The glass-transition point of the square-tiling model is shown not to be an isolated point but a point of confluence of a large number of higher-order phase transition lines. This multiphase nature of the glass-transition point is a consequence of the competition of the internal energy with the domain-wall energy that drives the glass transition in the model.

An alternating electric field is applied to a planarly aligned nematic liquid crystal with a positive dielectric anisotropy sandwiched between two electrodes. This leads to a reorientation of the director when the critical threshold for the Fréedericksz transition is exceeded. Triggered by this reorientation process, patterns arise. In the experiments presented, a transient periodic structure showing up as a system of fairly regular stripes parallel to the initial orientation of the director is observed. This pattern seems to be caused by a secondary instability of the homogenous reorientation process.

Using data from a single simulation we obtain Monte Carlo renormalization-group information in a finite region of parameter space by adapting the Ferrenberg-Swendsen histogram method. Several quantities are calculated in the two dimensional N=2 Ashkin-Teller and Ising models to show the feasibility of the method. We show renormalization-group Hamiltonian flows and critical-point location by matching of correlations by doing just two simulations at a single temperature in lattices of different sizes to partially eliminate finite-size effects.

High-lying Rydberg states (11≤n≤34) of helium hydride have been observed. They were produced by laser excitation of a fast molecular beam and detected by field ionization. Ionization potentials, quantum defects, and the binding energy of ${\mathrm{HeH}}^{+}$ were determined. Pure rotational autoionization leads to break offs of the series. From missing lines it is concluded that B ${}_{}{}^2{}_{}{}^{}\mathcal{’}$) state decays by predissociation.

Hedin’s Coulomb-hole and screened-exchange (COHSEX) approximation for the one-electron Green-function self-energy is examined for small molecules through second order in the bare interaction (COHSEX2). Numerical examples suggest that the COHSEX2 approximation works better for ionization potentials and generalized overlaps (Dyson amplitudes) than does either Koopman’s theorem or the usual second-order Green-function (GF2) approximation. This result has been traced to the superior quality of Hedin’s GW approximation evaluated to second order in the bare interaction (GW2). (The GW self-energy is the simple product of the Green function G and the screened interaction W in the time-and-position space representation.) The COHSEX2 approximation is found to be a rather crude approximation for the GW2 self-energy at the center of the highest occupied molecular orbital–lowest unoccupied molecular orbital energy gap, but is still superior to the GF2 approximation in most of our calculated results and is amenable to limited dynamical corrections. The primary potential advantage of the COHSEX approximation over the GW approximation is that no sums over virtual orbitals need be performed once the static screened interaction or polarization is known. Our results suggest that accurate density-functional approximations for the static screened interaction or polarization can lead to self-energies of accuracies beyond both Koopmans’s theorem and the GF2 level.

The N=3 series of the ${}_{}{}^1{}_{}{}^{}\mathrm{S}_{}^{\mathrm{e}}{}_{}{}^{}$ helium states have been investigated by partial-wave analysis and by observing the shape densities. The K-classification scheme has been recovered. The strong radial-radial correlation region (SRRCR) has been found. The process of energy transfer occurring inside the SRRCR has been inspected in detail and two types of mechanisms, the ‘‘direct push’’ and the ‘‘head-on collision,’’ have been discovered.

Nature provides us with two alternatives for the origin of electromagnetic zero-point energy (ZPE): existence by fiat as part of the boundary conditions of the universe, or generation by the (quantum-fluctuation) motion of charged particles that constitute matter. A straightforward calculation of the latter possibility has been carried out in which it is assumed that the ZPE spectrum (field distribution) drives particle motion, and that the particle motion in turn generates the ZPE spectrum, in the form of a self-regenerating cosmological feedback cycle. The result is the appropriate frequency-cubed spectral distribution of the correct order of magnitude, thus indicating a dynamic-generation process for the ZPE fields.

Two infinite series of resonance states of muonic molecular ions (ppμ${)}^{+}$ and their isotopes converging to the dissociation limit n=2 are theoretically studied within nonrelativistic quantum mechanics. These resonance states are supported by the attractive long-range dipole potential originating from the linear Stark effect and behaving as $R^{\mathrm{-}2}$. The positions ${\epsilon }_v$ (v=0,1,2,. . .) of the resonances relative to the dissociation threshold satisfy a simple power law ${\epsilon }_v$=A${\alpha }^v$ for high v, the constant α being easily calculable in terms only of the total angular momentum and the masses of the nuclei and the muon. The size of a muonic molecule in a state ${\epsilon }_v$ is ∼${10}^{\mathrm{-}8}$ cm/[4 √‖${\epsilon }_v$ (eV)‖ ], which is comparable to (or even larger than) the size of ground-state electronic molecules if the resonance lies within a fraction of an electron volt from the dissociation threshold. The theory is useful in the classification of resonances in muonic molecules. The systems (dtμ${)}^{+}$ and (ddμ${)}^{+}$ are analyzed as examples.

General time-dependent, bilinear classical Lagrangian mechanics can be interpreted as a charged particle interacting with a gauge scalar and vector potential. For an arbitrary discrete number of degrees of freedom, there are enough symplectic symmetries in classical mechanics to make this system canonically identical to the most general discrete spectrum quantum system. It follows that the general invariance group of the Schrödinger system of equations is the symplectic group Sp(2N), not U(N). Several examples show the physical naturalness of the classical coordinates. In the adiabatic limit Berry’s phase is identified as the cumulative change of the angle of action-angle coordinates of a normal mode. A generalization of Berry’s phase, the time component of the adiabatic connection and its associated electric curvature, is shown to be on an equal footing with the usual Berry phase.

The density matrix is determined for H(n=3) atoms produced in axially symmetric electron-transfer collisions of 80-keV protons on helium. In the experiment axial or transverse electric fields with respect to the proton beam are applied to the collision region. The intensity and polarization of Balmer-α radiation emitted by the H(n=3) atoms are measured as a function of the strength of the external electric field. Detailed analysis of the measured optical signals, taking into account the time evolution of the H(n=3) atoms in the applied electric field, makes it possible to extract the complete density matrix of the H(n=3) atoms at the moment of their formation, averaged over all impact parameters. Significant improvements in the experimental technique and in the data analysis associated with the fit of the density matrix to the optical signals have eliminated systematic effects that were present in our previous work [Phys. Rev. A 33, 276 (1986)].

The improvements in the apparatus are as follows: application of electric fields using electrodes with a simple geometry for the axial and transverse orientations that allows accurate calculation of the spatial variation of the electric field inside the collision chamber; use of high-quality optical elements and a rotatable, single-unit design for the polarimeter; automated gas handling for background subtraction; and full computer control of the electric fields, polarimeter, gas handling, and data acquisition. The analysis incorporates the following improvements: hyperfine structure of the H(n=3) manifold; cascade from the H(n=4) manifold; nonuniform detection efficiency over the viewing region; and modeling of the nonuniform electric fields, the nonuniform gas density, and the exponential decrease of the proton beam current in the gas cell due to electron transfer. With these improvements the results from axial electric field measurements are in good agreement with results obtained independently from transverse electric fields. Moreover, the extracted density-matrix elements are found to be within their physically meaningful bounds. The major results from 80-keV collisions are that the H(n=3) density matrix has an average coherence of 81%±1%, an electric dipole moment of 3.50±0.09 a.u., and a first-order moment of the electron current density distribution 〈(L×${\mathrm{A})}_z$,s〉 of -0.13±0.02 a.u. Results from a recent calculation show qualitative agreement with the experiment.

Observations of electron-excited 4$d^{10}$4$f^0$→4$d^9$4$f^1$ giant resonances of Ba in the high-$T_c$ superconductor ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ are compared with previous work on the corresponding La transition in various environments. Breakdown of dipole selection rules is observed even at electron primary energies of a few keV, but for low-angle scattering it is possible to rationalize the results in terms of symmetry-related selection and intensity rules appropriate to intermediate coupling. This interpretation is supported by atomic Hartree-Fock calculations of the final-state multiplets.

Within a second-order approximation to the Faddeev treatment of the exact transition operator for 1s→1s electron capture in ion-atom collisions, expressions are derived in terms of $F_4$ generalized hypergeometric functions for that part of the full amplitude involving electronic-nuclear potentials only. For totally symmetric collisions, the amplitude is evaluated in terms of ${}_3{}^{}{}_{}{}^{}\mathrm{F}_2^{}{}_{}{}^{}$ functions. When near-the-energy-shell anomalies of the Coulomb scattering are neglected, the amplitude is seen to reduce to a symmetric impulse-approximation form, and, when the explicit Coulomb nature of the problem is neglected, to a second-order Born approximation form. As a special case, the amplitude is evaluated at the momentum transfer value where the differential cross section exhibits a local maximum—the Thomas peak. The values of the various amplitude norms at the Thomas peak are compared.

Absolute differential cross sections are reported for collisions between 0.5, 1.5, and 5.0-keV-energy H atoms and He, Ne, Ar, Kr, and Xe over the laboratory-frame angular range 0.018°–0.5°. The scattered neutral particles are detected, and the measured cross sections include both elastic and inelastic events. The H-He results are in excellent accord with previous measurements at larger angles. Empirical interaction potential-energy curves have been extracted from the data for all collisions studied.

Measurements of absolute differential cross sections for direct and charge-transfer scattering of ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ by the rare gases have been made. Direct scattering cross sections are reported at 1.5 keV for collisions of ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ with Ne, Ar, Kr, and Xe over the laboratory angular range 0.03°–1.0°. Charge-transfer cross sections are reported for the laboratory scattering angles below 1.0° for ${\mathrm{H}}^{+}$-Ar, Kr at 0.5, 1.5, and 5.0 keV, for ${\mathrm{H}}^{+}$-Xe at 5.0 keV, and for ${\mathrm{He}}^{+}$-Ne at 1.5 keV. The data exhibit a wealth of structure over the experimental angular range, and cross sections have been integrated over angle to provide absolute integral cross sections.

Detailed theoretical results are presented for the electron-detachment cross section, doubly differential in both the electron momentum and angle, for the process 0.5-MeV ${\mathrm{H}}^{\mathrm{-}}$+He→H(n=2)+${\mathit{e}}^{\mathrm{-}}$+${\mathrm{He}}^{\mathrm{*}}$. As discussed briefly elsewhere [C. R. Liu and A. F. Starace, Phys. Rev. Lett. 62, 407 (1989)], the laboratory-frame doubly differential cross sections (DDCS’s) for electron detachment in the forward direction are shown to depend sensitively on the low-energy states of the H(n=2)-$e^{\mathrm{-}}$ three-body system. In particular, the angular dependence of characteristic cusp and shape resonance features is presented. We find that the projectile frame DDCS for detached electron energies in the vicinity of the shape resonance peak is nearly isotropic. This is due in part to the ${}_{}{}^1{}_{}{}^{}\mathrm{P}$ symmetry of the resonance feature, which limits the angular distribution to constant and ${\cos }^2$θ terms, and in part to cancellation in the integral over momentum transfer on which the coefficient of the ${\cos }^2$θ term depends.

We also find that the rapid variation of these cusp and shape resonance features with angle in the laboratory frame requires that experimental angular and energy resolutions be accounted for in order to obtain good agreement with the measured results of M. G. Menendez and M. M. Duncan [Phys. Rev. A 36, 1653 (1987)] on the energy spectrum of detached electrons coincident with the formation of H(2p). The DDCS’s for 0.5-MeV ${\mathrm{H}}^{\mathrm{-}}$+He→H(1s)+$e^{\mathrm{-}}$+${\mathrm{He}}^{\mathrm{*}}$ are also presented. When these latter results are added to those for producing H(n=2), the sum gives good agreement with the experimental data of M. G. Menendez and M. M. Duncan [Phys. Rev. 20, 2327 (1979)], which include all final states of the H atom, thereby confirming the important contribution the H(n=2) states make to the total-detachment cross section. We present evidence on the sensitivity of these results to the choice of the average excitation energy of the helium target. Finally, we pinpoint the origin of our predicted Gailitis-Damburg oscillations in the DDCS near threshold as stemming from a rapid decrease of an analytically known phase appropriate for long-range dipole fields.

The electron-impact ionization cross section for highly charged ions is calculated as a triple partial-wave expansion of scattering amplitudes obtained from lowest-order QED theory. The interaction between electrons includes static, magnetic, and retardation effects. The target atomic ion is described by a Dirac-Fock approximation and the radial partial waves are computed in relativistic distorted-wave potentials. The QED cross-section results for ${\mathrm{U}}^{91+}$ and ${\mathrm{U}}^{90+}$ are compared with nonrelativistic and relativistic theories as well as a recent heavy-ion channeling experiment.

We have calculated differential cross sections as a function of the projectile scattering angle for positron-helium and positron-krypton collisions using the classical-trajectory Monte Carlo technique. These intermediate-velocity collisions have been simulated by various independent-electron and n-electron models, using both screened Coulomb and quantum model potentials to approximate the effects of electron-electron interactions. These several models all indicate that scattering of positrons to large angles in ionizing collisions persists to high impact velocities. In a previous work [Phys. Rev. A 38, 1866 (1988)] we proposed that the recent experiments that have measured the total cross section for positronium formation could be affected by the loss of positron flux due to incomplete confinement after large-angle scattering. Here, utilizing these newly calculated differential-scattering cross sections, adjustments are computed that account for the difference between the experimental and theoretical behaviors of the positronium formation cross section. Further, it is demonstrated that large-angle scattering in the elastic channel is important for one of the experiments. We have also computed total cross sections for ionization and charge transfer for collisions of protons with krypton. Good agreement is obtained in these cases with experimental measurements.

Estimates of frequency-shift enhancement factors, binary cross sections for spin exchange and spin relaxation, chemical equilibrium constants, and spin-exchange and spin-rotation interactions in van der Waals molecules are presented for alkali-metal atoms interacting with noble-gas atoms. These results are compared to experiments and are also presented for those pairs which have not been studied experimentally.

Calculations of the energy dependence of the electron-scattering cross section in the presence of thermal background radiation (Planck’s field) are done in the semiclassical approximation. It is shown that the cross section remains finite and is peaked around the initial energy with the width proportional to the radiation temperature.

The photoionization cross sections of the 2$s^2$, 2$p^6$, and 3$s^2$ subshells of atomic magnesium and angular distribution asymmetry parameters for the 2$p^6$ subshell have been calculated using many-body perturbation theory. Double-electron resonance structure near the 3s threshold has been included. At higher energies, resonance structures due to the 2s→np and 2p→nd(ms) (n>=3, m≥4) excitations have also been included. The effects of spin-orbit interactions on the 2p→nd(ms) resonances are examined. The calculated asymmetry parameter for the 2$p^6$ subshell including the 2s→np resonance structure is compared with the calculations of Deshmukh and Manson [Phys. Rev. A 28, 209 (1983)].