In a recent comment [J. A. Leegwater and G. Szamel, Phys. Rev. Lett. 67, 408 (1991)] we showed that the (t √ln ${)}^{\mathrm{-}1}$ decay of the velocity-autocorrelation function in a two-dimensional lattice gas should be attained in times accessible in simulations. Here we study in greater detail the properties of solutions to the self-consistent mode-coupling equations on which this result was based. We propose a scenario for the decay of the velocity autocorrelation function of a two-dimensional lattice-gas cellular automaton.

The shortest-path aggregation in a two-dimensional square lattice is studied numerically. We find universal behavior of the cluster formation when the released particles are weakly correlated, and a distinct universal behavior for clusters generated by a strongly correlated release. In particular, we find the fractal dimension D=1.20±0.01 when the released particles are weakly correlated, while a one-dimensional object is obtained when the correlation is strong. We also find the anisotropic exponent δ=1.0 in the weak-correlation region.

Fast ions are emitted from the focus of a high-intensity laser beam irradiating a plasma. The self-focusing of the laser beam is caused by the dependence of the index of refraction on the relativistic mass of the electrons, which again depends on the electric-field strength. The ions are accelerated out of the laser focus due to the combined action of nonlinear forces and double layers. Results for the maximal energy and angular distribution of the ions are presented and compared with experimental data.

In a recent paper, S. V. G. Menon, V. K. Kelkar, and C. Manohar [Phys. Rev. A 43, 1130 (1991)] apply Baxter’s model for hard spheres with surface adhesion to the theory of cloud points of nonionic surfactant solutions. Their statement, ‘‘Despite its ability to quantitatively account for a number of experimental properties, this insightful work has not attracted much attention,’’ is testimony to the fact that they must be unaware of a large number of papers, from which it follows that Baxter’s model has proven to be very useful for describing the attractions in microemulsions and sterically stabilized colloidal dispersions. In this Comment, we would like to draw the attention of the readers to these papers.

We incorporate the Scott correction into the momentum-space energy functional of the Thomas-Fermi model and so improve the description of the strongly bound electrons. The resulting differential equation is then discussed, and we report numerical results for neutral mercury.

We extend previous calculations on ${\mathrm{H}}_2^{\mathrm{-}}$ to the lowest ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ states of ${\mathrm{HF}}^{\mathrm{-}}$ and ${\mathrm{HCl}}^{\mathrm{-}}$. Anion potential-energy curves are computed in the single-configuration close-coupling aproximation. Fixed-nuclei electron-molecule eigenphase sums are also computed. Static-exchange results are improved by including a correlation-polarization potential. The avoided crossing between the lowest anion state and the infinite series of dipole-bound states for ${\mathrm{HF}}^{\mathrm{-}}$ is tracked as the neutral and anion curves approach each other at smaller internuclear separations. The present method goes beyond previous calculations of this nature by retaining all long-range multipole moments in the asymptotic potential.

We report a calculation for ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ resonance parameters in electron-hydrogen scattering converging on the N=3 to 9 hydrogen thresholds. Resonance energy positions and widths are calculated by using a method of complex-coordinate rotation, with quantum numbers K, T, N, and n given to each resonant state. Results are compared with the recent experimental measurements and other theoretical values.

A Coulomb-Born approximation is used to compute the triple-differential cross section for electron-impact inner-shell (1s) ionization of carbon. We employ a perturbation series that allows the use of Coulomb waves with arbitrary ${\mathit{Z}}_{\mathrm{eff}}$ for the incoming, scattered, and ejected electrons. Most of the features of the triple-differential cross section observed experimentally are reproduced, even though these wave functions are distorted by an effective Coulomb potential and therefore do not satisfy the plane-wave boundary conditions at infinity. In order to explain some features that appear in the cross section, and in order to probe the validity of a dipole approximation, we make a multipole expansion of the transition matrix and show that the amplitudes of the multipole components are similar to those obtained in the Born approximation, while the relative phases of the multipoles differ greatly.

In a two-step pulsed-laser atomic-beam experiment we have studied doubly exicted 4fnf series of barium with energy of ∼11 eV above the atomic ground state (6${\mathit{s}}^2$) and 6 eV above the first ionization limit (6s). Starting from 5${\mathit{d}}^2$ ${}_{}{}^3{}_{}{}^{}$${\mathit{F}}_3$,${\mathrm{}}^1$${\mathit{G}}_4$ metastable states, 4${\mathit{f}}_{5/2}$n’f J=2–6 (9≤n’≤46) states and 4${\mathit{f}}_{7/2}$n’’f J=3–6 (n’’=19, 20, 21, 25, and 40) states were excited using intermediate 5dnf autoionizing Rydberg states. The 4${\mathit{f}}_{5/2}$n’f J=2–6 states strongly interact with 4${\mathit{f}}_{7/2}$n’’f J=2–6 (8≤n’’≤20) and 7pn’’’f J=2–5 (6≤n’’’≤10) states. The excitation spectra were analyzed and interpreted using multichannel quantum-defect theory as well as a limited Slater-Condon analysis. The quantum defects of the 4fnf series are large (0.5–1.4), which is an indication for considerable two-electron correlation effects.

A Monte Carlo computer program was developed to calculate the angular distribution of fragments resulting from the breakup of fast hydrogen clusters ${\mathrm{H}}_{\mathit{n}}^{+}$ when traversing thin amorphous carbon foils. The three-dimensional relative coordinates of each proton in the cluster are given as input. The code begins with a generation of a random orientation of clusters. Next, the foil is divided into slabs and the effects of Coulomb explosion, multiple scattering, and energy loss on each fragment are calculated for successive slabs. The distributions of separations and relative velocities at the exit surface as well as the angular distributions of fragments are then obtained. Therefore, the cluster-stopping-power ratio is given. The use of the code is illustrated in the case of 30-, 40-, 60-, and 80-keV/p clusters, with n=2,3 to 21 odd, impinging on a 2-μg/${\mathrm{cm}}^2$ carbon foil, where experimental results are available.

Total and partial cross sections are calculated for single-electron capture in ${\mathrm{B}}^{3+\mathrm{-}}$He collisions for projectile energies from 1.0 to 500 keV. Results for a one-electron model and a full two-electron treatment of the electronic wave function are compared. Both procedures compare well with experimental data for total cross sections. However, the two-electron model, which incorporates correlation and relaxation effects, compares most favorably, particularly when partial cross sections are considered. The total single-capture cross sections for higher velocities (v≊2–8 a.u.) decay in average according to a ${\mathit{v}}^{\mathrm{-}7.2}$ behavior, close to the ${\mathit{v}}^{\mathrm{-}7}$ behavior expected from the Bohr-Lindhard model. The discussion focuses on the role of correlation effects during the collision.

The behavior of subexcitation electrons in gaseous mixtures of ${\mathrm{O}}_2$ and ${\mathrm{N}}_2$ is studied by using the Spencer-Fano theory and its simplified continuous-slowing-down approximation. Because of its strong resonance around 2 eV, ${\mathrm{N}}_2$ is overwhelmingly dominant over ${\mathrm{O}}_2$ in energy-loss processes. Addition of ${\mathrm{N}}_2$ to ${\mathrm{O}}_2$, even a few percent, causes significant changes in some yields of ${\mathrm{O}}_2$. In particular, yields for electron attachment and rotational excitation for ${\mathrm{O}}_2$ show a strong nonlinearity as a function of composition, while all yields of ${\mathrm{N}}_2$ depend linearly on composition.

Absolute total cross sections for the scattering of electrons by cesium atoms between 2 and 18 eV have been measured using the atomic-recoil technique in the scattering-out mode. Our results are somewhat lower than those of Visconti, Slevin, and Rubin [Phys. Rev. A 3, 1310 (1971)] above 2 eV.

By employing a previously proposed model [A. Jain, Phys. Rev. A 34, 3703 (1986); J. Phys. B 22, 905 (1988)], we report calculations on the total (elastic plus inelastic) electron-scattering cross sections in a wide energy range (10–5000 eV) from several diatomic and polyatomic molecular targets (${\mathrm{H}}_2$ ${\mathrm{Li}}_2$, HF, ${\mathrm{CH}}_4$, ${\mathrm{N}}_2$, CO, ${\mathrm{C}}_2$${\mathrm{H}}_2$, HCN, ${\mathrm{O}}_2$, HCl, ${\mathrm{H}}_2$S, ${\mathrm{PH}}_3$, ${\mathrm{SiH}}_4$, and ${\mathrm{CO}}_2$). A model complex optical potential (composed of static, exchange, polarization, and absorption terms) is calculated for each collision system from the corresponding molecular wave function at the Hartree-Fock level. The resulting complex optical potential, free from any adjustable parameter, is treated exactly in a variable-phase approach to yield scattering complex phase shifts and the total cross sections. In the intermediate- and high-energy region, the small contribution due to the nonspherical nature of the target is treated perturbatively in the first-order Born approximation. The present method is quite simple in nature and is able to reproduce fairly well the experimental total cross sections in the present energy region. Results are also given for individual elastic and absorption (accounting for all energetically possible inelastic processes in an approximate way) cross sections. In addition, we provide Born-Bethe parameters for all the above molecules including those of ${\mathrm{H}}_2$O and ${\mathrm{NH}}_3$. We have also examined the correlation between molecular properties and the total-cross-section parameter. For molecules possessing a permanent dipole or quadrupole moment, the present results are only roughly reliable above 100 eV.

Relative intensity ratios for the differential electron-impact excitation of the metastable states of the rare gases neon, argon, and xenon at the incident energy of 30 eV and scattering angles 10°–120° are presented and are compared with available theory.

Velocity-dependent total elastic-scattering cross sections are measured for metastable argon scattered from krypton in the velocity range 500 to 5000 m/sec. An interaction potential for the reaction is derived from the data by both a semiclassical analysis and a full quantum calculation. The results are compared with previous measurements.

We have measured the angular distribution of electrons ejected from doubly excited autoionizing Rydberg 3pns J=1 states of magnesium, where n=10–20. Two dye lasers cross an atomic beam and excite 3${\mathit{sns}}^1$${\mathit{S}}_0$ states of Mg. A third linearly polarized laser excites the 3pns states. The angular distribution is of the form (σ/4π)[1+β${\mathit{P}}_2$(cosθ)]. We measure β as a function of the energy of the third laser. The β parameter varies over its full range of values, -1 to 2. Our data agree quite well with the predictions of the reaction-matrix–multichannel-quantum-defect theory.

Rate constants for Rydberg-atom destruction through electron transfer in collisions between K(np) Rydberg atoms and ${\mathrm{SF}}_6$ and ${\mathrm{CCl}}_4$ have been measured for values of principal quantum number n up to n∼400 using an apparatus specifically developed for very-high-n collision studies. Analysis of the data using the free-electron model provides cross sections for electron attachment to ${\mathrm{SF}}_6$ and ${\mathrm{CCl}}_4$ at electron energies down to ∼10 μeV, which are far below those accessible using any alternate technique. The measured cross sections are inversely proportional to electron velocity and are consistent with the Wigner threshold law for s-wave attachment.

The velocity dependence of the rate constant for free-ion production via the Rydberg electron-transfer reaction K(np)+${\mathrm{SF}}_6$→${\mathrm{K}}^{+}$+${\mathrm{SF}}_6^{\mathrm{-}\mathrm{*}}$ has been investigated at intermediate n. The data provide evidence of a postattachment interaction between the product ions in which internal energy from the ${\mathrm{SF}}_6^{\mathrm{-}\mathrm{*}}$ ion is converted into translational energy. A similar conclusion is reached from measurements of the velocity and angular distributions of the product ${\mathrm{K}}^{+}$ ions.