Two groups of ions are observed in an aluminum plasma produced by focusing a Raman-compressed KrF-laser beam (268 nm) on thick planar targets in the intensity range 5×${10}^{11}$–${10}^{13}$ W/${\mathrm{cm}}^2$. The angular distribution, velocity distribution, energy partition between the two groups, and scaling of the ion velocities with laser intensity are presented. The role of lateral energy transport in generating the two groups of ions is discussed.

The Feynman-Hellmann theorem shows that the exact ground-state energy of a quantum system may be obtained by integrating the potential energy with respect to a coupling constant. For approximation schemes in which the energy is actually calculated from an energy functional, we show that direct and coupling-constant integration evaluations of the energy functional are identical, provided that the energy functional is optimized.

The electron plasma wave excited at the beat frequency of two laser radiation in a hot plasma is unstable and suffers strong parametric decay instability into an ion acoustic wave and another electron plasma wave. It is noticed that the threshold of the instability is quite low and the growth rate is very large at moderate beat-wave amplitude.

Static and dynamic light scattering and small-angle x-ray scattering measurements are reported for vapor-phase aggregates of silica. From the static scattering data the fractal dimension is found to be ∼1.84±0.08, in agreement with the prediction of the cluster-cluster aggregation model. The Rayleigh linewidth is found to vary as the 2.7 power of the momuntum transfer for large momentum transfer.

Using the inverse-curve method for graphical iterations of one-dimensional maps, we propose a geometric proof of a recent conjecture by Yorke et al. [Phys. Rev. Lett. 54, 1095 (1985)] which scales the parameters for onset, period-doubling bifurcation, and crisis of period windows. The universal ratio $m_c$={z[1+(2z${)}^{1/\left(z\mathrm{-}1\right)}$] -1}/(2z) for maps with the extremum (at x=c) of the symmetric form f(μ,x)∼‖x-c${\Vert }^z$, with z>1, should be discernible in experiments.

A new method is introduced which allows a direct measurement of the largest positive or negative Liapunov exponent ${\lambda }_m$ of simple dynamical systems. It is shown that ${\lambda }_m$ can be determined experimentally by varying the coupling between two equal systems and observing the mutual correlation of their motions. An electronically simulated driven pendulum is studied as an example. The measured values of ${\lambda }_m$ agree well with results obtained by other methods. The method can only be applied to systems for which one knows the variables in phase span, and for which the coupling can be realized experimentally.

It is shown that the purely static (magnetic or electric) field-induced Fréedericksz transition in a planar parallel oriented nematic-liquid-crystal cell is always second order. But with an additional optical field, the magnetic-field-induced Fréedericksz transition can become first order and bistable. For the electric field, if 9ν/4>w>0, the electric-field-induced first-order transition can be enhanced by the optical field, where ν=($n_c$/$n_o$${)}^2$-1, w=${\epsilon }_{?}$/${\epsilon }_{\perp }$-1, $n_o$ and $n_c$ are the ordinary and extraordinary indices of refraction, ${\epsilon }_{\perp }$ and ${\epsilon }_{?}$ are the dielectric constants perpendicular and parallel to the local nematic director. The exact and small-angle approximate solutions describing the nematic’s orientation are obtained. The first-order transition enhancement tricritical optical field intensity and criterion are also given.

The influence of an external electric field on thermal collisions between a sodium atom excited in a ‘‘circular’’ Rydberg state (n=l+1=m+1=20) and a ground-state helium atom is studied numerically within the framework of the impulse approximation. The effect of the field is determined by using parabolic wave functions for the initial and final hydrogenic atomic states. The removal of degeneracy induced by the field appears to have no significant effect for fields in the range of 0–400 V/cm. However, the state-to-state transition cross sections are strongly dependent on the initial orientation as found in previous calculations without electric field.

The laser photoelectron spectra of ${\mathrm{Ge}}^{\mathrm{-}}$ and ${\mathrm{Sn}}^{\mathrm{-}}$ are reported. Transitions in the electron detachment from the ${}_{}{}^4{}_{}{}^{}\mathrm{S}_{3/2}^{}{}_{}{}^{}$ ground state of the ions to the ${}_{}{}^3{}_{}{}^{}\mathrm{P}_0^{}{}_{}{}^{}$,1,2 states of the neutral atom are used to determine the electron affinities, 1.233±0.003 eV for Ge and 1.112±0.004 eV for Sn. The relative transition strengths to the fine-structure sublevels of the neutral do not follow the 1:3:5 statistical ratio, indicating the systematic breakdown of L-S coupling for these species.

The complex-coordinate method is applied to the resonance states of a potential introduced by Ginnochio and studied by Alhassid, Iachello, and Levine. It is shown that the potential is not dilatation analytic, and so the complex-coordinate method fails for this potential. Resonance energies and lifetimes can be obtained by applying the Siegert criterion, however.

We complete the study of the Painlevé (P) analysis and integrability of the N coupled quartic anharmonic oscillators defined by $H_N$=1/2 ${\mathcal{J}}_{\mathrm{i}=1\mathrm{}}^{\mathrm{N}}$ ${\mathrm{p}}_{{\mathrm{x}}_{\mathrm{i}}}^2$+ ${\mathcal{J}}_{\mathrm{i}=1\mathrm{}}^{\mathrm{N}}$ ${\mathrm{A}}_{\mathrm{i}}$${\mathrm{x}}_{\mathrm{i}}^2$+ ${\mathcal{J}}_{\mathrm{i}=1\mathrm{}}^{\mathrm{N}}$ ${\mathrm{\alpha }}_{\mathrm{i}}$${\mathrm{x}}_{\mathrm{i}}^4$ +1/2 ${\mathcal{J}}_i$,${\mathit{j}=1\mathrm{}}^{\mathrm{N}}$ ${\mathrm{\beta }}_{\mathrm{ij}}$${\mathrm{x}}_{\mathrm{i}}^2$${\mathrm{x}}_{\mathrm{j}}^2$, i≠j, by listing all the P cases [including those cases which we did not present in Lakshmanan and Sahadevan, Phys. Rev. A 31, 861 (1985)] and deriving the appropriate N involutive integrals for each one of them.

McGuire [Phys. Rev. A 28, 53 (1983)] has suggested that the mean excitation energy I for the stopping power of metallic aluminum should be ‘‘in the range of 145–150 eV,’’ as opposed to the currently recommended value of ∼166 eV. We have reexamined all pertinent information from two independent sources, i.e., measurements of proton stopping power and the semiempirical determination of the dielectric-response function over the entire spectral range. Our conclusion is that the value of 166 eV is essentially correct. Moreover, we point out a number of deficiencies in McGuire’s arguments; some of our remarks concern the values of inner-shell corrections to the Bethe stopping-power formula as evaluated by McGuire [Phys. Rev. A 28, 49 (1983)].

Replies are made to comments made by Bichsel et al. on the choice of inner-shell correction, experimental energy-loss-data set used, neglect of range data, and the relevance of current optical oscillator-strength data to the metallic Al I value.

A new formulation of ‘‘the most-stable-inference approach’’ is suggested. The present version, unlike the original one [as presented by Tikochinsky, Tishby, and Levine, Phys. Rev. A 30, 2638 (1984)], is invariant under orthogonal transformation of the relevant variables. The criterion for a stable distribution consists now of a single test and does not involve any diagonalization.

Spectral profiles of gain coefficients at soft-x-ray wavelengths near 200 Å in laser-driven exploding foils and laser-produced magnetically confined plasma columns are shown not only to be influenced by thermal Doppler broadening, but very likely also by collisional narrowing of some lines and by Doppler effects from hydrodynamic turbulence. The multiply charged ions, z=24 and 5, in these dense and relatively low-temperature plasmas are highly collisional, with ion-ion mean free paths of about 20 and 200 Å, respectively. They involve plasma flows with Reynolds numbers ≳${10}^5$. Collisional narrowing and turbulent broadening may have combined to spoil the predicted gain of the λ=183 Å selenium line in the foil experiment. Any turbulent flow must have a fundamental wavelength exceeding a critical size ranging from ∼40 μM for the 206- and 209-Å selenium lines to ∼90 μm for the 183-Å selenium line for observable gain to occur in the single-pass oscillator experiments.

The binding energy of positronium molecules is calculated variationally by using extensive Hylleraas-type wave functions in which all six interparticle coordinates are used. The binding energy against dissociation into two positronium atoms is determined as 0.0302 Ry. The present result is consistent with the value of 0.0303±0.0005 Ry, obtained by Lee using the Green’s-function Monte Carlo method.