Two exactly solvable second-quantized models, namely, a one-fermion-one-boson model and the four-point Hubbard model, are presented. The connection with quantum chaotic behavior is discussed.

Using a screening function based upon the Onsager model for a dielectric fluid, the scattering length for an excess electron in liquid argon is calculated. The screening function vanishes near the atomic number density 0.012 atoms/${\mathrm{\AA }}^3$. This in turn causes the scattering cross section to be a minimum at this density, which is in qualitative agreement with experiment.

A network representation is used to derive nonlinear evolution equations for Brownian motion.

The confusion over the nature of the useful restriction on the allowable forms of constitutive relations (‘‘material frame-indifference’’, or ‘‘objectivity’’) is due to the vague language of its formulation. In the final analysis, the confusion arises because the concept of general covariance of physical laws is applied in the inappropriate setting of the three-dimensional space instead of the four-dimensional space-time.

In a recent article [Phys. Rev. A 30, 1277 (1984)] it is stated that the equation for the $S$ matrix which we published in J. Comput. Phys. 13, 445 (1973) is incorrect when some channels are closed. We disagree, and in this Comment prove that the published equation is correct.

The ground and the excited states of both the $s$ and $p$ states of the ${\left(dt\mu \right)}^{+}$ molecule are calculated using the variational method of moments. Our best energy values are -319.117 and -34.776 eV for the $s$ states, and -232.436 and -0.628 eV for the $p$ states.

We treat the positronium negative ion adiabatically in hyperspherical coordinates. The potential curves of the ground state and of the first ${}_{}{}^1{}_{}{}^{}S$ doubly excited state are calculated variationally. The corresponding energy levels are in good agreement with previous calculations, showing that the approximate separation of the wave function in hyperspherical coordinates has roughly the same validity as in ${\mathrm{H}}^{-}$.

The spin-polarization parameters for photoelectrons from xenon atoms have been measured in the wavelength range between 96 and 100 nm in an angle-resolving experiment using circularly polarized synchrotron radiation. Theoretical calculations (relativistic random-phase approximation and multichannel quantum defect theory) generally reproduce the wavelength dependence of the parameters, but there are some systematic deviations from the experimental data.

Relative intensities and polarization rates of $n{}_{}{}^1{}_{}{}^{}P\to 1{}_{}{}^1{}_{}{}^{}S$ heliumlike Lyman x rays emitted in collisions of 4-keV/amu ${\mathrm{Ne}}^{9+}$ ions with ${\mathrm{H}}_2$ have been measured. Our experimental results are discussed in connection with molecular calculations for the near-system ${\mathrm{F}}^{9+}$+H. High polarization rates (∼60%) are measured for direct x rays, indicating a strong predominance of $m=0\mathrm{}$ substates in final $n{}_{}{}^1{}_{}{}^{}P$ states, in agreement with the theory. This shows the existence of a strong rotational coupling in the molecular frame. The difference of polarization observed for the $2P\to 1S$ and $3P\to 1S$ x rays may originate from a higher anisotropy of the low-angular-momentum states with respect to the high ones, as predicted by the theory.

Swift Rydberg projectiles produced by ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ impacts on a carbon foil are field ionized by the electric field in the electron analyzer placed at 0°. Between the target foil and the electron analyzer is set a "deflector" which is used to deflect free secondary electrons emitted from the foil and to preionize the Rydberg projectiles. Even after deflecting free secondary electrons, the electron spectra observed with the analyzer show two distinct peaks on which a weak oscillatory structure is superimposed. The oscillatory structure is interpreted as a "quantum beat" between the Stark substates of the Rydberg projectiles.

Measurements of the cross section for photoionization of the excited $3p$ state of sodium have been made over a significant energy range. Calculations at the central-field and Hartree-Fock levels have also been carried out. Agreement between theory and experiment is excellent.

The rotational branching ratios resulting from (1+1) resonant-enhanced multiphoton ionization of NO via the $A{}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ Rydberg state are analyzed. Theoretical results using ab initio molecular parameters agree reasonably well with recent experimental data. More importantly, the analysis underscores the importance of the molecular nature of the problem and its resulting complexities. It is shown that, for photoionization of a $\Sigma$ state that leaves the ion in a $\Sigma$ state, the allowed rotational states of the ion satisfy the selection rule $\Delta N+l=\mathrm{odd}$, where $\Delta N$ is the difference in (electronic + rotational) quantum numbers for the neutral and for the ion, and $l$ is the partial wave of the electron. Based on this selection rule, it follows that the predominantly gerade $3s\sigma$ Rydberg orbital of the $A{}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ state couples only to the ungerade channel in the continuum ($l$ odd), thereby suppressing the $\Delta N=\pm 1$ peaks, in agreement with experiment. The molecular nature of the ionic potential leads to strong $l$ mixing in electronic continuum orbitals. In fact, the influence of a nearby shape resonance causes the $f$ wave to be dominant in the $\sigma$ channel.

The effect of external noise on the dynamic behavior of an intrinsic optical-bistable system is studied experimentally. Under conditions of critical slowing down we observe a transient bimodality in the intensity distribution as well as a reduction of the switching delay due to fluctuations. Our experimental results are in good qualitative agreement with theoretical predictions.

Two problems in the analysis of diffusion-limited aggregation are studied here: the isotropy of the growing aggregate and the meaning of the large-$N$ limit as a practical matter. The isotropy of the aggregate is quantified by the ratio of the radii of gyration of the aggregate about its principal axes. The ratio varies from ∼0.70 for $N=200\mathrm{} \mathrm{to} \sim 0.90$ for $N=50\mathrm{}000$. The next particle capture radius is directionally dependent with respect to the principal axes and scales with the respective radii of gyration. A lower bound is obtained for the size $N$ necessary for the emergence of a single dominant length scale by taking this as the size for which the radii of gyration are equal. In $d=2\mathrm{}$ the lower bound is $N\simeq 1.5\times {10}^6$; in $d=3\mathrm{}$ it is $N\simeq 8\times {10}^5$.

The phase-separation process in a micellar solution has been examined in an unstable region above its lower critical mixing point. We find that phase separation for a critical mixture pentaethylene glycol mono-$n$-dodecyl ether and water is quite analogous to spinodal decomposition observed in critical binary systems near their critical mixing points. A comparison is made of the time dependence of the scattered light intensity between recent theoretical predictions of spinodal decomposition and the experimental results.

We have applied the freeze-fracture technique to polar liquid-crystalline systems in which there exists a fluid antiphase $S_{\tilde{A}}$ and a bilayered smectic $S_{A_2}$. In the case of the $S_{\tilde{A}}$ phase the electron microscope gives (i) a definite evidence of the two-dimensional array of this mesophase and (ii) the first proof that the antiphase domains are separated by real walls. In the case of $S_{A_2}$ the smectic layered structure is seen for the first time in a thermotropic mesogen and in a fluid mesophase.

A high-resolution light-scattering study of the divergence of the mode-two nematic director viscosity in a geometry selecting nearly pure twist fluctuations shows that the exponent for this viscosity is close to the mean-field value for the three materials studied.

In a previous paper [Phys. Rev. A 30, 1229 (1984)] we applied the scaling variational method formulated in terms of the SO(2,1) dynamical group to screened Coulomb potentials. Here we generalize that method by scaling a linear combination of SO(2,1) basis states, solving for the eigenvalues by determinant, and minimizing through a search algorithm. The method is applied with high accuracy to the simple Yukawa potential.