Zurek, Habib, and Paz [Phys. Rev. Lett. 70, 1187 (1993)] have characterized the set of states of maximal stability defined as the set of states having minimum entropy increase due to interaction with an environment and shown that coherent states are maximal for the particular environment model examined. To generalize these results, I consider entropy production within the Lindblad theory of open systems, treating environment effects perturbatively. I characterize the maximally predicitive states that emerge from several forms of effective dynamics, including decoherence from spatially correlated noise. Under a variety of conditions, coherent states emerge as the maximal states.

We apply recent methods for semiclassical time propagation involving non-Cartesian variables to the repulsive one-dimensional potential V(x)=${\mathit{x}}^{\mathrm{-}2}$,x≥0. In order to properly treat non-Cartesian variables, a quantum regularization is first performed which leads to a Langer-type potential correction term in the Gutzwiller–Van Vleck propagator. A nonuniform semiclassical treatment of V(x)=${\mathit{x}}^{\mathrm{-}2}$ using this regularization improves earlier unregularized results, and a uniform regularized propagator is very nearly exact for all times. © 1996 The American Physical Society.

Both the nonrelativistic scattering and the spectrum in the presence of the Aharonov-Bohm potential are analyzed and the single-particle density of states for different self-adjoint extensions is calculated. The single-particle density of states is shown to be a symmetric and periodic function of the flux, which depends only on the distance from the nearest integer. The Krein-Friedel formula for this long-range potential is shown to be valid when regularized with the ζ function. The limit when the radius R of the flux tube shrinks to zero is discussed. For R≠0 and in the case of an anomalous magnetic moment ${\mathit{g}}_{\mathit{m}}$≳2 (note, e.g., that ${\mathit{g}}_{\mathit{m}}$=2.002 32 for the electron) the coupling for spin-down electrons is enhanced and bound states occur in the spectrum. Their number does depend on a regularization and generically does not match with the number of zero modes in a given field that occur when ${\mathit{g}}_{\mathit{m}}$=2. Provided the coupling with the interior of the flux tube is not renormalized to a critical one, neither bound states nor zero modes survive the limit R→0. The Aharonov-Casher theorem on the number of zero modes is corrected for the singular field configuration.

Whenever a bound state does survive the R→0 limit it is always accompanied by a resonance. The presence of a bound state manifests itself in the asymmetric differential scattering cross section that can give rise to the Hall effect. The Hall resistivity is calculated in the dilute vortex limit. The magnetic moment coupling and not the spin is shown to be the primary source for the phase-shift flip that may occur even in its absence. The total energy of the system consisting of particles and field is discussed. An application to persistent currents in the plane for both spinless and spin one-half fermions is given. Persistent currents are also predicted to exist in the field of a cosmic string. The second virial coefficient of anyons with a short-range δ-function interaction is calculated. The coefficient is shown to be remarkably stable when such an interaction is switched on. Several suggestions for new experiments are given.

Using the classical trajectory we quantize the motion of a pointlike particle of mass m and energy 1/2${\mathit{mx}\mathit{̇}}_0^2$ under the influence of the force ${\mathit{F}}_{\mathit{n}}$=-α‖ẋ${\mathrm{\Vert }}^{\mathit{n}}$, α≳0, n=1,2,.... Such forces are frictional only for ẋ≳0 and antifrictional for ẋ<0 and can be simulated through the gradient of a one-parameter class of energy-dependent potentials ${\mathit{V}}_{\mathit{n}}$(x;x${\mathrm{̇}}_0$), which increase monotonically in x. This permits one to construct a class of Lagrange and Hamilton functions that do not contain any integrating functions. We then proceed to quantization and study the quantum scattering problem assuming that ${\mathit{F}}_{\mathit{n}}$ acts on a finite interval of the x axis only. The stationary problem can be solved analytically for all n, and quantitative examples are shown for n=2. The time-dependent scattering problem is discussed with emphasis on Ehrenfest’s theorems and on linear damping n=1. When the quantum-mechanical probability for reflection is small the method provides an approximation to the motion of a wave packet through a dissipative medium, with velocity-power forces ${\mathit{F}}_{\mathit{dn}}$=-α‖ẋ${\mathrm{\Vert }}^{\mathit{n}\mathrm{-}1}$ẋ. © 1996 The American Physical Society.

The density operator is defined as a function of a generalized invariant for the system of time-dependent harmonic oscillators. Applying this to the Hamiltonian with two asymptotic regions, we calculate the temperature change driven by a time-varying Hamiltonian. Furthermore, the squeezing properties of an eigenstate and a coherent state of the initial Hamiltonian are discussed. © 1996 The American Physical Society.

We report on a model for the intensity of ‘‘forbidden’’ 3${\mathit{d}}^{\mathit{k}}$-3${\mathit{d}}^{\mathit{k}\mathrm{-}1}$4s electric quadrupole (E2) transitions in ions with ground states of the form 3${\mathit{p}}^6$3${\mathit{d}}^{\mathit{k}}$ (k=1 through 9) across a broad range of temperatures and densities. (Molybdenum, Z=42, has been chosen as a representative element because of its role in magnetically confined fusion experiments and the availability of experimental data.) We make an identification of a 3${\mathit{d}}^8$-3${\mathit{d}}^7$4s E2 line in Mo XVII. In ions where strong E2 lines are not seen (ions with ground states 3${\mathit{d}}^{\mathit{k}}$, 1≤k≤7), the suppression of the lines is explained by dipole decays to low-lying levels other than the ground state that become allowed through configuration interaction between 3${\mathit{d}}^{\mathit{k}\mathrm{-}1}$4s states and excited states that have electric dipole (E1) decays to the 3${\mathit{p}}^5$3${\mathit{d}}^{\mathit{k}+1\mathrm{}}$ levels (and in like manner mixing between the 3${\mathit{p}}^5$3${\mathit{d}}^{\mathit{k}+1\mathrm{}}$ configuration and other configurations with E1 decays to the levels of 3${\mathit{d}}^{\mathit{k}\mathrm{-}1}$4s). For k=8 and 9, we find that radiative cascades from high-lying levels play an important role in populating upper states of the E2 transitions. The role of direct, collisional ionization from valence and inner subshells of adjacent charge states in populating the upper states of 3d-4p E1 and 3d-4s E2 decays in Mo XVI and Mo XVII is found to be negligible. General agreement is found between observations of the E2 to E1 brightness ratio of Mo XVI made in a tokamak plasma and the predictions of the present model. Sensitivity to changes in electron density in the ratio of E2 to E1 decays can be used as a diagnostic for fusion plasmas. © 1996 The American Physical Society.

High-resolution measurements of the K${\mathrm{\beta }}_{1,3}$ low-energy satellites of ${}_{42}{}^{}{}_{}{}^{}\mathrm{Mo}$, ${}_{44}{}^{}{}_{}{}^{}\mathrm{Ru}$, ${}_{46}{}^{}{}_{}{}^{}\mathrm{Pd}$, ${}_{48}{}^{}{}_{}{}^{}\mathrm{Cd}$, and ${}_{50}{}^{}{}_{}{}^{}\mathrm{Sn}$ were performed. The photoinduced x-ray spectra were measured with a transmission-type bent-crystal spectrometer. Particular groups of K-MM radiative Auger effect (RAE) transitions could be identified. The intensity ratios I(K-MM RAE) / I(K${\mathrm{\beta }}_{13}$) were extracted. They are compared to relativistic Hartree-Fock theoretical predictions of Scofield. The experimental energies of the RAE edges are compared to calculated Auger transition energies. The present experiment provides experimental RAE results for solid elements with Z≥42. © 1996 The American Physical Society.

Muonic three-body bound states and resonances are treated within a hyperspherical adiabatic expansion scheme. A new method for determining the basis functions of this expansion is developed: decomposing these functions into Faddeev-type components, an equivalent treatment of all two-body contributions, and thus the correct asymptotics, are guaranteed. This approach is characterized by its high symmetry and a considerable reduction of the numerical effort. Using partial wave and B-spline expansions for the components, wave functions and energies of the dtμ and ${\mathit{d}}^3$Heμ molecules are calculated in extreme and uncoupled adiabatic approximation. For dtμ good agreement with alternative calculations, which are based on a much higher number of expansion functions, is found, and the results for the ${\mathit{d}}^3$Heμ system are rather close to variational calculations. © 1996 The American Physical Society.

We investigate the classical dynamics of the helium atom in which one electron is replaced by a heavy particle with a negative charge, such as an antiproton. The general properties of motion and the conditions for chaotic dynamics are studied via the derivation of the planetary map. The regime of strongly correlated motion of two particles is also analyzed. The properties of quantum motion are briefly discussed. © 1996 The American Physical Society.

Multielectron atoms in external fields are essentially more complicated than hydrogen with regard to theoretical treatments. Experimental spectra of helium as well as R-matrix quantum-defect calculations revealed discrepancies between the diamagnetic hydrogen atom and general Rydberg atoms. They appeared most transparent as novel resonance structures in constant scaled-energy recurrence spectra of nonhydrogenic atoms at positions where no hydrogenic resonances exist. To reveal the physical origin of these resonances we performed a rigorous semiclassical investigation of nonhydrogenic atoms in magnetic fields. The ionic core is introduced into the Hamiltonian via a short-ranged core potential. For this Hamiltonian we analyze in detail the classical dynamics of closed orbits. Classical core-scattering results in the creation of a huge number of new closed orbits. They appear to be composed of a sequence of slightly different hydrogenic orbits, interconnected by the core-scattering, and can be grouped into families accordingly. With a semiclassical closed-orbit theory generalized to arbitrary quantum defects of the ionic core and with the closed orbits at hand we are able to calculate photoabsorption spectra of nonhydrogenic atoms. Although each of the new orbits has a low amplitude, the interference of all members of a family results in clearly visible resonances in the Fourier transform recurrence spectra, in good agreement with experiment and quantum calculations. The novel structures in nonhydrogenic spectra are now identified and semiclassically interpreted in terms of families of core-scattered classical orbits. © 1996 The American Physical Society.

Using monochromatized synchrotron radiation and atomic beam technique the photoion spectra of Fe, Co, and Ni in the region of the 3p resonances were measured. For the interpretation of the spectra the photoionization cross sections were calculated, taking into account strong interconfiguration mixing of the type (3d,4s${)}^{\mathit{N}}$ and the thermal population of the different fine-structure levels in the ground states according to the temperature of about 1800 K for the evaporation of the metals. The calculations were performed in the framework of overlapping resonances interacting with many continua. Good agreement of the main features with the experimental results were obtained. Special emphasis is given to the discussion on the origin of doubly charged photoions. © 1996 The American Physical Society.

Accurate quartet- and doublet-state potential-energy surfaces for the interaction of a hydrogen atom and an oxygen molecule in their ground states have been determined from an ab initio calculation using large-basis sets and the internally contracted multireference configuration interaction method. These potential surfaces have been used to calculate the H-${\mathrm{O}}_2$ electron-spin-exchange cross section; the square root of the cross section (in ${\mathit{a}}_0$), not taking into account inelastic effects, can be obtained approximately from the expressions 2.390${\mathit{E}}^{\mathrm{-}1/6}$ and 5.266–0.708 ${\log }_{10}$(E) at low and high collision energies E (in ${\mathit{E}}_{\mathit{h}}$), respectively. These functional forms, as well as the oscillatory structure of the cross section found at high energies, are expected from the nature of the interaction energy. The mean cross section (the cross section averaged over a Maxwellian velocity distribution) agrees reasonably well with the results of measurements. © 1996 The American Physical Society.

Measurements of argon photoion yields obtained in coincidence with K-${\mathit{L}}_{2,3}$${\mathit{L}}_{2,3}$ Auger emission as a function of incident photon energy across the K-shell threshold are reported. These results are interpreted within the framework of lowest-order scattering theory, which describes the virtual creation and decay of 1s-hole states. Cross sections for the production of singly ionized spectator Auger states [2${\mathit{p}}^2$]np and the doubly ionized [2${\mathit{p}}^2$] states are calculated using nonrelativistic Hartree-Fock wave functions and their physical interpretation is discussed. When the behavior of the np spectator electron during and after the subsequent Auger cascade that fills the two core 2p holes is taken into account, excellent agreement with experiment is obtained. The mechanism for loss of the np electron in this cascade is shown to be a final Auger decay in which the np electron participates and np shake-off is found to be negligible. © 1996 The American Physical Society.

A rigorous method of describing the energy dependence of rotational polarization in rearrangement collisions is proposed by exploring both the kernel function of intrinsic nature and the distorted-wave functions of dynamic nature. From this study the energy dependence of rotational polarization and favored geometric configuration is well understood in an explicit manner. It is also found that the rotational polarization is not affected by the interference of partial waves. © 1996 The American Physical Society.

An effective-potential formalism, previously developed for electron scattering by a neutral target, is extended to apply to electron-ion scattering, with the requirement of antisymmetrization now accounted for explicitly. A minimum principle for the effective potential is derived, valid for scattering below the ionization threshold and applicable when, as is usually the case, the target wave functions are imprecisely known. The basis for the minimum principle is the Rayleigh-Ritz property that is satisfied by the modified Hamiltonian in terms of which the effective potential is defined. An analysis of single-channel, zero-energy scattering for a particular partial wave is presented; it is based on the effective-potential formalism and leads to an absolute definition of the zero-energy phase shift δ(0) of the form δ(0)=μ(∞)π, where μ(n) is the quantum defect of the nth energy level. This result may be thought of as an extension of Levinson’s theorem for scattering by short-range potentials. © 1996 The American Physical Society.

X-ray-absorption spectra of a ${\mathrm{Sr}}^{2+}$ aqueous solution have been studied in order to assess the contribution of double-electron excitation channels to the atomic background. Anomalies in the spectra have been identified that are assigned to the simultaneous excitation of 1s4s, 1s3d, and 1s3p electrons, referred to as ${\mathit{KN}}_1$, ${\mathit{KM}}_{4,5}$, and ${\mathit{KM}}_{2,3}$ channels. A reliable determination of the double-electron edge parameters has been obtained by performing an analysis of the structural contribution in the correct framework of the radial distribution function theory. The experimental values of the energy onsets of the double-electron features are in excellent agreement with the predictions of the Z+1 approximation. The influence of double-electron effects on the determination of the structural parameters has been studied by using asymmetric peaks to model the Sr-O and Sr-H coordination shells. It has been found that an accurate determination of the structural parameters is possible only if double-electron channels are accounted for. The exclusion of these effects results in systematic errors on the structural parameters and, in particular, in a severe underestimation of the coordination numbers. © 1996 The American Physical Society.

Dipole-allowed transitions for the inner-shell ${\mathit{C}}_{1\mathit{s}}$(2${\mathrm{\sigma }}_{\mathit{g}}$)→2${\mathrm{\Pi }}_{\mathit{u}}$ in ${\mathrm{CO}}_2$ and 2${\mathit{t}}_{1\mathit{u}}$→6${\mathit{a}}_{1\mathit{g}}$, 2${\mathit{t}}_{1\mathit{u}}$→2${\mathit{t}}_{2\mathit{g}}$, and 2${\mathit{t}}_{1\mathit{u}}$→4${\mathit{e}}_{\mathit{g}}$ in ${\mathrm{SF}}_6$; for X${\mathrm{}}^1$${\mathrm{\Sigma }}^{+}$→A${\mathrm{}}^1$Π and X${\mathrm{}}^1$${\mathrm{\Sigma }}^{+}$→C${\mathrm{}}^1$${\mathrm{\Sigma }}^{+}$ in CO; for excitation of ${\mathit{F}}_2$ I${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$ and the electronic states of ${\mathrm{SO}}_2$ are investigated at small scattering angles through the generalized oscillator strength using a recent universal function [A. Z. Msezane and I. A. Sakmar, Phys. Rev. A 49, 2405 (1994)]. The results cover the electron energy between 20 eV and 2.5 keV. Good agreement with existing experimental data and calculations is obtained for the inner-shell excitation of ${\mathrm{CO}}_2$ and the 2${\mathit{t}}_{1\mathit{u}}$-6${\mathit{a}}_{1\mathit{g}}$ transition in ${\mathrm{SF}}_6$, implying that dynamic effects are unimportant at small scattering angles. The unmeasured differential cross sections (DCS’s) in the angular range of about 0°≤θ≤2° are found to contribute significantly to the integral cross sections, ranging from 40% to 69% at 300 and 500 eV in CO. The universal function approach provides an independent check of small-angle theoretical and experimental DCS’s. Given reliable small-angle DCS’s, the universal formula can be used to obtain reasonable values of optical oscillator strengths. Dynamic effects can also be investigated and are shown to be significant in the fourth positive band of CO at 500 eV, even near zero scattering angles. In contrast, dynamic effects are unimportant in the inner-shell excitation of ${\mathrm{CO}}_2$ at 1290 eV, up to large momentum-transfer-squared values, even though for the transition the first Born approximation should not be applicable. Results are presented and discussed. © 1996 The American Physical Society.

In the present work we propose a method for solving the Schrödinger equation in the adiabatic approximation within the molecular context. We employ this method to solve problems with non-Galilean invariance, and an attempt is made to explain some theoretical aspects of it. Simple applications are also considered. This method, which we could call the central-field method (or linear combination of central fields), enables a better understanding of the problem of non-Galilean invariance. © 1996 The American Physical Society.

In collisions of Rydberg atoms with charged projectiles at velocities approximately matching the speed of the Rydberg electron $v_n$ (matching velocity), $n$ being the principal quantum number of the Rydberg level, the dipole-forbidden transitions with large angular-momentum transfer $\Delta l\gg 1$ substantially dominate over dipole-allowed transitions $\Delta l=1\mathrm{}$, although both are induced by the dipole interaction. Here it is shown that as the projectile velocity decreases the adiabatic character of the depopulation depends on the energy distribution of states in the vicinity of the initial level. If the spectrum is close to degeneracy (as for high-$l$ levels) the dipole-forbidden depopulation prevails practically over the entire low-velocity region, down to velocities $\sim n^3\left[\frac{\Delta E}{\mathrm{Ry}}\right]v_n$, where $\Delta E$ is the energy spacing adjoining to the level due to either a quantum defect or the relevant level width or splitting, whichever is greater. If the energy gaps are substantial (as for strongly nonhydrogenic $s$ and $p$ levels in alkali-metal atoms), then the fraction of dipole transitions in the total depopulation reaches a flat minimum just below the matching velocity and then grows again, making the progressively increasing contribution to the low-velocity depopulation. The analytic models based on the first-order Born amplitudes (rather than the two-level adiabatic approximation) furnish reasonable estimates of the fractional dipole-allowed and dipole-forbidden depopulations.