-coupling cross sections and one for intermediate coupling, whereby theoretical resonant-transfer-excitation cross sections can be modified to take account of this anisotropy when making comparisons with experimental results deduced from observations of radiation at a particular beam angle. We have carried out such calculations for a number of ions initially in an S state, viz. ${\mathrm{F}}^{6+}$, ${\mathrm{Ca}}^{\mathit{q}+}$ (q=16–19), and ${\mathrm{Nb}}^{\mathit{q}+}$ (q=29–31). In all cases, neglecting hyperfine structure, the allowance for anisotropic radiative emission at right angles to the beam axis was found to result in only a small increase (10–15 %) in the cross section over results that assumed isotropy. Allowance for hyperfine structure reduced even this anisotropy by 20% for ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}_{}^{6+}{}_{}{}^{}$ (I=1/2) and by 80% for ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$ (I=9/2) ions; results for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ (I=0) ions remain unchanged.

Electron-correlation and spin-orbit-interaction effects are known to play an important role in the quantitative description of multiphoton ionization of heavy atoms. In this paper an ab initio approach to two-photon ionization (2PI) of closed-shell atoms in the framework of the relativistic time-dependent Dirac-Fock theory is proposed. This formulation is known to contain important electron-correlation corrections and includes the spin-orbit interaction by use of relativistic wave functions. Computational results for nonresonant 2PI total cross sections of the rare gases are given. The approach is suitable for calculations of angular distributions, branching ratios, and autoionizing resonances.

L-shell-ionization cross sections of Si, P, S, Cl, and Ar have been obtained for incident ${\mathrm{H}}^{+}$ energies of 0.4 to 2.0 MeV and for ${\mathrm{H}}_2^{+}$ energies of 0.4 to 1.2 MeV. These relative cross sections were obtained from Auger-electron yields measured from gaseous targets of ${\mathrm{SiH}}_4$, ${\mathrm{PH}}_3$, ${\mathrm{SO}}_2$, ${\mathrm{CH}}_3$Cl, and Ar. The normalized experimental L-shell-ionization cross sections are compared to existing experimental L-shell-ionization cross sections and to various theoretical predictions.

A fully numerical multiconfiguration Hartree-Fock program has been modified for performance of calculations on atomic quasibound states using the complex-coordinate (complex dilation) technique. We present results of a lowest-order calculation of the 2s2p ${}_{}{}^{1,3}{}_{}{}^{}$P° autodetaching states of He using this method, and we examine the dilational stability of our calculations. Because the numerical method exhibits a high degree of dilational stability, we need not perform auxiliary calculations to stabilize the energy with respect to the dilation parameter, as is necessary in most basis-set calculations. We also report some small-scale multiconfiguration calculations in which we account for correlation in the closed channels but attempt no improvement of the open-channel part of the wave function. As the closed-channel space is enlarged, our results show a variational collapse of the width similar to (but more pronounced than) that observed in early basis-set studies using the dilation method. The resonance position, on the other hand, is well behaved and appears to be converging to agreement with established values.