Instabilities in nonequilibrium systems described by deterministic differential equations are investigated. Using group-theoretical arguments we find a rule similar to that valid for the equilibrium case: A spatial pattern appears necessarily through a first-order transition if a cubic invariant can be constructed from the amplitudes of the slow modes.

The simplest molecule is treated theoretically using hyperspherical coordinates. It is argued, and demonstrated semiquantitatively, that the adiabatic body-frame approximation in hyperspherical coordinates is nearly identical to the Born-Oppenheimer approximation.

A new class of coherent states is defined, having all the properties of the usual coherent states except that the uncertainty product of position and momentum need not be minimum. From the stationary-action principle, the dynamical equations of motion for the expectation values and uncertainties for position and momentum are deduced. For the time-dependent harmonic oscillator, the equation for the uncertainty in the position is found to be the well-known Lewis constraint.

The existence of the doubly charged dimer ion Ne${\mathrm{Kr}}^{2+}$ is substantiated by electron-impact ionization of the mixed van der Waals dimer NeKr. The stability of this doubly charged molecule is discussed with the use of semiquantitative potential energy curves. The electron-impact-ionization appearance potential confirms the prediction from the potential-energy curves.

In shellwise stopping-power calculations, the velocity-independent constant term distinct from the constant term contributing to the mean excitation energy is evaluated for $K$ and $L$ shells. Although the term vanishes for the H atom, a large contribution from it arises from $K$ shells for a few of the light atoms considered in this paper. Known values of the Hartree-Slater oscillator strengths are used to obtain $K$- and $L$-shell asymptotic stopping-number formulas for carbon, oxygen, and neon atoms.

Capture of $1s$ electrons into partially stripped projectile ions is treated in the eikonal approximation. A simple expression is obtained for the eikonal cross-section formula with the use of a model—a single active electron interacting with the ion through a modified Coulomb potential. Numerical calculations are performed for ${\mathrm{Li}}^{q+}$ and ${\mathrm{C}}^{q+}$ colliding with H. Comparison is made with our previous Oppenheimer-Brinkman-Kramers calculations.

Doppler-free two-photon spectroscopy was applied to excite hyperfine-induced transitions from the $5s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ ground state to the $F=I$ component of the hyperfine multiplet of the $5sns{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ Rydberg series of ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}$ ($n=50,\dots ,85\mathrm{}$). The experimental data confirm the interpretation of hyperfine-induced singlet-triplet mixing which is related to the singlet-triplet energy separation.

The behavior of the critical isotherm near the critical point has been studied starting from a numerical solution of the Percus-Yevick equation for the Lennard-Jones potential. The results show the usual asymptotic gas-liquid symmetry, i.e., a purely classical behavior. This result solves a problem brought up recently by Fishman and Fisher.

Non-Markovian thermal Brownian motion of a particle over a barrier is studied using thermal noise with a small but finite bath-memory correlation time. Starting from the corresponding non-Markovian Smoluchowski master equation, valid in the over-damped limit, the rate of escape $\lambda$ is evaluated, and it is shown that a renormalization of the bare damping occurs. The modeling of the rate $\lambda$ for a special class of bistable, driven non-Markovian nonequilibrium systems is sketched.

Excitation ($n=2\mathrm{}$ level) of the hydrogen atom by electron impact has been studied by using a Callaway-type variant of the polarized-orbital method. The incident wave contains the effect of exchange polarization. Two sets of differential cross sections at three incident energies near the threshold have been obtained. Our results of model II are in good agreement with measured values. The results of our model I are unsatisfactory at large scattering angles.

We present a sequence of variational principles for scattering problems consisting of functionals of fractional form. Schwinger's variational principle and the functional recently proposed by Takatsuka and McKoy are discussed as special cases. For high scattering energies a correspondence to the Born series is established.

It is shown that the procedure described by Olson and Salop for classical-trajectory Monte Carlo treatment of ion-atom collisions does not provide a uniform statistical distribution of all the parameters defining the initial conditions of a trajectory. Impact-ionization and charge-transfer cross sections for collisions of ${\mathrm{H}}^{+}$ with H at H energies between 25 and 600 keV are recalculated eliminating this failing and compared with those obtained using the procedure of Olson and Salop and with experimental results.

A full calculation of the probability of ionization of a $K$-shell electron during nuclear $\beta$ decay, including the effect of final-state interaction (direct-collision mechanism), has been carried out using nonrelativistic hydrogenic wave functions. Numerical results are presented for ${}_{28}{}^{63}{}_{}{}^{}\mathrm{Ni}$, ${}_{46}{}^{107}{}_{}{}^{}\mathrm{Pd}$, and ${}_{62}{}^{151}{}_{}{}^{}\mathrm{Sm}$; they are found to be larger than the predictions of shake-off theory by 12-15%. A comparison with other recent theoretical results is made; significant differences are found.

We report new, more extensive photoexcitation spectra of Ba autoionizing states which demonstrate that appearent interferences between discrete autoionizing states are in fact not interferences as previously proposed. A simple alternative interpretation of the "interference"-like line shapes as being due to variations in the spectral density of the autoionizing states and their overlap integrals with the bound initial state is presented and shown to agree with experiment. We argue that such spectra allow perhaps the most accurate determination of quantum defects, and should be a useful spectroscopic probe of autoionizing states.

We report measurements of the $K$-edge photoabsorption spectrum of the octahedral complex Mo${\mathrm{}\left(\mathrm{CO}\right)\mathrm{}}_6$ and a theoretical calculation of this spectrum using the self-consistent-field $X\alpha$ multiple-scattered-wave approach. Two strong absorption peaks near threshold are shown to lie in the continuum region of the spectrum and to be of "shape resonance" character.

A numerical analysis is presented for a hybrid acousto-optic bistable device subject to the small amount of external noise. It is shown by iterating a one-dimensional map with additive and multiplicative noise that bifurcation sequence is severely truncated.

We present the first evidence of interference between four- and six-wave mixing in multiple coherent scattering near the two-photon resonance of biexcitons in CuCl. The experimental data are quantitatively explained by taking proper account of propagation effects and by a model for ${\chi }^{\mathrm{}\left(5\right)\mathrm{}}$ involving no adjustable parameters.

Optically inverted barium ions in the $6p_{\left(\frac{1}{2}\right)}$ excited state served as the nonlinear medium for doubly resonant four-wave parametric generation of coherent radiation at 167 nm. The excited barium ions were produced via selective autoionization. Stimulated-emission photons at 650 nm corresponding to the $6p_{\left(\frac{1}{2}\right)}-5\mathrm{}{d}_{\left(\frac{3}{2}\right)}$ transition were mixed with input 451-nm laser photons turned to the $6p_{\left(\frac{1}{2}\right)}-6\mathrm{}{f}_{\left(\frac{5}{2}\right)}$ two-photon resonance to produce the 167-nm output photons.

Long-time stimulated Brillouin scattering oscillations may occur in subcritical plasmas with supersonic flow against the incident wave owing to a feedback of the scattered radiation. They are studied in the frame of both the parametric approximation and the mode-coupling theory.