Theoretical structure and surface energy of the reconstructed {01.2} form of calcite (CaCO3) crystal

Two different reconstructions of the (01.2) face (Ca or CO₃ terminated) of calcite (CaCO₃) were studied: (i) R1 reconstruction: the outermost layer is based on the [0 1 0] × 1/3[2 1 1] rectangular mesh, which is symmetrical with respect to the c glide plane of the crystal, thus fulfilling the 2D symmetry of the face and (ii) R2 reconstruction: the outermost layer is based on a lozenge shaped mesh that does not respect the 2D symmetry of the face.The , , and slabs geometry optimizations of calcite (CaCO₃) were performed either at DFT level or by using empirical potentials; the results obtained with these two different calculation methodologies are in good agreement. With respect to their arrangement in the bulk, the CO₃ groups of the outermost layer are significantly rotated about the crystallographic a-axis and about the normal to the 01.2 plane; further, the thickness of the outermost layer is significantly lower than that of the underneath ones.The surfaces energies (γ) at 0 K, for relaxed and unrelaxed , , and faces, were determined either at DFT level or by using empirical potentials. Independently of the method of calculation employed, the stability order of the relaxed faces is < < < . Concerning the unrelaxed faces, whose energies were evaluated by using empirical potentials only, the stability order is instead < < < ; such different ordering shows the importance of geometry relaxation in the calculation of the surface energy. The values of the relaxed surface energies are , , and erg/cm².     

Step formation on hydrogen-etched 6H-SiC{0 0 0 1} surfaces

The formation of step bunches and/or facets on hydrogen-etched 6H-SiC(0 0 0 1) and () surfaces has been studied, using both nominally on-axis and intentionally miscut (i.e. vicinal) substrates. It is found that small miscuts on the (0 0 0 1) surface produce full unit-cell high steps, while half unit-cell high steps are observed on the () surface. The observed step normal direction is found to be for both surfaces. Hence, for intentionally miscut material, a miscut oriented towards this direction produces much better order in the step array compared to a miscut oriented towards a direction. For (0 0 0 1) vicinal surfaces that are miscut towards the direction, the formation of surface ripples is observed for 3° miscut and the development of small facets (nanofacets) is found for higher miscut angles. Much less faceting is observed on miscut () surfaces. Additionally, the (0 0 01) surface is found to have a much larger spatial anisotropy in step energies than the () surface.     

Structure of light hypernuclei

The structure of light hypernuclei with strangeness S=−1 and −2 is investigated with the microscopic cluster model and the Gaussian expansion method (GEM). We emphasize that the cluster picture as well as the mean-field picture is invaluable to understand the structure of Λ hypernuclei, Σ hypernuclei and double Λ hypernuclei. A variety of aspects of Λ hypernuclei is demonstrated through a systematic study of p-shell hypernuclei (,, , , , , ) and sd-shell ones (, ): for example, the appearance of genuine hypernuclear states with new spatial symmetry which cannot be seen in ordinary nuclei, the glue-like role of the Λ particle which shrinks the size of nuclear core and thus reduces the B(E2) value, and the halo and skin structures in and etc. The typical light hypernucleus is thoroughly investigated, including its production, structure and decay. Precise three-body and four-body calculations of , and using GEM provide important information on the spin structure of the underlying ΛN interaction, by comparing with recent experimental data from γ-ray hypernuclear spectroscopy. The Λ–Σ coupling effect is studied in and . The binding mechanism of is discussed together with the possible existence of , emphasizing the fact that the study of is useful for extracting information on the ΣN interaction differing from that from . A systematic study of double-Λ hypernuclei, constrained by the NAGARA data () within a four-body cluster model indicates that the recently observed Demachi–Yanagi event can be interpreted as the 2⁺ state of . The effect of hyperon mixing in and is investigated using one-boson-exchange potentials and quark-cluster-model interactions for the S=−2 sector. A close relation between nuclear deep hole states and hypernuclei is discussed, emphasizing the selection rule for fragmentation of the s-hole in light nuclei, which is promising for understanding the production mechanism of double-Λ and twin-Λ hypernuclei via Ξ-atomic capture.     

A mid-infrared spectrometer based on difference frequency generation

A mid-infrared spectrometer operating in the range from 3.42 to based on difference-frequency mixing of a tunable Ti:Sapphire laser and a diode-pumped monolithic Nd:YAG laser in periodically poled LiNbO₃ (PPLN) crystals was developed. A system line width of about 36 MHz was obtained. An energy conversion efficiency of 0.6 mW/W² was obtained at . The direct absorption spectra of pure methane and pure carbon dioxide samples were measured to test the performance of the spectrometer.     

Absolute photoionization cross sections with ultra-high energy resolution for Ar, Kr, Xe and N2 in inner-shell ionization regions

The high-resolution absolute photoionization cross sections for Ar, Kr, Xe and N₂ in the inner-shell ionization region have been measured using a multi-electrode ion chamber and monochromatized synchrotron radiation. The energy ranges of the incident photons for the target gases were as follows: Ar: 242–252 eV (2p Rydberg excitation), Kr: 1650–1770 eV (near the 2p ionization thresholds), Xe: 665–720 eV (near the 3d ionization thresholds) and 880–1010 eV (near the 3p ionization thresholds), N₂: 400–425 eV (N 1s excitation and ionization). It is the first time to measure the absolute ionization cross sections of Ar, Kr, Xe and N₂ over the present energy ranges with the energy resolution of over 10,000. The natural lifetime widths of , , and resonances for Ar, resonance for Xe, and resonance for N₂ have been obtained based on the cross sections determined. The ionization energies into the Ar⁺ (), Ar⁺ () and Xe⁺ () ionic states are also determined using the Rydberg formula.     

Optical–optical double resonance spectroscopy of the transition of CaOH

The state of CaOH was investigated using optical–optical double resonance spectroscopy. A combined least-squares fit of the double resonance transition data along with optical transition data and the millimeter-wave pure rotational data of the state was performed using an effective Hamiltonian. The spin–rotation constant was determined for the state for the first time. An analysis of these constants showed that the Ca–O bond length and spin–rotation parameter of the state have the smallest values of all the observed ²Σ⁺ states of CaOH. This evidence suggests the assignment of the state as arising from a Ca⁺ atomic orbital of mainly 5sσ character. This atomic orbital assignment was shown to be consistent with both previous work on CaF and recent theoretical calculations on CaOH.     

Observation of the state of CH2 by optical–optical double resonance

We report the observation of levels in the state of CH₂ via optical–optical double resonance spectroscopy. Direct transitions between the lowest singlet state and the state are allowed by symmetry, but weak because they correspond to a two electron excitation in the single configuration approximation to the electronic wavefunction. The observed transitions involve sequential single photon absorptions at visible and near infrared wavelengths using state intermediate levels. Recent ab initio results (S.N. Yurchenko et al., J. Mol. Spectrosc. 208 (2001), 136) predicted the positions of some of the levels which are confirmed by the present results. The new spectra provide accurate energies for rotational levels in the , l = 0 level of the state.     

Theoretical study of optical recording with a solid immersion lens illuminated by focused double-ring-shaped radially-polarized beam

Based on the Richards–Wolf vector diffraction theory, the intensity distributions in the recording sample near a solid immersion lens are calculated for two different radially-polarized beams ( and modes). Numerical results show that a double-ring-shaped mode focusing has some excellent features in near-field optical storage, compared with a single-ring-shaped mode focusing. The recording density is markedly improved, the focal depth of the near-field recording system is substantially increased, and a subsurface recording is effectively obtained using the mode focusing.     

Boundary Lax pairs for the Toda field theories

Based on the recent formulation of a general scheme to construct boundary Lax pairs, we develop this systematic construction for the affine Toda field theories (ATFT). We work out explicitly the first two models of the hierarchy, i.e. the sine-Gordon () and the models. The Toda theory is the first non-trivial example of the hierarchy that exhibits two distinct types of boundary conditions. We provide here novel expressions of boundary Lax pairs associated to both types of boundary conditions.     

Scaling and long-range dependence in option pricing I: Pricing European option with transaction costs under the fractional Black–Scholes model

This paper deals with the problem of discrete time option pricing by the fractional Black–Scholes model with transaction costs. By a mean self-financing delta-hedging argument in a discrete time setting, a European call option pricing formula is obtained. The minimal price of an option under transaction costs is obtained as timestep , which can be used as the actual price of an option. In fact, is an adjustment to the volatility in the Black–Scholes formula by using the modified volatility to replace the volatility σ, where is the Hurst exponent, and k is a proportional transaction cost parameter. In addition, we also show that timestep and long-range dependence have a significant impact on option pricing.     

Existence of different intermediate Hamiltonians in type A -fold supersymmetry

Type A -fold supercharge admits a one-parameter family of factorizations into product of first-order linear differential operators due to an underlying symmetry. As a consequence, a type A -fold supersymmetric system can have different intermediate Hamiltonians corresponding to different factorizations. We derive the necessary and sufficient conditions for the latter system to possess intermediate Hamiltonians for the case. We then show that whenever it has (at least) one intermediate Hamiltonian, it can admit second-order parasupersymmetry and a generalized 2-fold superalgebra. As an illustration, we construct a set of generalized Pöschl–Teller potentials of this kind.     

Low mass dilepton production at ultrarelativistic energies

Dilepton production in pp and Au+Au nucleus–nucleus collisions at as well as in In+In and Pb+Au at is studied within the microscopic HSD transport approach. A comparison to the data from the PHENIX Collaboration at RHIC shows that standard in-medium effects of the ρ,ω vector mesons—compatible with the NA60 data for In+In at and the CERES data for Pb+Au at —do not explain the large enhancement observed in the invariant mass regime from 0.2 to 0.5 GeV in Au+Au collisions at relative to pp collisions.     

Elliptic quantum group , Hopf algebroid structure and elliptic hypergeometric series

We propose a new realization of the elliptic quantum group equipped with the H-Hopf algebroid structure on the basis of the elliptic algebra . The algebra has a constructive definition in terms of the Drinfeld generators of the quantum affine algebra and a Heisenberg algebra. This yields a systematic construction of both finite- and infinite-dimensional dynamical representations and their parallel structures to . In particular we give a classification theorem of the finite-dimensional irreducible pseudo-highest weight representations stated in terms of an elliptic analogue of the Drinfeld polynomials. We also investigate a structure of the tensor product of two evaluation representations and derive an elliptic analogue of the Clebsch–Gordan coefficients. We show that it is expressed by using the very-well-poised balanced elliptic hypergeometric series .     

Three equations of state for solids considering thermal effect

 The Einstein model to consider thermal effect in universal equations of state (UEOS) is modified. It is proposed that the zero-point vibration term should be deleted in a thermal UEOS, and the parameters cannot be directly taken as experimental data at a reference temperature, V_R, B_R, and , but their values at absolute zero temperature, V₀, B₀, and . An approach is proposed to solve V₀, B₀, and from V_R, B_R, and . The approaches are applied to three typical universal EOSs, including the Baonza, mGLJ and Morse EOSs. The numerical results show that the solved values of parameters are almost identical for different EOSs. And the thermo-physical properties predicted through different EOSs are almost identical at zero- and low-pressure conditions, once the same approach and input experimental data are used to solve the parameters. It is concluded that the prediction of thermo-physical properties at zero- and low-pressure conditions cannot be taken as the criteria to judge the applicability of a universal EOS.     

Temperature-tunable nanosecond optical parametric oscillator based on periodically poled

We report a compact quasi-phase-matched optical parametric oscillator (OPO) using periodically poled MgO-doped LiNbO₃ with different grating periods. The OPO is pumped by a diode-pumped passively Q-switched Nd:YAG laser providing 4.8-ns pulses at 5.4-kHz repetition rate. The OPO generates signal and idler wavelengths tunable in the ranges of 1.5– and 2.8–, respectively, by changing the crystal temperature between room temperature and . The temperature-dependent Sellmeier equation for the extraordinary refractive index of MgO-doped LiNbO₃ is modified in the Mid-IR region, which gives an accurate prediction of the experimental temperature-tuning results. The linewidth of the signal wave is in the range of 0.5–1.0 nm without any controlling element.     

Widely tunable high power OPO based on a periodically poled MgO doped lithium niobate crystal

An optical parametric oscillator (OPO) based on a highly MgO doped periodically poled lithium niobate (PPMgLN) crystal was experimentally demonstrated and the result is presented in this report. The PPMgLN wafer was fabricated from a MgO doped (with 6 mol% doping concentration) lithium niobate crystal by means of high voltage pulse trigged domain reversal technique and has 20 domain reversal periods from 27.8 to with a step of between the neighbor periods. An acousto-optic (AO) Q-switched Nd³⁺:YVO₄ laser was used as the pumping laser. A maximum laser output power of 4.8 W has been achieved for the OPO when the pumping power is 10.8 W and it corresponds to an optic-optic conversion efficiency of 44%. By shifting the PPMgLN wafer, the periods of the domain structure on the PPMgLN wafer can be changed, thus enabling a wide spectral tuning range of the laser output from 1.42 to (for the signal light) and from 2.76 to (for the idler light).     

Quantum-dot size dependence of exciton fine-structure splitting

A systematic variation of the exciton fine-structure splitting with quantum dot size in single MOCVD-grown self-organized InAs/GaAs quantum dots is observed, ranging from several tens to as much as , thus covering more than one order of magnitude. Piezoelectricity is identified to be the dominant factor governing the observed trend. A change in sign of the fine-structure splitting is reported for the first time, originating from quantum dots with confinement potentials elongated in the and crystal direction, respectively.     

Fractional quasiexcitons in incompressible electron liquids

A new kind of many-body excitonic state composed of fractionally charged constituents is introduced. The constituents are a trion (X^-) embedded in an incompressible electron liquid and Laughlin quasiholes (QH's). Laughlin electron–trion correlations lead to an effective trion charge of -e/3. This many-body excitation is called “quasiexciton” and denoted by to distinguish it from a normal trion. The can bind one or two (e/3)-charged QH's, giving a neutral or a positive . The energy spectra and photoluminescence from radiative quasiexciton decay are studied numerically and interpreted using a generalized composite Fermion model of the e–X^- fluid.     

Measurement of at

We present a measurement of the cross section for Z boson production times the branching fraction to tau lepton pairs in collisions at . The measurement is performed in the channel in which one tau lepton decays into a muon and neutrinos, and the other tau lepton decays hadronically or into an electron and neutrinos. The data sample corresponds to an integrated luminosity of 1.0 fb⁻¹ collected with the DØ detector at the Fermilab Tevatron Collider. The sample contains 1511 candidate events with an estimated 20% background from jets or muons misidentified as tau leptons. We obtain , which is consistent with the standard model prediction.