In order to understand the self-organized critical behavior of a one-dimensional, finite-size cellular automaton with a continuous state variable, proposed by Y. C. Zhang [Phys. Rev. Lett. 63, 470 (1989)], calculations are performed. Analytical results for the distribution functions and the critical energy of finite chains are in complete agreement with the numerical results, and do not agree with earlier predictions.

Calculations are carried out for the cross section for x-ray emission by n=2 and 3 states resulting from the radiative recombination onto bare and hydrogenlike ions of titanium and iron from a beam of electrons with energies of several kilo electron volts. The calculation includes the contribution coming from direct recombination and cascades from higher-energy states. The density matrix of the magnetic sublevels is included in the calculation and results are given for the emission at 90° to the direction of the incoming electron beam and its degree of linear polarization. The calculation is carried out relativistically assuming the incoming electrons move in a central potential. The bound states of the heliumlike ions are treated using a configuration-interaction code using basis states derived from a relativistic average-configuration Hartree-Fock code for the calculation of both the radiative-recombination and bound-state transition-matrix elements.

We show that for lattice trees attached to a surface, ${\mathrm{\theta }}_1$=θ+1 in any dimension, where ${\mathrm{\theta }}_1$ is the critical exponent describing the subdominant behavior of lattice trees attached to the lattice surface and θ is the corresponding bulk exponent. Estimates of the surface interaction required to produce the adsorption transition for trees are also given.

Spatiotemporal behaviors involving coexisting attractors are investigated in discrete complex time-dependent Ginzburg-Landau equation systems. Complex dynamics connecting local attractors and an ‘‘attractor complex’’ born from destabilized coexisting equilibria are studied through numerical simulations. Majority-rule-based switching among two surviving attractors, inherent unstable motions reflecting the nature of the attractor complex, and ‘‘history-dependent’’ path formation resulting in the recovery of memory are shown in weakly coupled regimes. A relation with a continuum limit is briefly discussed.

The Boltzmann-Lorentz equation for Maxwell molecules is used to study tracer diffusion in uniform shear flow. It is shown that some values of the mass ratio may prevent the establishment of a hydrodynamic regime. In the region where a hydrodynamic solution exists, a diffusion tensor has been derived by considering terms up to first order in the tracer concentration gradient. This tensor is a highly nonlinear function of both the shear rate and the mass ratio. A comparison with earlier results has been performed.

A first-principles molecular-dynamics study of atomic dynamical correlations in liquid silicon is presented. The properties studied here include the van Hove correlation function, velocity autocorrelation function, spectral density, and non-Gaussian corrections to the incoherent van Hove function. It is shown that these correlation functions exhibit an oscillatory behavior at short and intermediate times due to stretching vibrations of covalent bonds that form in the metallic liquid. Quantitative estimates are given for the time scale of typical ionic relaxation times and for the self-diffusion coefficient.

We have tested a separation-of-variables approximation for the electron velocity distribution function in the Boltzmann equation. In this approximation, the distribution function ${\mathit{f}}_{\mathit{e}}$(z,${\nu }_{\mathit{z}}$,${\nu }_{\mathit{r}}$,t) is represented as the product of two functions F(z,${\nu }_{\mathit{z}}$,t) and G(z,${\nu }_{\mathit{r}}$,t). This approximation can represent very anisotropic distributions, while effectively reducing the dimensionality of the calculation. We have implemented this approximation using a method of characteristics, and have applied it to argon and neon gas for a wide range of applied electric fields.

We consider the photoelectron spectra produced by a high-intensity short-duration laser pulse on a metal and present the results of a computer simulation of the electron-energy variations in a diode and beyond it, taking into account the space-charge effect. We show that the energy increase in the diode is indeed responsible for the unexpectedly high-electron-energy spectrum observed in a recent experiment by Farkas and Toth [Phys. Rev. A 41, 4123 (1990)].

An exchange in the wave action (number of quanta) is analyzed by means of the perturbation theory for a soliton-soliton collision in the nonlinear Schrödinger equation with a nonlinear damping term that conserves the total wave action (it may account for the intrapulse Raman scattering in the model of a lossless optical fiber, or for the nonlinear Landau damping in a plasma). It is demonstrated that, if the colliding solitons have a sufficiently large relative velocity, the analytical results are in very good accordance with recently published numerical simulations [S. Chi and S. Wen, Opt. Lett. 14, 1216 (1989)]. This warrants application of the present variant of the perturbative technique to other physical problems.

We analyze the retrieval dynamics of analog ‘‘neural’’ networks with clocked sigmoid elements and multiple signal delays. Proving a conjecture by Marcus and Westervelt, we show that for delay-independent symmetric coupling strengths, the only attractors are fixed points and periodic limit cycles. The same result applies to a larger class of asymmetric networks that may be utilized to store temporal associations with a cyclic structure. We discuss implications for various learning schemes in the space-time domain.

We discuss the apparent disagreement between the recent numerical results of Kessler and Levine [Phys. Rev. A 41, 3197 (1990)] and previous analytical results concerning the linear stability analysis of large-amplitude cells in directional solidification, in particular in relation to the existence of an oscillatory instability of cell tips. We argue that some of the conclusions drawn by these authors are not justified.

In a recent paper Carlson and Schieve [Phys. Rev. A 40, 5896 (1989)] obtained a pair of coupled cubic equations for the Gaussian effective potential for the four-leg potential and indicated how it can be solved approximately. This Comment reduces the equations to a single cubic equation for each of the two possible cases that arise and hence completely solves the equations.

A self-consistent study of the function f(r)=ρ(r)+ρ’(r)/(2Z), where ρ(r) is the spherically averaged electron density of the ground state of an atom, shows that f(r)≥0 everywhere. This allows us to obtain several inequalities relating the atomic electronic density at the nucleus ρ(0) and atomic radial expectation values 〈${\mathit{r}}^{\mathrm{\alpha }}$〉. In particular, we generalize upper bound found by Hoffmann-Ostenhof, Hoffmann-Ostenhof, and Thirring [J. Phys. B 11, L571 (1978)] to ρ(0). We also obtain accurate inequalities between the radial expectation values 〈${\mathit{r}}^{\mathrm{\alpha }}$〉 of atomic systems.

Relativistic correlation energies are determined by taking the difference between the energies derived from the relativistic many-body perturbation method and those from the Dirac-Fock method for the resonance transitions of Li-, Na-, and Cu-like ions. These correlation energies are combined with the Dirac-Fock energies and ‘‘screened’’ QED corrections based on approximate methods. The resulting theoretical transition energies are compared with available experimental data along isoelectronic sequences to identify irregularities in the data and to predict transition energies of ions whose values are unknown or uncertain.

Following Jones and Dahler [Phys. Rev. A 37, 2916 (1988)] we study the theory of the process of ionization within the framework of the Feshbach projection-operator formalism, with the discrete fine-structure states (before ionization) and the continuum states (after ionization) as the two separate subspaces of Hilbert space. For the Ne*(3s)-Ar and Ne**(3p)-Ar systems we have calculated ab initio autoionization widths. In the approximation in which only two electrons play an active role, the coupling matrix element between the two subspaces is a linear combination of two-center two-electron integrals for the exchange and the radiative mechanisms. In general, our calculations support the semiempirical results of Morgner [J. Phys. B 18, 251 (1985)] for the coupling matrix elements as derived from experimental data. The autoionization widths ΓJ′,JΩ are presented for initial states |J,Ω〉 of the Ne*(*) atom and final states |J′〉 of the Ar+ ion. They show a pronounced Ω dependence and a strong correlation of initial and final states, e.g., |0,0〉→|3/2〉 and |2,2〉→|3/2〉. For the Ne*(3s) states the two-center two-electron calculation is in good agreement with the two-state basis of Driessen et al. [Phys. Rev. A 42, 4058 (1990)], based on a one-electron overlap approximation. In a semiclassical model the polarized-atom ionization cross sections are calculated. For the Ne**(3p)-Ar system the energy dependence of both the polarization effect and the average cross-section value is reproduced very well, in contrast to the one-electron approximation. For the Ne*(3s)-Ar system we have to conclude that the ab initio results cannot explain all experimental observed features, such as the large cross-section ratio Q(P30)/Q(P32).

An alternative method is described for the measurement of absolute optical oscillator strengths (cross sections) for electronic excitation of free atoms and molecules throughout the discrete region of the valence-shell spectrum at high energy resolution (full width at half maximum of 0.048 eV). The technique, utilizing the virtual-photon field of a fast electron inelastically scattered at negligible momentum transfer, avoids many of the difficulties associated with the various direct optical techniques that have traditionally been used for absolute optical oscillator strength measurements. The method is also free of the bandwidth (line saturation) effects that can seriously limit the accuracy of photoabsorption cross-section measurements for discrete transitions of narrow linewidth obtained using the Beer-Lambert law [${\mathit{I}}_0$/I=exp(nl${\mathrm{\sigma }}_{\mathit{p}}$)]. Since the line-saturation effects are not widely appreciated and are only usually considered in the context of peak heights, a detailed analysis of this problem is presented, with consideration of the integrated cross section (oscillator strength) over the profile of each discrete peak.

The suitability of the high-resolution dipole (e,e) method for general application to atomic and molecular electronic spectra is evaluated by test measurements of the absolute dipole (optical) oscillator strengths for the photoexcitation and photoionization of helium, since for this atom detailed quantum-mechanical calculations using highly correlated wave functions have been reported. The absolute scale is obtained from the Thomas-Reiche-Kuhn sum-rule normalization of the Bethe-Born transformed electron-energy-loss spectrum and does not involve the difficult determinations of photon flux or target density. The measured dipole oscillator strengths for helium excitation (1 ${}_{}{}^1{}_{}{}^{}$S→n ${}_{}{}^1{}_{}{}^{}$P, n=2–7) are in excellent quantitative agreement with the calculations reported by Schiff and Pekeris [Phys. Rev. 134, A368 (1964)] and by Fernley, Taylor, and Seaton [J. Phys. B 20, 6457 (1987)]. The absolute measurements are also compared with other experimental and theoretical oscillator strength determinations for photoexcitation and photoionization processes in helium up to 180 eV, including the 2snp and 3snp autoionizing resonances in the 59–72-eV energy region.

The double core vacancies in silane and tetrafluorosilane are theoretically investigated. The corresponding wave functions and energies are computed using propagator methods, and the results are analyzed in some detail. The analysis is performed by breaking up their binding energies into the most relevant components, such as the hole-hole interaction terms and many-body contributions. An unexpectedly large number of satellite states are predicted, which we take as a possible indication that a breakdown of the molecular-orbital picture of double ionization could also occur in core-vacancy situations. By comparing with self-consistent-field (SCF) results, we encounter an interesting singlet-triplet separation problem that should be typical for multiple vacancies and is shown to be attributed to a deficiency inherent to the SCF procedure itself. The results on the double core holes in Si${\mathit{X}}_4$ (X=H,F) are compared and related to single core vacancies and to experimental data on corresponding double-core-excited states.

The natural radiative lifetime of the 2s2${\mathit{p}}^3$ ${(}^5$${\mathit{S}}_2$) metastable state of ${\mathrm{N}}^{+}$ has been measured by counting for equal time intervals the 214-nm photons emitted when the metastable ions decay to the 2${\mathit{s}}^2$2${\mathit{p}}^2$ ${(}^3$${\mathit{P}}_{2,1}$) levels of ${\mathrm{N}}^{+}$. Although forbidden to decay by the LS selection rule ΔS=0, the ${}_{}{}^5{}_{}{}^{}$${\mathit{S}}_2$ state decays primarily as a consequence of spin-orbit mixing with other levels of the 2s2${\mathit{p}}^3$ configuration. The metastable ${\mathrm{N}}^{+}$ ions are produced inside a cylindrical electrostatic ion trap by electron bombardment of a parent ${\mathrm{N}}_2$ vapor maintained at pressures ranging from 5 to 25×${10}^{\mathrm{-}8}$ Torr. The ion trap consists of a 5.0-cm-diam, 7.5-cm-long outer cylinder with end caps and a concentric 0.003-cm-diam central wire maintained at a negative potential of about 140 V. Some of the photons emitted by the decaying ${}_{}{}^5{}_{}{}^{}$${\mathit{S}}_2$ ions are focused onto a 12-nm-bandwidth interference filter in front of a photomultiplier tube and counted. The mean lifetime is obtained from the slope of a straight-line least-squares fit to the appropriate region of a logarithmic plot of the decay counts. Our result, extrapolated to zero ${\mathrm{N}}_2$ pressure, for the natural radiative lifetime of the ${\mathrm{N}}^{+}$ ${(}^5$${\mathit{S}}_2$) metastable state is 5.4±0.3 msec.

We have measured cross sections for Δn=1 dielectronic recombination (DR) on He-like argon and found good agreement with theoretical calculations based on the Hartree-Fock atomic model. Experimental absolute cross sections were obtained by using the electron-energy dependence of yields of He-like and Li-like argon ions from the Kansas State University electron-beam ion source to measure the ratio of the DR cross section on He-like argon to the electron-impact-ionization cross section of Li-like argon and normalizing to the latter. The K x-ray emission spectra due to Δn=1,2 DR and n=1→2 electron-impact excitation of He-like argon were also observed with a Si(Li) detector placed at 0° relative to the electron-beam direction. By normalizing to the theoretical KLL integrated DR differential cross section, we obtained differential and partial differential DR cross sections and differential electron-impact excitation cross sections. We found good agreement with Hartree-Fock calculations for DR and with distorted-wave calculations for electron-impact excitation.

We present an extension of a simple configuration-interaction procedure to the photoionization of two-electron atoms. By using a finite basis set constructed from B splines, this nonvariational approach does not rely on any optimum procedure, which is often required in other more elaborate configuration-interaction calculations. The quantitative accuracy of this procedure is tested by examining the photoionization cross sections at photon energies immediately above the first ionization threshold, as well as near the doubly excited 2s2p ${}_{}{}^1{}_{}{}^{}$P resonance structure. The S- and P-wave phase shifts for the electron-hydrogen scattering calculated with this procedure are also presented. The excellent agreement between the present calculation and other existing theoretical and experimental results, in addition to the extensive recent applications of this procedure to the bound excited states of divalent atoms, has further demonstrated the effectiveness of this simple configuration-interaction procedure.