In the context of two coupled logistic maps, the behavior of period-doubling sequences is studied. The relationship between the codimensionality of the sequence limit and explicit and/or effective symmetries is discussed. It is shown how explicitly breaking the interchange symmetry between the two maps changes the codimensionality of the sequence limit from 2 to 1.

Possible fractal characteristics associated with quantum systems whose classical limits are chaotic are investigated. We analyze the eigenstates in a tight-binding model and the equivalent quantum kicked rotator and obtain both charge-density- and entropy-related fractal dimensionalities $D_{\rho }$ and $D_S$. We find $D_{\rho }$=$D_S$. The possible relevance of fractal dimensionality to quantum chaos is discussed.

We study the influence of nonlinear effects on the electrohydrodynamics of uniaxial nematic liquid crystals. To measure a novel reversible nonlinear coupling between an electric field, distortions of the director, and the stress tensor, we suggest an experimental setup and predict the occurrence of a flow in an initially static configuration. We show that the dissipative effects proposed by R. S.Akopyan and B. Ya. Zeldovich [Sov. Phys.—JETP 60, 953 (1985)] do not exist.

We have calculated the scattering cross section for a third-order process in which a hard x ray incident on an atomic system is absorbed with the emission of two lower-energy x rays. This process is resonant when one of the two lower-energy x rays has an energy equal to the K-shell binding energy. We calculated the resonant term in the scattering with a one-electron model using shielded hydrogenic wave functions. This work was motivated by a recent coincidence inelastic x-ray scattering experiment on copper which claimed to show by such scattering. We find that even at resonance the third-order scattering process is too weak by 3 orders of magnitude to account for the spectral feature which was attributed to it.

The physical meaning of the eigenvectors of the spin-adapted reduced-Hamiltonian matrices inspires the independent-electron-pair model, which permits the direct evaluation of the second-order reduced density matrices. Recently we have tested this method for singlet states of the beryllium isoelectronic sequence. Here, this same approach is applied to the doublet isoelectronic sequence of the lithium atom. In all the cases the theoretical results have been compared with experimental data when available and with results obtained in a parallel way with a full-configuration-interaction treatment, and the agreement is very satisfactory.

An experimental and theoretical study has been made of the 1s2s2$p^2$ ${\mathrm{}}^5$P–1s2$p^3$ ${\mathrm{}}^5$S transition in B ii. The experimental wavelength and lifetime (1323.92±0.07 Å and 0.65±0.01 ns), determined by beam-foil spectroscopy, are more than five times more accurate than previous experimental results. Our theoretical data, from multiconfiguration Hartree-Fock calculations, 1311.6 Å and 0.601 ns, are in excellent agreement with previous theoretical predictions of Beck and Nicolaides [Phys. Lett. 61A, 227 (1977)]. We have also observed the 1s2$p^3$ ${\mathrm{}}^5$S–1s2$p^2$3s ${\mathrm{}}^5$P transition, at 857.7±0.2 Å, in accord with the theoretical value 859.1 Å.

Cross sections for H(2p) charge-exchange excitation in ${\mathrm{H}}^{+}$-He, -Ne, and -Ar collisions have been measured for incident energies between 1 and 25 keV. Large discrepancies with previous experimental results are observed for small energies. The present results for helium are in good agreement with calculations by Kimura and Lin [Phys. Rev. A 34, 176 (1986)].

The Landau-Zener approximation is used to compute the charge-transfer recombination rate coefficients of ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Ni}}^{2+}$ in hydrogen at thermal energies. The energy separations of the adiabatic potential-energy curves of the quasimolecules ${\mathrm{FeH}}^{2+}$ and ${\mathrm{NiH}}^{2+}$ are obtained from one-electron calculations. The rate coefficients are of the order of ${10}^{\mathrm{-}9}$ ${\mathrm{cm}}^3$? sup -1— or greater. Charge transfer of ${\mathrm{Fe}}^{2+}$ occurs preferentially into the ground state of ${\mathrm{Fe}}^{+}$ so that the reverse process of charge-transfer ionization of ${\mathrm{Fe}}^{+}$ in collision with ${\mathrm{H}}^{+}$ also occurs rapidly above the reaction threshold.

An apparatus has been constructed for laser–radio-frequency double-resonance studies of very-low-energy-ion beams with collinear laser-ion geometry. The ion energy of only 1–2 keV leads to extremely narrow linewidths (∼60 kHz). This paper describes measurements of the hyperfine structure of ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}_{}^{+}{}_{}{}^{}$ and ${}_{}{}^{153}{}_{}{}^{}\mathrm{Eu}_{}^{+}{}_{}{}^{}$ in the level 4$f^7$(${}^8$$S^o$)5d ${}^9$$D_4^o$. The hyperfine constants A and B have been determined with a much higher accuracy than before. The present values of these constants (in MHz) are &=113.159(1), &=-215.356(10), &=-50.415(1), & =-548.357(10). .AE

The hyperfine splittings of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ 2$P_{3/2}$→2$S_{1/2}$, which are normally masked within the natural linewidth, are directly resolved for the first time by a line-narrowing technique of laser-induced fluorescence spectroscopy with use of a phase-switched laser. Observed splittings of 2$P_{3/2}$ levels are 9.41±0.10 MHz for (F’=2)-(F’=3), 6.00±0.16 MHz for 1-2, and 2.88±0.30 MHz for 0-1, which are consistent with reported hyperfine constants.

The effect of the mode distribution and the phase diffusion of different modes of the pump laser on resonance fluorescence is studied. Such a diffusion results in the redistribution of radiation which is shown to occur even in the conventional situation if the atom is irradiated by an additional laser, the strength of which controls the frequency spectrum of the redistributed radiation.

A path-integral formalism is used to describe a quantum system weakly coupled to a heat bath. The heat bath is described by a set of harmonic oscillators, which can be integrated out of the functional integral. The remaining functional integral shows how the quantum system approaches thermal equilibrium.

We discuss a method for constructing analytically solvable second-order linear differential equations with n-parameter variable coefficients (periodic or not). We show that an exact solution to this problem is possible if one can find another solution to a related subset problem (a subset equation formed with one of the variable coefficients). In the main body of this method, we demonstrate that (1) the exact solutions to the Hill-type equations presented by Casperson [Phys. Rev. A 30, 2749 (1984); 31, 2743(E) (1985)] and Wu and Shih [Phys. Rev. A 32, 3736 (1985)] can be readily constructed in a backwards manner and (2) a Pöschl-Teller equation can be solved exactly without using any special functions.

A method which enables one to estimate the level of noise from experimental time series in dissipative dynamical systems is introduced. It appears to be much faster than those in which a calculation of both the correlation integral and the dimension is needed. The proposed method should be especially useful for high-dimensional systems.

The recent derivation of the mean first-passage time for one-dimensional processes driven by additive dichotomous random processes [J. Masoliver, K. Lindenberg, and B. J. West, Phys. Rev. A 34, 2351 (1986)] can be extended to situations where the noise occurs multiplicatively and nonlinearly in the stochastic differential equation. For equations with Markovian dichotomous fluctuations in particular, this result allows for a complete and general probabilistic description of the statics and dynamics of the non-Markovian solution process in terms of stationary probability distributions and first-passage time statistics.

Some lower-lying S-wave resonances in positron-hydrogen scattering associated with the positronium N=2 and hydrogen N=3 thresholds are investigated using the method of complex-coordinate rotation and using an adiabatic treatment in hyperspherical coordinates. Both calculations indicate that the lowest resonance associated with the positronium N=2 threshold lies near E=-0.150279 Ry, in disagreement with Doolen’s prediction that the lowest resonance occurs at E=-0.222 Ry. We also report for the first time resonance parameters associated with the hydrogen N=3 threshold.

The negative muonium ion ${\mathrm{Mu}}^{\mathrm{-}}$≡${\mathrm{\mu }}^{+}$${\mathrm{e}}^{\mathrm{-}}$${\mathrm{e}}^{\mathrm{-}}$ has been produced by double electron pickup as a beam of positive muons passes through a foil. A clean signal was detected by electrostatically accelerating and analyzing the ions in a magnetic time-of-flight spectrometer. The ${\mathrm{Mu}}^{\mathrm{-}}$ beam at the focal plane of our spectrometer had an intensity 1.4×${10}^{\mathrm{-}5}$ times that of the incident ${\mu }^{+}$ beam or 2 ${\mathrm{s}}^{\mathrm{-}1}$, which corresponds to a ${\mathrm{Mu}}^{\mathrm{-}}$/${\mu }^{+}$ conversion probability of 0.5×${10}^{\mathrm{-}4}$ at the foil in agreement with the calculated value. The kinetic energies of ${\mathrm{Mu}}^{\mathrm{-}}$ at the foil are less than several keV as expected.

We report the first measurements of ejected-electron-energy distributions from slow glancing collisions of highly charged ions having K-shell vacancies with a solid surface. The spectra indicate two competing processes for filling the vacancy: one involving normal atomic Auger decay, and the other, vacancy transfer to inner shells of the solid via molecular orbital pseudocrossings. The number of electrons per incident ion resulting from the filling of the K-shell vacancy is of the order of unity, constituting only a small fraction of the total measured yield.

The full n=3 density matrices of hydrogen atoms formed after electron capture in ${\mathrm{H}}^{+}$-He collisions at 25–100 keV are calculated in a modified two-center atomic-orbital close-coupling expansion method. The integrated (over impact paramters) density matrix and its first-order moments are compared with recent experimental results. A charge-density plot is used to illustrate that the electron is lagging behind the projectile after the capture in the energy range considered. From the differential density matrix analysis, a ‘‘classical’’ orbital picture of the captured electron is proposed.