Laser cooling of a single Ca+ ion: Observation of quantum jumps

This paper describes trapping and laser cooling of a Ca⁺ ion in an rf quadrupole ion trap. A single Ca⁺ ion is laser cooled to below 130 mK and quantum jumps are observed by exciting the ion into the metastable D _5/2 state via the P _3/2 state. The lifetime of the metastable D _5/2 state is estimated from the distribution of the dark periods of the quantum-jump signal. Collision-induced jumps between the metastable D _3/2 state and the D _5/2 state in a background gas are also directly observed.     

Theory of spin diffusion in liquid-phase polymer systems

A general theory of spin diffusion in condensed media is constructed by the method of Zwanzig-Mori projection operators using the superpositional approximation to decouple the many-particle correlation functions. The spin diffusion coefficient is expressed in the form D _sp=D _tr+D _f , where D _tr is the contribution associated with translational displacements of the molecules and D _f is the contribution caused by intermolecular flip-flop processes. The expression for D _tr differs from the well-known Kubo-Green formula for the self-diffusion coefficient D _sd in that the integrand contains an additional factor P _f (t), which is the probability of the molecular spins not participating in intermolecular flip-flop transitions over the time t. A microscopic expression is obtained for D _f in the form of a time integral of the intermolecular dipole-dipole dynamic correlation functions. For liquid-phase polymer system with fairly high molecular mass the condition D _sp≫D _sd is satisfied. Zh. éksp. Teor. Fiz. 114, 538–554 (August 1998)     

Annihilation rates of ortho—positronium in organic liquids: correlation with liquid compressibility and polarization ratio

The bubble model of ortho—positronium annihilation rates customarily employs the value of the planar-surface tension in the estimation of the (surface) energy required to expand a normal interstitial cavity to form the bubble. However, bubble radii are estimated to be only about 0.4 nm; the surface of such a small bubble is expected to have a tension different from that of the planar surface. We have replaced the surface tension parameter by the isothermal compressibility, which is thought not to have a nanostructure limitation. The model has been further improved by introducing the polarization ratio (n ² _D ? 1)/(n ² _D + 2) as a parameter, n _D being the refractive index of the organic liquid. Calculations are presented for 20 liquids.     

C M ? C N D -computable state

The notions of D-computable state and D-concurrence are generalized to the C ^M ⊗ C ^N system. A class of D-computable state on C ^M ⊗ C ^N is given and the calculating method of the lower bound of D-concurrence is provided. The obvious expression of the lower bound of D-concurrence for the state mixed by two D-pure states is derived. Supported by the National Natural Science Foundation of China (Grant No. 60433050) and the Key Project of the Science Foundation of Xuzhou Normal University (Grant No. 06XLA05)     

Thermodiffusion of interstitials in a film

A general expression is obtained for the thermodiffusion coefficientD _T of a film, also for its dependence on temperature, film thickness and type of concentration distribution of the interstitials, according to its profile. In neglecting interaction of interstitials with each other in a model of a film with single-plane boundaries with the vacuum and the substrate, it is shown thatD _T>D _T ^(∞) is possible, whereD _T ^(∞) is the thermodiffusion coefficient of a bulk specimen. Ural State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–46, September, 1996.     

On Different Approaches to Estimate the Mass Fractal Dimension of Coal Aggregates

Several methods to measure the structures of coal aggregates are compared. Loose and compact coal aggregates were generated through flocculation of ultrafine coal particles (mean volume diameter of 12 μm) under specific shearing conditions. Aggregate structure in terms of mass fractal dimension, D_f, was determined using various methods; namely 2D and 3D image analysis, interpretation of intensity patterns from small angle light scattering, changes in aggregation state through light obscuration, and settling behavior. In this study, the measured values of D_f ranged from 1.84–2.19 for coal aggregates with more open structures, and around 2.27–2.66 for the compact ones. All of these approaches could distinguish structural differences between aggregates, albeit with variation in D_f values estimated by the different techniques. The discrepancy in the absolute values for fractal dimension is due to the different physical properties measured by each approach, depending on the assumptions used to infer D_f from measurable parameters. In addition, image analysis and settling techniques are based on the examination of individual aggregates, such that a large number of data points are required to yield statistically representative estimations. Light scattering and obscuration measure the aggregates collectively to give average D_f values of the particulate systems; consequently ignoring any structural variation between the aggregates, and leaving possible small contaminations undetected (e.g. by dust particles or air bubbles). Appropriate utilization of a particular method is thus largely determined by system properties and required data quality.     

Nematic ordering problem as the polymer problem of the excluded volume

Based on a solution of the polymer excluded volume problem, a technique is proposed to estimate some parameters at the isotropic-nematic liquid crystal phase transition (the product of the volume fraction of hard sticks and the ratio of the stick length, L, to its diameter, D; the maximum value of this ratio at which one cannot regard the stick as hard). The critical exponents are estimated. The transition of a swelling polymer coil to ideal is revealed as the polymerization degree of a macromolecule increases. The entanglement concentration obtained agrees with experimental data for polymers with flexible chains. The number of monomers between neighbor entanglements is assumed to be the ratio L/D. A comparison of the theory with other ones and recent experimental data is made.     

State of two-dimensional long-period superstructure in the metastable Fe-Nd-B phase

We investigated using transmission electron microscopy (TEM) the state of a long-period superstructure (LPS) composed of a metastable D0₃ phase, which emerged during crystallisation of Fe₈₉Nd₇B₄ amorphous alloys [Konno, Uehara, Hirosawa, et al., Phil. Mag. A 79 2413 (1999)]. Diffraction studies showed that it is a two-dimensional (2D) LPS characterized by 1/4a ₀?111? antiphase boundaries (APBs) perpendicular to ?100? directions and 1/2a ₀?100? APBs perpendicular to ?110? directions, where a ₀ is the unit cell parameter of the D0₃ cell. Dark field images and high-resolution TEM showed that superperiods estimated from diffraction patterns, 3.2 and 2.4?nm, respectively, represent an average structure; and real arrangements of APBs are rather diverse in terms of both periodicity and APB planes. These observations indicate that the 2D LPS emerged in the following reaction sequence: amorphous?→?A2?→?D0₃ with 2D LPS?→?D0₃, where all the phases are metastable.     

Ground states of two-dimensional quasicrystals

Hamiltonians for nonperiodic tilings are considered. It is shown that the quasicrystalline tiling obtained by the cut-and-strip method from aD-dimensional cubic lattice may bs a ground state only if the tiling possesses a high orientational symmetry: the (2,D)-quasicrystal should haveD-fold symmetry ifD is even and 2D-fold symmetry ifD is odd. For interactions of a finite range the restrictions are stronger: only a (2, 5)-quasicrystal (Penrose tiling) may be a stable ground state.     

[2.2]Paracyclophane: theoretical study of its lower excited states and of the zero-field splitting parameters D

The lower excited singlet and triplet states and the zero-field splitting parameters D of [2.2]paracyclophane are studied within a semiempirical π theory which takes into account overlap effects between the two benzene rings, transanular and through-bond interaction via the methylene bridges. Whereas the singlet energies depend strongly on the through-bond interaction and the mutual polarization of σ core and π system this is not the case for the energies and zero-field splitting parameters D of the two lowest triplet states. The deformations of the benzene rings in [2.2]paracyclophane lead only to a small decrease of the excitation energies of about 0·2 eV. The D parameter can be written as a sum D = D_A + D_B + D_AB with the intrasubunit contributions D_A and D_B of the conjugated subunits A and B of the phane and an intersubunit term D_AB . We demonstrate that the deformations reduce the intrasubunit terms D_A and D_B and that they are crucial for the decrease of the D values of [2.2]paracyclophane with respect to p-xylene. The difference between the D values of the first and second triplet states is governed by the intersubunit term D_AB which has a different sign in the two states. However, this difference does not depend markedly on the transanular interaction. A further reduction of D_A and D_B in the first triplet state only is caused by transanular interaction by means of symmetrical charge-transfer terms in the wavefunction.     

Zur Bestimmung des D2O-Gehaltes in schwerem Wasser nach der Schwimmer-Methode

For the evaluation of float measurements all individual steps of the calculations are comprised under the expression of “precise float formula”. From this simplified approximations can be deduced. Their errors are estimated under little restraining conditions. The rather simple “difference formula” in the range of high D₂O-concentration together with a density scale for pure D₂O gained by interpolation suffice for most practical purposes. This is proved by numerical comparing with the precise formula.     

A simulation of the mixed spin 3–spin 3/2 ferrimagnetic Ising model

The mixed spin 3–spin 3/2 ferrimagnetic Ising model was simulated using cooling algorithm on cellular automaton (CA). The simulations were carried out in the intervals ?4 ≤ D_A/J ≤ 8 and ?4 ≤ D_B/J ≤ 8 for the square lattices with periodic boundary conditions. The ground-state phase diagram of the model has different types of ferrimagnetic phases. Although only the antiferromagnetic nearest-neighbor interaction was contained in the Hamiltonian, the compensation points emerged through D_A/J = 2 at kT/J = 0. The values of the critical exponents (ν, α , β and γ) were estimated within the framework of the finite-size scaling theory and power-law relations for the selected D_A/J values (?2, 0, 1, 2, and 4). The estimated critical exponent values were in good agreement with the universal values of the two-dimensional Ising model (ν = 1, α = α′ = 0, β = 0.125, β′ = 0.875 and γ = γ′ = 1.75).     

Oscillations in the Determination of Renyi Dimension

To describe the degree of chaos of a strange attractor created by a nonlinear map, GRASSBERGER [1] revived Renyi Dimension D_q which is a common generalization of both metric capacity D₀ and information dimension D₁. But often, the numerical determination of D_q is complicated by an oscillating effect first investigated by BADII and PUOLITI [5] for a dimension similar to D₀. This effect is studied in the present paper. We consider the conditions for the appearance of oscillations and the dependence on q, and we give some numerical examples.     

Zeta function for the Laplace operator acting on forms in a ball with gauge boundary conditions

The Laplace operator acting on antisymmetric tensor fields in a D-dimensional Euclidean ball is studied. Gauge-invariant local boundary conditions (absolute and relative ones, in the language of Gilkey) are considered. The eigenfuctions of the operator are found explicitly for all values of D. Using in a row a number of basic techniques, as Mellin transforms, deformation and shifting of the complex integration contour and pole compensation, the zeta function of the operator is obtained. From its expression, in particular, ζ(0) and ζ'(0) are evaluated exactly. A table is given in the paper for D=3,4,...,8. The functional determinants and Casimir energies are obtained for D=3,4,...,6. Received: 2 May 1996 / Accepted: 20 July 1996     

Electromagnetic mass splittings of heavier hadrons in quantum chromodynamics

The electromagnetic mass splittings of heavier hadrons are estimated in the framework of gauge theory model where ligher quarks are taken to behave relativistically and the spatial wave functions are described by the spin-spin interaction affected relative distances between quarks. The predictions for (Ξ⁻-Ξ⁰), (Σ*⁰−Σ*⁺), (Ξ^*−-Ξ^*0), (D _c ⁺−D _c ⁰) and (D _c ^*+ −D _c ^*0 ) are in fair agreement with the experimental data available whereas those for (D _b ⁻ −D _b ⁰ ) and (D _b ^*− −D _b ^*0 ) are in qualitative agreement with other theoretical estimates.     

Fast-beam-spectroscopy by combined gas cell-laser excitation for cascade-free lifetime measurements of highly excited states

The fast-beam-spectroscopy is used for cascade-free high-precision lifetime measurements of highly excited atomic states, which are populated by a two-stage excitation as resulting from gas cell and laser interactions. An experimental extension of the method is presented demonstrating the selective population of high lying levels even from shorter-living intermediate states by an intracavity dye-laser excitation. A first example for this type of experiments is given for the lifetime of the Li 3d ² D level, which was determined to be τ(3² D)=14.60±0.13 ns. The appropriate experimental set-up is described in detail and an approximate expression for signal calculation is presented, by which the applicability of this method to other levels can be estimated.     

Transport coefficients of hard sphere fluids

New calculations have been made of the self-diffusion coefficient D, the shear viscosity η_s, the bulk viscosity η_b and thermal conductivity λ of the hard sphere fluid, using molecular dynamics (MD) computer simulation. A newly developed hard sphere MD scheme was used to model the hard sphere fluid over a wide range up to the glass transition (～0.57 packing fraction). System sizes of up to 32 000 hard spheres were considered. This set of transport coefficient data was combined with others taken from the literature to test a number of previously proposed analytical formulae for these quantities together with some new ones given here. Only the self-diffusion coefficient showed any substantial N dependence for N < 500 at equilibrium fluid densities (ε 0.494). D increased with N, especially at intermediate densities in the range ε ～ 0.3–0.35. The expression for the packing fraction dependence of D proposed by Speedy, R. J., 1987, Molec. Phys., 62, 509 was shown to fit these data well for N ～ 500 particle systems. We found that the packing fraction ε dependence of the two viscosities and thermal conductivity, generically denoted by X, were represented well by the simple formula X/X ₀ = 1/[1 ? (ε/ε₁)]^m within the equilibrium fluid range 0 > ε > 0.493. This formula has two disposable parameters, ε and m, and X ₀ is the value of the property X in the limit of zero density. This expression has the same form as the Krieger-Dougherty formula (Kreiger, I. M., 1972, Adv. Colloid. Interface Sci., 3, 111) which is used widely in the colloid literature to represent the packing fraction dependence of the Newtonian shear viscosity of monodisperse colloidal near-hard spheres. Of course, in the present case, X _o was the dilute gas transport coefficient of the pure liquid rather than the solvent viscosity. It was not possible to fit the transport coefficient normalized by their Enskog values with such a simple expression because these ratios are typically of order unity until quite high packing fractions and then diverge rapidly at higher values over a relatively narrow density range. At the maximum equilibrium fluid packing fraction ε = 0.494 for both the hard sphere fluid and the corresponding colloidal case a very similar value was found for η_s/η_o ?30–40, suggesting that the ‘crowding’ effects and their consequences for the dynamics in this region of the phase diagram in the two types of liquid have much in common. For the hard sphere by MD, D_o/D ～ 11 at the same packing fraction, possibly indicating the contribution from ‘hydrodynamic enhancement’ of this transport coefficient, which is largely absent for the shear viscosity. Interestingly the comparable ratio for hard sphere colloids is the same.     

On the interpretation of the RHEED intensity oscillations during the growth of vicinal faces

A quantitative treatment of the crystallization kinetics in MBE growth of vicinal surfaces results the relation l ²=2D _sK between the surface diffusion coefficient D _s, the time for a monolayer deposition and the interstep distance l at which the RHEED intensity oscillations disappear. The correction factor K depends on the size and the energy of the two-dimensional critical nucleus and it is estimated to be smaller than 10^–2. The currently used interpretation of the RHEED intensity oscillations ignores the correction factor K and, therefore, the calculated values of D _s are several orders of magnitude smaller than its real values. The surface transport during the time of growth interruption is discussed in connection with the tendency to three dimensional growth at every second interface (where a deposition of the material with strong intermolecular bonds starts) of a small period superlattice.     

Investigation of proton diffusion in Nafion®117 membrane by electrical conductivity and NMR

The proton dynamics in Nafion ^®117 is investigated by comparison of the diffusion coefficient D_NMR estimated from PFG-NMR with that of D_σ estimated from electrical conductivity. At high water content region, D_σ is about two times higher than D_NMR as a result of Grotthuss mechanism. At low water content region, D_σ and D_NMR are in good agreement with each other. Both of the diffusion coefficients decrease steeply at low water content region. It can be explained as a result of the percolation transition due to the isolation of ion clusters, which is suggested by the recent small angle X-ray scattering data.