An analysis of the types of correlation found in a nearly exact $X\alpha$ treatment of ${\mathrm{C}}_2$ and ${\mathrm{Si}}_2$ suggests new self-consistent procedures that tend to reconcile the fractional-occupation-number and broken-symmetry approaches.

An investigation is presented of how each angular momentum transfer during reaction contributes to a given state-to-state reactive transition. The new finding from this study is that some direct state-to-state reactive scattering systems which favor collinear configuration prefer the largest angular momentum transfer as a result of reactive collision and that such preference of the largest angular momentum transfer is shown to occur in both forward- and backward-peaked reactive scattering.

We report the first calculations on a molecular collision system using a fully self-consistent time-dependent Hartree-Fock (TDHF) method. The nuclear motion is treated classically with the forces determined by the time propagating electronic charge density. The electronic state is generated using a finite-difference TDHF calculation. We present results including a typical reactive trajectory, a corresponding time evolution of the electronic energy, and density plots of the molecular wave function evolving through the collision.

Critical points, which represent minima in differential scattering cross sections as a function of scattering angle and incident projectile energy, are theoretically predicted for elastic scattering of low-energy positrons by Ar, Kr, and Xe. It is demonstrated that these points arise due to low-energy positron diffraction effects.

The $M_{4,5}{N}_{4,5}{N}_{4,5}$ Auger-electron spectrum of free palladium atoms has been measured by means of a new high-temperature spectrometer using electron-beam excitation. The experimental spectrum has been compared with the theoretical profile calculated in a nonrelativistic mixed-coupling scheme applying $\mathrm{jj}$ coupling to the initial state and intermediate coupling to the final one. The energies have also been compared with the theoretical results obtained from relativistic intermediate-coupling calculations. Apart from the Auger energies, the free-atom $3d$ binding energies $E_B\left({3d}_{\frac{5}{2}}\right)=341.13\mathrm{}\left(15\right)\mathrm{}$ eV and $E_B\left({3d}_{\frac{3}{2}}\right)=346.45\mathrm{}\left(15\right)\mathrm{}$ eV have also been determined with the aid of optically known two-hole final-state energies. Comparisons with the solid-state photoelectron and Auger-electron measurements give free-atom-metal shifts of 1.3 eV for the 3d binding energies and 11.3 eV for the $M_{4,5}{N}_{4,5}{N}_{4,5}\left({}_{}{}^1{}_{}{}^{}G_4^{}{}_{}{}^{}\right)$ Auger energies, also referring the solid-state energies to the vacuum level.

New measurements of time-integrated and time-resolved spectra of the 535-nm laser emission in photo-dissociated thallium iodide are presented. The initial frequency differences in the emission spectra of the two natural thallium isotopes produce a self-induced dynamic Stark splitting of the resonance lines. It is shown that at high intensities the Stark splitting saturates. This saturation is explained by the reduction of the lifetime of the excited thallium atoms by stimulated emission.

We consider the centrifugal instability of the viscous fluid flow between concentric circular cylinders in the small-gap limit. The amplitude of the Taylor vortex is allowed to depend on a slow time variable, a slow axial variable, and the polar angle $\theta$. It is shown that the amplitude of the vortex cannot, in general, be described by a single amplitude equation. In the absence of any slow axial variations it is shown that a Taylor vortex remains stable to wavy vortex perturbations.

A new method is presented for calculating the leading Lyapunov exponent directly from experimental data for systems having a strange attractor with dimensionality near 2. The method is exact for one-dimensional maps and gives good results for systems that have approximate one-dimensional maps associated with them even in the presence of some noise. Numerical examples are given.

Using a fast algorithm we have calculated the Lyapunov exponents at about 6000 parameter points in the range $0.1<r<\mathrm{}520\mathrm{}$, $\sigma =10\mathrm{}$, and $b=\frac{8}{3}$ of the Lorenz model. In the chaotic region we find a large number of narrow windows containing periodic orbits—somewhat similar to what is the case in the one-dimensional logistic map.

The method of complex coordinates has long been known to allow $L^2$ calculations of $t$-matrix amplitudes for short-range potentials, but to yield divergent results for long-range forces. Using a spherical long-range potential as an example, it is shown here that the Padé method of summation can be used in conjunction with the diverging complex-coordinate calculations to obtain accurate values of the scattering amplitude.

Dielectronic recombination has been directly observed with a crossed, modulated electron and calciumion beams technique. The stabilizing photons (about 397 nm) and the 500-eV Rydberg-state neutral atoms were detected in coincidence following electron-impact excitation in the vicinity of doubly excited ${\mathrm{Ca}}^{**}$ resonant states below the ${\mathrm{Ca}}^{+}\left(4p{}_{}{}^2{}_{}{}^{}P\right)$ excited ionic state. A peak ${\mathrm{Ca}}^{+}\left(4P{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)$ excitation cross section of 1.7 × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ was measured simultaneously with the peak dielectronic recombination cross section of 1.8 × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ which is about double the Burgess-Mertz theoretical value.

The $1s$ Lamb shift in hydrogenlike chlorine has been determined from a precision measurement of the ${2p}_{\frac{3}{2}}-{1s}_{\frac{1}{2}}\left(\mathrm{Ly}{\alpha }_1\right)$ and ${2p}_{\frac{1}{2}}-{1s}_{\frac{1}{2}}\left(\mathrm{Ly}{\alpha }_2\right)$ x-ray transitions using beam-foil excitation. The x rays are emitted from high-velocity chlorine-ion beams at several ion velocities produced by a Van de Graaf accelerator. The $1s$ Lamb shifts obtained from the $\mathrm{Ly}{\alpha }_1$ and $\mathrm{Ly}{\alpha }_2$ measurements are 0.84(12) and 0.90(10) eV, respectively, compared with a calculated value of 0.9384(6) eV. The fine-structure splitting of the $2p$ level was also determined in this experiment and found to be 3.889(30) eV compared with a theoretical value of 3.827 18(2) eV. A precision measurement of the $\mathrm{Ar} K\alpha$ x rays was made in order to establish the energy scale for $\mathrm{Cl} \mathrm{Ly}\alpha$ x rays. The newly determined energies are 2957.813(8), 2955.684(13), and 2977.51(6) eV for the $K{\alpha }_1$, $K{\alpha }_2$, and $K{\alpha }_4$ energies, respectively.

We report a direct measurement of the barrier height of the ${\mathrm{Na}}_2$ $B$-state potential curve. The technique is a two-step spectroscopy—optical pumping followed by photodissociation—on a beam of rotationally cold ${\mathrm{Na}}_2$. Our measured value is 366 ± 8 ${\mathrm{cm}}^{-1\mathrm{}}$ above the energy of the separated atoms ($\mathrm{Na} 3s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}+\mathrm{Na}+3p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$). Based on observed structure due to tunneling, we propose a form of the potential valid near the top of the barrier.

Cooperative single-photon excitations of two ($K+L$) and three ($K+L+M$) electrons in nickel were studied using x-ray absorption spectroscopy. Each of the edges detected has an energy higher by about 164 ± 3 eV than the sum of those required for exciting the electrons involved independently. The probabilities for the two- and three-electron excitation are found to be 0.25% and 0.08%, respectively, of that for a single $K$-electron excitation.

We solve numerically the simplest Fokker-Planck equation which describes the effects of amplitude noise in absorbitive optical bistability. When the semiclassical solution exhibits critical slowing down, the probability distribution becomes two-peaked in a sizable time interval during the approach to the one-peaked steady-state distribution. The switching time undergoes considerable fluctuations, and on the average it is shorter than predicted by semiclassical theory. These noise effects seem accessible to experimental observation.

Detuned-lasers systems which have anomalous dispersion effects at the lasing wavelength are predicted to have period-doubling bifurcations for injected light signals. The basic idea is derived from the dependence of the active-region refractive index on population inversion density. The response of detuned lasers with injected light signals is shown to be governed by the generalized Van der Pol equations with external driving forces that are nonlinear in nature. Experimental results with a LiNd${\mathrm{P}}_4$${\mathrm{O}}_{12}$ miniature solid-state laser are shown, demonstrating period-doubling bifurcations.

We report the successful application of the freeze fracture technique for obtaining transmission-electron-microscope pictures of a thermotropic cholesteric material and its blue phase. It is shown that under rapid quenching these phases supercool and conserve their structure at liquid-${\mathrm{N}}_2$ temperature. The micrographs obtained confirm the body-centered-cubic symmetry of the blue phase I.