A complete period-doubling sequence in four-dimensional symplectic maps is determined by following a special bifurcation pass in the parameter plane. Stability diagrams for lower periods in the parameter plane are shown. Within numerical accuracy, there exist certain relations between the scaling exponents of the period-doubling sequence.

Laser fluctuations are measured and characterized with a new technique based on the concept of first-passage-time distributions. This first-passage-time technique makes it possible to discern quantum noise in a dye laser even in the presence of pump fluctuations that are many orders of magnitude larger. We report new analytic and experimental results for the mean, variance, and skewness of the first-passage-time distributions. The analytic results agree well with numerical computations and experimental measurements. Our technique is particularly suited to the quantitative description of laser fluctuations above threshold; it complements the conventional photoelectric counting and correlation methods which are valuable for lasers below and near threshold but are difficult to implement for lasers far above threshold. The limits of validity of the theory containing a cubic nonlinearity are examined in the context of passage-time measurements. The effects of multiplicative noise and saturation on the variance of the intensity fluctuations are also discussed. A new signature of multiplicative noise is predicted.

Lonberg and Meyer [Phys. Rev. Lett. 55, 718 (1985)] have recently discovered in polymer nematics the existence of a critical value $r_c$=0.303 for the ratio r=$K_2$/$K_1$ between the twist and splay Frank elastic constants, below which a periodic splay-twist distortion is energetically favored with respect to the well-known aperiodic splay distortion which appears in a Fréedericksz transition. In this paper the effect of weak-anchoring conditions on the critical r value and on the other parameters of interest is theoretically investigated. Analytical expressions between these parameters are given. It is shown that the periodic transition is not allowed in the range 0.5<r<2. Outside this range either the periodic or aperiodic transition appears, according to the surface treatment, the sample thickness, and the direction of the magnetic field. Hence the critical value of r can be controlled in a wide range.

This paper is the first in a series of theoretical studies of singular cells in the small solute Peclet number limit (P→0) of two-dimensional models of directional solidification. In this limit solute diffusion in the frame of the moving front is nearly Laplacian in which case solidification cells and Saffman-Taylor fingers are closely related. Here Langer’s moving symmetric model in the absence of temperature gradient (which also describes solidification in a channel of width λ at unit undercooling) is considered. A boundary integral equation describing steady-state cells is derived and it is shown that in the P→0 limit this equation can be expressed in terms of a single dimensionless parameter σ∝$d_0$l/${\lambda }^2$. The endpoint singularity is studied analytically and physically admissible solutions are found numerically to only exist for a discrete set of values of σ. The small P dependence of σ is also examined.

We report, for the first time to our knowledge, on high-resolution x-ray scattering measurements of the liquid crystal 4’-butoxyphenylester 4-decyloxybenzoic acid (4OP10OB) with emphasis on the smectic-C phase and the smectic-A to smectic-C phase transition. From angular scans in reciprocal space we found that the smectic-C layer planes undergo a continuous tilt ${\phi }_p$ with respect to temperature that can be described either by a Landau-type mean-field theory (which includes a sixth-order term in ${\phi }_p$) or by a simple scaling form: ${\phi }_p$∼[($T_c$-T)/$T_c$${]}^{0.44}$, where $T_c$ is the smectic-A–smectic-C transition temperature. Simultaneous measurements of the lattice spacing in the smectic-C phase suggest that the molecules do not behave like rigid rods. We found that the diamagnetic part of the molecule strongly couples to the magnetic field and tilts independently of the aliphatic end chains. The end chains are melted and thus maintain an almost-temperature-independent contact angle to the layer planes. Our measurements are consistent with the ‘‘zigzag’’ model of Bartolino, Doucet, and Durand.

Three related systems, two of which describe diffusion of an ideal gas through a porous plug, are optimized so as to minimize the work required to move the plug from one equilibrium position to another equilibrium position in a given time τ. All systems follow a ‘‘turnpike’’ (i.e., boundary-singular-boundary branch) trajectory, and the dissipation (work required) is proportional to (Δl${)}^2$/τ, where Δl is the distance moved, at least for slow processes. The result is of interest as a lower bound for the separation of gases by diffusion.

In this paper formulas and recursion relations for the expectation values of the operators {1-exp[-a(r-$r_e$${\left)\right]\mathrm{\}}}^n$, (r-$r_e$${)}^n$, exp[-a(r-$r_e$${\left)\right]}^n$, and (r-$r_e$){exp[-a(r-$r_e$${\left)\right]\mathrm{\}}}^n$ are derived for a rotating Morse oscillator. These equations can be used to calculate the diagonal (v=v’, J=J’) and off-diagonal (v≠v’, J≠J’) matrix elements. Asymptotic approximations for the diagonal elements of the (r-$r_e$${)}^n$ operator, 〈vJ‖(r-$r_e$)‖vJ〉 and 〈vJ‖(r-$r_e$${)}^2$‖vJ〉, are also obtained.

On the basis of a contour-integral representation for the Fermi-Dirac functions ${\mathrm{scrF}}_{\alpha }$(z) considered in a previous paper, some preliminary relations and new integral representations in the form of an infinite integral and a contour integral are obtained for these functions. From one of these relations an interesting functional expansion is deduced which, in its turn, enables us to derive a general expression in terms of elementary functions that approximates ${\mathrm{scrF}}_{\alpha }$(z) fairly well when α,z are both real and z varies in the range 1≤z<∞ and that, in addition, has a proper asymptotic behavior for large values of z. As a consequence of the vast field of applications of ${\mathrm{scrF}}_{\alpha }$(z) to different branches of physics when α=1/2,(3/2), special emphasis is paid to these cases and approximations are specifically proposed for them which approximate ${\mathrm{scrF}}_{\alpha }$(z) to an accuracy of nine significant figures ?z∈[1,∞], even though more accurate expressions can be easily obtained for them from the general expression. For the overwhelming part of the ${\mathrm{scrF}}_{\alpha }$(z) applications, with α=1/2,(3/2), these approximations are, from a practical point of view, as precise as if we had ${\mathrm{scrF}}_{\alpha }$(z) in an exact analytic form in the range 1≤z≤∞. Finally, a new functional, asymptotic expansion is also proposed for ${\mathrm{scrF}}_{\alpha }$(z).

Our examination of the classical relativistic equations for the two-body Coulomb problem leads to a natural definition of a ‘‘strong’’ Coulomb potential. A classical explanation for the limiting values, or ‘‘breakdown’’ of the Dirac hydrogenic atom equations emerges. We also find the surprising result that it is the Dirac equation and not the Klein-Gordon equation that displays a correspondence to the classical relativistic equations.

The single-configuration, Hartree-Fock-term energy separations of the 2snd ${\mathrm{}}^1$D and ${}_{}{}^3{}_{}{}^{}\mathrm{D}$ Rydberg states in berylliumlike fluorine agree remarkably well with the observed separations. It is shown that, in the ${}_{}{}^1{}_{}{}^{}\mathrm{D}$ series, interaction with 2$p^2$ raises the energy of the 2snd levels whereas the remaining interactions lower the levels. The combined effect is such that the ${}_{}{}^1{}_{}{}^{}\mathrm{-}_{}^3{}_{}{}^{}$D separation remains essentially unchanged when correlation effects are added.

New results for doubly excited ${}_{}{}^1{}_{}{}^{}\mathrm{S}_{}^{\mathrm{e}}{}_{}{}^{}$ autoionizing states of helium atoms converging on the N=2 to N=6 ${\mathrm{He}}^{+}$ thresholds are calculated by use of a method of complex-coordinate rotation. Resonance parameters (both energy and width) obtained by using Hylleraas-type wave functions with 308 terms are compared with the recent close-coupling and hyperspherical-coordinate calculations.

Quasiclassical estimates of nonrelativistic s-wave resonance energies for penetrable barriers like $C_2$/$r^2$+$C_n$/$r^n$ are presented and discussed. Such barriers are considered for the case $C_2$<0, $C_n$>0, and 0<n<2 as well as for the case $C_2$>0, $C_n$<0, and n>2. One starts from the typical analytical forms characterizing the quasiclassical extremal values of the corresponding Schrödinger Hamiltonian. Then one proceeds by use of the analytic continuation of the underlying phase-space quantum towards complex values.

A general construction procedure for singularity-free Hill equations with compact solutions is discussed. A part of the result obtained by Wu and Shih [Phys. Rev. A 32, 3736 (1985)] for the same subject is included in the proposed procedure.

Cross sections for the single ionization of ${\mathrm{H}}_2$ forming ${\mathrm{H}}_2$${\mathrm{}}^{+}$(1s${\mathrm{\sigma }}_{\mathrm{g}}$) have been measured using ${\mathrm{H}}^{+}$ (${\mathrm{D}}^{+}$) and ${\mathrm{He}}^{+}$ projectiles. The energies of the ${\mathrm{H}}^{+}$ (${\mathrm{D}}^{+}$) projectiles ranged from 80 to 3500 keV/amu. The energies of the ${\mathrm{He}}^{+}$ projectiles ranged from 25 to 750 keV/amu. The results are compared with published data on the single ionization of helium by the same projectiles. For projectile energies above 200 keV/amu, the cross sections for the two targets differ by a factor of 2. Previously published measurements of the double-ionization cross sections of ${\mathrm{H}}_2$ and helium are also compared. The ${\mathrm{H}}_2$ cross section is smaller and falls off more rapidly with projectile velocity.

Cross sections for the single and double ionization of helium by ${\mathrm{He}}^{+}$ projectiles have been measured for projectile energies between 25 and 750 keV/amu. Above 400 keV/amu, where charge capture is small, the charge and velocity dependence of the double-ionization cross section is compared to that induced by other projectiles. It is found that ${\mathrm{B}}^{5+}$, ${\mathrm{Li}}^{3+}$, and ${\mathrm{He}}^{2+}$ projectiles yield double-ionization cross sections which vary as $Z^4$f(v). The same is true for ${\mathrm{He}}^{+}$ projectiles if the effective charge of the ${\mathrm{He}}^{+}$ is chosen to be about 1.6. Electrons and protons yield a double-ionization cross section with a different velocity dependence.

K-atom selection by an inhomogeneous magnetic field was used to demonstrate that atomic K is needed to produce three-beam ${\mathrm{Na}}^{\mathrm{*}}$ fluorescence in a (K,NaCl, laser) triple-beam experiment. When the magnet is energized, the atomic flux and the three-beam ${\mathrm{Na}}^{\mathrm{*}}$ fluorescence both approximately double, thereby demonstrating that K atoms are involved in the process giving rise to ${\mathrm{Na}}^{\mathrm{*}}$. This supports the previous interpretation of three-beam ${\mathrm{Na}}^{\mathrm{*}}$ fluorescence as due to the laser-assisted reaction K+NaCl+hν→${\mathrm{Na}}^{\mathrm{*}}$+KCl. .AE

Symmetric resonant charge transfer (RCT) in ${\mathrm{H}}^{+}$+H and ${\mathrm{He}}^{2+}$+He collisions has been investigated in the ultralow-collision-energy range ${10}^{\mathrm{-}3}$–${10}^{\mathrm{-}7}$ eV. The RCT cross section has been computed by partial-wave expansion in the molecular-orbital expansion method within the fully quantum-mechanical formalism. The calculated RCT cross sections become constant below E≃${10}^{\mathrm{-}6}$ eV, corresponding to a scattering length of ∼6$a_0$ and ∼2$a_0$ for ${\mathrm{H}}_2$${\mathrm{}}^{+}$ and ${\mathrm{He}}_2$${\mathrm{}}^{2+}$, respectively.

Evidence is cited which supports the belief that Efimov states should exist in trimers of spin-polarized Λ and Σ-hypernuclear tritium. Macroscopic samples of the two hypernuclear-atom systems should also manifest most of the properties of helium.

The factorized distorted-wave impulse approximation (DWIA) is used to analyze the momentum profiles of the noncoplanar symmetric (e,2e) transitions from the helium-atom ground state to the ${\mathrm{He}}^{+}$ n=1 and n=2 states. The overlap function used for the calculation of the DWIA cross section is derived from a very accurate configuration-interaction wave function of the helium-atom ground state. The DWIA cross sections provide a better fit to the experimental data than the equivalent plane-wave impulse-approximation cross sections, although when the n=1 to (summed) n=2 cross-section ratio is depicted, this does not seem to be the case.

The theoretical model of Montenegro and Sigaud is used for the description of the experimental total K-shell ionization cross sections for 2.2-MeV/u ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ on 24 targets from ${}_{21}{}^{}{}_{}{}^{}\mathrm{Sc}$ to ${}_{83}{}^{}{}_{}{}^{}\mathrm{Bi}$ obtained by Seidel et al. The predictions of the model, which considers both binding and static polarization effects within the framework of adiabatic perturbation theory, are very good for the majority of the measured data in the region of validity of the model. The electron-capture process that can contribute in the region of the largest values of relative velocity ${\xi }_K$ is also analyzed.