Steps corresponding to (110), (211), (310), (222), and (321) facets in monocrystals of blue phase I (BP I) are described. We show that close to equilibrium, surfaces of BP I monocrystals contain facets and rounded parts on which a series of steps can be distinguished. During growth, the round parts are eliminated and the remaining facets [(110) and (211)] meet at sharp edges. In view of these results, blue phases are model systems for recent theories in which crystal shapes are described in terms of an equilibrium distribution of steps and of step mobility on crystal surfaces. New observations of the (321), (310), and (222) facets lend additional support for the $O_8\left(I{4}_{1}32\right)$ model of blue phases proposed previously by several authors.

Using renormalization theory, Zisook has shown that at small values of the dissipation (e.g., for a planar map of constant Jacobian B=0.999) the apparent rate of convergence, δ, of the parameter values for period doubling descends (‘‘crosses over’’) from its conservative value (δ=8.721 097 2. . .) to its dissipative value (δ=4.669 201 6. . .) as we consider higher and higher bifurcations. Moreover, this apparent δ at the nth bifurcation is a universal function, depending only on &. Employing a technique of Ghendrih and renormalization theory, I obtain an analytical expression for this function and show that it does not descend monotonically but has a minimum at $B_e$,min≃3×${10}^{\mathrm{-}6}$. I also analytically calculate the (orbit) scaling factor α at $B_e$=0 and at $B_e$=1 using some results of a second-order renormalization equation which I derive here. Finally, I obtain an analytical expression for the bifurcation values $C_n$(B) of a particular map (the Hénon map) as a function of n and B.

A wide-band capacitive detector has been constructed to make time-resolved measurements of acoustic pulses generated in aluminum and in other solids by ns pulses of MeV protons. The near-field signal observed traveling in the beam direction is a measure of the initial pressure distribution along the path of the stopping protons. The measured amplitudes and shapes of such signals are consistent with the thermoelastic model of sound generation. From the signal rise time (<2 ns), it can be concluded that the conversion into heat of the energy loss of a slowing proton is localized within a radius of several micrometers. For the data presented, the fraction of beam-pulse energy absorbed from acoustic radiation by the detector is about 5×${10}^{\mathrm{-}14}$. Acoustic signals which generate ${10}^{\mathrm{-}2}$ eV of electrical energy in the detector (∼4 μV into 50 Ω for 5 ns) are easily discernible after signal averaging. Acoustic signals were used to probe the formation of microbubbles in hydrogen-implanted aluminum. From bubble growths inferred from acoustic measurements, the diffusivity of hydrogen in aluminum is estimated at a temperature where the diffusivity is 8 orders of magnitude smaller than in previous measurements.

Plasma noise effects on the beat-wave resonance condition and the subsequent reduction of the accelerating electric field for the laser beat-wave accelerator are investigated. Plasma noise or turbulence causes the accelerating electric field to saturate at a reduced level ε=$L_{\mathrm{eff}/\mathrm{L}}$ of the ideal coherent accelerating field, where $L_{\mathrm{eff}}$ is the effective growth length for the plasma wave and L is the ideal growth length. When the noise parameter σ=〈(δn${)}^2$〉/$n^2$ is above a threshold value, we find $L_{\mathrm{eff}\mathrm{\simeq }2\mathrm{c}/{\omega }_p^2{\tau }_c\mathrm{\sigma }}$, where ${\tau }_c$ is the correlation time of the noise spectrum along ω=${\mathrm{kv}}_p$. Slower noise is less effective in limiting the plasma wave growth. For strong noise $L_{\mathrm{eff}}$ becomes shortened to the correlation length in the noise $L_c$=$v_p$${\tau }_c$. In the case of slowly increasing mismatch in the beat-wave resonance condition, the effective growth length $L_{\mathrm{eff}}$ becomes the geometric mean of the density gradient scale length $L_n$ and the collisionless skin depth ($L_n$c/${\omega }_p$${)}^{1/2}$. .AE

The fundamental time cross-correlation function 〈v→(t)ω${\to }^T$(0)〉 is characterized for the first time using a computer simulation of the effect of an external electric field on 108 interacting dichloromethane molecules in the liquid at 296 K. Here v→ is the molecular center-of-mass linear velocity and ω→ the angular velocity of the same molecule.

A new derivation is given of the set of Schrödinger-like equations for the nonadiabatic behavior of an ensemble of charged particles in inhomogeneous magnetic fields, starting from the Liouville equation for the ensemble. The nonadiabatic loss of charged particles from magnetic-mirror traps thus appears in the nature of quantum tunneling of the adiabatic potential with the initial value of the first action invariant playing the role of ħ. The equations also predict one-dimensional interference-like effects in periodic magnetic fields. Different equations of the set describe different modes of the nonadiabatic behavior of a ‘‘pure’’ ensemble prepared with δ-function distributions for the controllable (in the sense used by Khinchin) integrals of motion of the system. A new concept of ‘‘ensemble modes,’’ as distinct from the collective modes, is thus introduced. These ensemble modes have indeed been observed as manifested through the recently observed multiplicity of lifetimes in the nonadiabatic decay.

The connection between the three-dimensional hydrogen atom and a four-dimensional harmonic oscillator (or equivalently a coupled pair of two-dimensional harmonic oscillators) subjected to a constraint condition is further explored. In particular, the role the constraint condition plays in determining the phase relationship between the pair of two-dimensional oscillators is examined. Furthermore, the connection is discussed in a group-theoretical context involving the Lie algebras of SO(4), SO(3,1), E(3), SO(4,2), and Sp(8,R).

We show within the framework of quantum-defect theory that bound states in the continuum (BIC) can occur in systems of at least three coupled Coulombic channels due to the interference of resonances belonging to different channels. As a physical realization of such BIC, we discuss the Schrödinger equation describing a hydrogen atom in a uniform magnetic field.

A comparison of various methods of calculation of the effect of spin-exchange interaction on the density matrix of hydrogen and alkali-metal atoms in their ground state is made. The elements connected to the (F,$m_F$0)⇆(F-1,0) transition are calculated. Matrices necessary for the calculation of any other element are also given.

The Kohn-Sham equation and its duplicated formalism for the Liouville equation for arbitrary time-dependent ensembles are derived.

The cross sections for the double ionization of ${\mathrm{H}}_2$ by 0.025–0.875-MeV/amu ${\mathrm{He}}^{+}$ are reported for the ${\mathrm{H}}_2$ internuclear axis oriented at 90° and 30° relative to the ion-beam direction. At low projectile velocities, there is an apparent angular dependence for the cross section, with the 90° results being larger.

Atomic single– and double–electron-detachment cross sections from ${\mathrm{Br}}^{\mathrm{-}}$ ions in He, Ne, Ar, Kr, and Xe, from 10 to 100 keV, are reported. The data fit well with other halogen-negative-ion cross sections on the same targets. There are indications that the double-detachment cross section is the same, up to about 5×${10}^5$ cm/s, for all halogen ions on He. Above this energy, and for other beams, the cross section increases both with the beam-atom mass and with the target-atom mass. The single-detachment cross section can be fitted by the Gauyacq theory, except at the highest energies of our experiments.

We present an extension of the analytical method of Macías and Riera to calculate radial couplings, to include model potentials or (local and nonlocal) pseudopotentials, in the Hamiltonian. As an illustration, energies, couplings, and momentum matrix elements are presented and discussed for the two-effective-electron NaH quasimolecule, as a stringent test case.

A comparison is made between the number of Efimov States present in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ trimers as calculated using the Faddeev equations in the Faddeev coordinate-momentum approach with estimates predicted by N=(1/π)ln(‖a‖/$r_0$) using realistic phenomenological He-He potentials. It is found that there is good agreement for systems supporting few states and that agreement remains when the Efimov states are forced to disappear by mathematically altering the potentials.

Our earlier measurements of the energy dependence of K-shell photoelectric cross sections for Y, Mo, Ag, and Sn in the energy region 18–44 keV have been extended to elements Ti, Fe, Ni, and Zn in the energy range 9≤E≤18 keV. The experiment has been performed under improved experimental conditions using a modified double-reflection geometrical setup and Si(Li) detector in place of a NaI (Tl) detector used in the earlier measurements. The results compare well with the theoretical calculations, confirming the earlier trend down to 9 keV.

This paper generalizes some recent results of F. T. Hioe [Phys. Rev. A 30, 2100 (1984)]. It is found that a two-level system driven by a resonant pulse with temporally symmetric amplitude modulation and antisymmetric frequency modulation may be completely inverted. In addition, it is shown that certain amplitude-modulated– frequency-modulated combinations may be mapped into Hioe’s (hyperbolic cosecant and hyperbolic tangent) solution.

The effect of amplitude fluctuations of a radiation field on the motion of a two-level atom is calculated. The results are compared with a similar calculation of Cook for the effect of phase fluctuations on such motion.

The transition from a mode-locked torus to a chaotic fractal attractor via the generic saddle-node bifurcation is considered. Although superficially the transition seems to be one of the known types of intermittency, it is shown to be in fact discontinuous. All the invariants that characterize chaos show a distinct jump. It is also argued that the power spectra are not sensitive to the discontinuous nature of the transition.

Examples of asymmetric unimodal maps are presented which fail to exhibit the metric universality discovered by Feigenbaum. In these cases the period-doubling cascade proceeds in oscillatory and divergent fashion rather than a universal geometric progression. Since measurements of physical systems are usually restricted to a limited number of bifurcations, similar routes to chaos may also be observed in experiments which are characterized by globally asymmetric maps.

We have measured the emission lines of the heliumlike Ti xxi impurity radiation from Ohmically heated Doublet-III tokamak plasma discharges. The measured wavelengths are in good agreement with recent theoretical and experimental results. The theoretical and experimental line-intensity ratios are also in good agreement for the pure-dielectronic-recombination satellite lines. Furthermore, collisional inner-shell excitation processes are observed to contribute significantly to the q lines in tokamak plasmas.