The microwave ionization of the hydrogen atom involves most of the open issues concerning classical and quantum chaos. Much recent research has considered quasi-one-dimensional extended states for which ionization thresholds have been estimated using a classical picture in which ionization proceeds through the overlap of an infinity of nonlinear resonances. Using a canonical transformation to Deprit’s ‘‘Lissajous elements’’ which makes the two-dimensional nature of the problem explicit, an accurate and improved ionization threshold, compared to previous resonance overlap criteria, is obtained through the overlap of only two nonlinear resonances in the one-dimensional limit.

The path integral for the propagator is reduced to an ordinary integral in terms of the generators of a canonical transformation, and is evaluated exactly for square potential barriers in one dimension and for the radial square-well potential in two dimensions.

Symmetry transforms in $N_2$ space dimensions of $N_1$-dimensional spherically symmetric Schrödinger Hamiltonians have been treated for $N_2$≠$N_1$. Accordingly, the quantum number of the angular momentum and the number of space dimensions become subject to related mappings. One proceeds using suitable transformations of the radial coordinate and of the radial state function so as to exhibit the form invariance of the Laplace operator. The symmetries established in this way concern potentials which can be represented by power-series expansions. Such symmetry transforms are generated by rational values of underlying power exponents. Symmetry properties of 1/N energy estimates are also discussed.

Measurement of the differential cross sections of the electron capture of ${\mathrm{He}}^{+}$ in Ne in the energy range 0.5–5 keV has been made. From these the total cross sections were calculated by integration. The present values are compared with those from previous measurements and with a recent diabatic calculation, with which good agreement has been found.

The following cross sections for $9^2$$D_{3/2}$⇆$9^2$$D_{5/2}$ fine-structure mixing in Rb, induced in collisions with ground-state Rb and noble-gas atoms, have been measured using methods of atomic fluorescence spectroscopy: Q${(9\mathrm{}}^2$$D_{3/2}$→$9^2$$D_{5/2}$) =93, 9, 6, 26, and 42; Q${(9\mathrm{}}^2$$D_{3/2}$←$9^2$$D_{5/2}$) =62, 6, 3, 17, and 23, for Rb, He, Ne, Ar, and Kr, respectively, in units of ${10}^{\mathrm{-}14}$ ${\mathrm{cm}}^2$. The measured cross sections are in good agreement with recent theoretical calculations of Sirko and Rosiński.

We propose a method for calculating electron-scattering cross sections which consists of a combination of the minimum-variance approach to optimizing a trial wave function and pseudospectral techniques for evaluating exchange contributions. Tests in simple applications indicate that this hybrid approach is remarkably efficient. Only one-electron matrix elements and quantities depending on the trial function and its derivatives evaluated at grid points are required. The extension to more complex systems is discussed.

We report nonrelativistic many-body f values for the La transitions 2s2$p^n$→2$s^2$2$p^{n\mathrm{-}2}$3p, where n=5,6. The largest of these transitions, computed using the first-order theory of oscillator strengths and including all nonorthonormality effects, is about 0.009.

Measurements of optical rotary-echo decay of the $R_1$(-1/2),σ transition of ${\mathrm{Cr}}^{3+}$ in dilute ruby at 2 K are described and compared with predictions of two recent modifications (Gauss-Markov and random-telegraph models) of the optical Bloch equations (OBE’s). While the modified OBE approximately describes the free-induction decay behavior both in ${\mathrm{Pr}}^{3+}$:${\mathrm{LaF}}_3$ and ruby, we show that rotary-echo decay in ruby is instead described by the standard OBE. Various aspects of the spin flip-flop model used in the theories are discussed in regard to ruby, as well as other possible dephasing contributions.

Self-organization and anomalous diffusion are discussed for a plasma just above the threshold for dissipative electromagnetic drift-wave instability in a gravitational field. The enhancement of the plasma diffusion owing to the electromagnetic fluctuation is shown to be small.

The nonlinear propagation of an external magnetic-field-aligned circularly polarized electromagnetic wave in electron-positron plasma is investigated. Relativistic and the time-derivative ponderomotive nonlinearities are considered. A new kind of envelope soliton in the magnetoactive plasma is obtained. A large-amplitude localized electromagnetic radiation may exist in the pulsar magnetosphere.

The normal procedure for numerical simulation of exponentially correlated colored noise is superseded by the novel algorithm presented here. A differential algorithm is replaced by an integral algorithm which is faster, more accurate, and permits the use of longer step sizes.

Two-dimensional axisymmetric single solitons in nematic liquid crystals, which appear as white rings under white light, are generated by radial pressure gradients in homeotropic nematic disk cells. The pressure at the center is maintained at atmospheric pressure, while that at the rim is varied. Photographs of the propagating single solitons taken at regular time intervals are presented. The time dependence of the radial position and the width of the white ring are given. As the white ring moves inward, the width increases with time before reaching a constant, which decreases slightly with the pressure gradient. The observed results show reproducible properties when the pressure is cycled repeatedly, i.e., no hysteresis effect is observed.

Excitation of the $3s{}_{}{}^3{}_{}{}^{}S_{}^{\circ }{}_{}{}^{}$ and $3p{}_{}{}^3{}_{}{}^{}P$ states of atomic oxygen has been studied in detail for electron impact energies from 13.87 to 100 eV by use of a close-coupling approximation. The target states included in the expansion of the total wave function are represented by accurate configuration-interaction wave functions. The present results are in good agreement with the recent experiments for the dipole-allowed ${}_{}{}^3{}_{}{}^{}P-3s{}_{}{}^3{}_{}{}^{}S_{}^{\circ }{}_{}{}^{}$ transition, but for the forbidden ${}_{}{}^3{}_{}{}^{}P-3p{}_{}{}^3{}_{}{}^{}P$ transition a large unresolved discrepancy exists.

A method of simultaneously determining the magnitude of the cross section for photoionization of an excited atom and the atomic density of the ground state is presented. Measurements of $\sigma$ for $\mathrm{Ba}\left(6s6p{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$, $\mathrm{K}\mathrm{}\left(4p\right)\mathrm{}$, and $\mathrm{Na}\mathrm{}\left(3p\right)\mathrm{}$ at photon ionizing energy 3.51 eV (3533 Å) are reported and compared with previous values. Application of this technique to the determination of the density in an atomic beam is discussed.

An energy-independent transformation of the generalized eigensystem used in eigenchannel calculations is shown to give the energy dependence of the $R$ matrix in semianalytic form. The transformation gives insight into the energy dependence of the short-range parameters used in multichannel quantum-defect theory. We present a simple method for setting up the many-electron basis set which integrates naturally with the noniterative eigenchannel method. The approach is used to calculate energy-dependent quantum defects for the ${}_{}{}^1{}_{}{}^{}S_{}^e{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}P_{}^e{}_{}{}^{}$ symmetries of silicon near the first ionization threshold, with spin-orbit effects described by a frame transformation.

We demonstrate how the topological phase associated with Rabi flopping in two-level atoms in optical fields can be measured by quantum-beat experiments. We use the Zeeman coherences in $j=0\mathrm{}$ to $j=1\mathrm{}$ transition which is excited by both broad-band field and circularly polarized pulses.

The interaction of nearly degenerate TE${\mathrm{M}}_{01}$ and TE${\mathrm{M}}_{10}$ modes of a laser is investigated. When the difference between the oscillation frequencies of the two modes is decreased, a transition occurs from a nearly sinusoidal "mode-beating" intensity modulation via periodic and irregular pulsing to frequency-locked steady-state emission in a TE${\mathrm{M}}_{01}^{*}$ hybrid mode. The formation of this hybrid mode by frequency locking is a simple example of the recently predicted emergence of stable transverse patterns in nonlinear optical resonators, brought about by frequency locking of near-degenerate, competing transverse modes.

We report the first observation of optical nutation in a collinear fast-ion-beam-laser experiment. 35-keV ${\mathrm{Ba}}^{+}$ ions are suddenly tuned into resonance with a strong laser field by post acceleration over a short distance. The degree of excitation as a function of time is monitored by observing the spontaneously emitted light along the ion beam. Oscillations as a function of transition, laser intensity, and laser frequency detuning have been studied. Theoretical curves have been calculated in the density-matrix formalism.