On the Convergence Rate of the Euler-α, an Inviscid Second-Grade Complex Fluid, Model to the Euler Equations

We study the convergence rate of the solutions of the incompressible Euler-α, an inviscid second-grade complex fluid, equations to the corresponding solutions of the Euler equations, as the regularization parameter α approaches zero. First we show the convergence in H ^s , s>n/2+1, in the whole space, and that the smooth Euler-α solutions exist at least as long as the corresponding solution of the Euler equations. Next we estimate the convergence rate for two-dimensional vortex patch with smooth boundaries.     

Calculation of Energy Levels of Nucleus ^127I in the Particle-Triaxial-Rotor Model

Theoretical calculations have been performed for nucleus ^127I in the framework of the particle-triaxial-rotor model.The calculated results indicate that both the 5^ /2 and 7^ /2 bands are oblate deformed bands.Their comfigurations are associated with the πd5/2[402]5/2 and πg7/2[404]7/2 orbitals and the strong mixing between them.Meanwhile a possible explanation of the strong mixing is given.     

Theoretical Calculation of Rotational Bands of ^179Pt in the Particle-Triaxial-Rotor Model

Theoretical calculations have been performed for nucleus ^179Pt in the particle-triaxial-rotor model with variable moment of inertia. The obtained energy spectrum agrees with the experimental data quite well. The calculated results indicate that the bands 1/2^- and 7/2^ are triaxial deformation bands and originate mainly from the v[521]1/2^- and v[633]7/2^ configurations respectively.     

Dynamical Calculation of Θ+ Mass and Decay width in the Quark Model

In this paper we study the mass splitting and the decay width of pentaquark (Θ⁺) at the ground states in the framework of flux tube, quark delocalization and color screening model. We consider the pentaquark as diquark-triquark configuration and obtained closer values of mass splitting and the decay width of Θ⁺ to the experimental data.     

Study of the Isospin Mixing in 6Li with α + p + n Three-Body Model

We calculate the isospin mixing probabilities for both T = 0 and T = 1 states of ⁶Li systematically, and compare them to clarify the relation between the structure of ⁶Li and the isospin mixing probabilities. As a result, the effect of halo structure on the isospin mixing cannot be seen clearly. The effect of the coupling to the continuum states such as of ⁵He + p and ⁵Li + n is suggested.     

Calculation of the Parameters of a One‐Coordinate Model of the VGaSAs and VGaSnGa Complexes in Gallium Arsenide

Experimental optical bands of the emitting complexes (a gallium vacancy with a donor at the nearest, from the vacancy, sublattice site) V_GaS_As and V_GaSn_Ga in GaAs are investigated in a wide temperature range. The parameters of a onecoordinate model of these centers are determined. A configurationcoordinate diagram of the V_GaS_As complex is constructed. Calculation of the field dependences of emission rates is carried out in terms of the parameters of the onecoordinate model of the V_GaS_As complex and the data obtained are compared with the results of experimental studies of the emission of electron holes from a deeplying center of the V_GaS_As complex.     

Intermolecular Vibrational Coupling A Model Calculation for the Out-of-Plane Vibration of CO3 −- in Compounds with the Aragonite Structure

Abstract

¹³CO₃ ^?- substituted compounds with the aragonite structure show a fine structure of the out-of-plane vibration in the infrared spectra. A simple quantum mechanical model of coupled oscillators is developed to describe quantitatively the observed spectra. The spectra can be interpreted in terms of isolated ^12CO ₃ ^?- and ¹³CO₃ ^?- clusters, whose eigenfunctions interact. The heavy ions have localized vibrations, whereas clusters of the light ion with more than one ion show only localized vibrations at small coupling; stronger coupling results in resonant modes. Intensitytransfer from light to heavy ion bands is explained and the consequences of interaction between different clusters are discussed.     

Coupled-Channels Faddeev Equations for the K ??+?d Break-Up Reaction and the Shape of the ��(1405) Resonance

Coupled-channels Faddeev equations are derived for the K ^? + d break-up reaction with inclusion of the isospin breaking effect of the ${\bar{K}^0-K^-}$ mass difference.     

Model of grain-boundary self-diffusion in α- and β-phases of titanium and zirconium

A model of the grain-boundary self-diffusion process in metals undergoing phase transitions in the solid state is proposed. The model is based on the ideas and approaches of the theory of nonequilibrium grain boundaries. It is shown that the range of application of basic relations of this theory can be extended, and they can be used to calculate the parameters of grain-boundary self-diffusion in high-temperature and low-temperature phases of metals with phase transition. Based on the constructed model, activation energies of grainboundary self-diffusion in titanium and zirconium are calculated, and their anomalously low values in the low-temperature phase are explained. The calculated activation energies of grain-boundary self-diffusion are in good agreement with experimental data.     

Study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge

A study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge is presented in the case of the gauge group SU(2)$SU\left(2\right)$ and for different Euclidean space–time dimensions. Explicit examples of classes of normalizable zero modes and corresponding gauge field configurations are constructed by taking into account two boundary conditions, namely: (i) the finite Euclidean Yang–Mills action, (ii) the finite Hilbert norm.     

ΛΛ 6 He and Λ 9 Be systems in the three-body cluster model treated on the basis of differential Faddeev equations

The _ΛΛ ⁶ He and _Λ ⁹ Be hypernuclei are treated as the S=0, T=0 (for the former) and S=1/2, T=0 (for the latter) bound states of the three-cluster systems ΛΛα and Λαα, respectively. The cluster-reduction method is used to solve the s-wave differential Faddeev equations for these systems. On the basis of the MT I–III model, the ΛΛ interaction potential is specified in the form $V_{\Lambda \Lambda } = \frac{2}{3}V_{NN} $ . Phenomenological potentials are used to describe Λα and αα interactions. The binding energies of the _ΛΛ ⁶ He and _Λ ⁹ Be hypernuclei and the parameters of low-energy Λ-hyperon and α-particle scattering on a _Λ ⁵ He hypernucleus are calculated. It is shown that the proposed ΛΛ interaction potential makes it possible to reproduce faithfully the binding energy of the _ΛΛ ⁶ He hypernucleus and that scattering in the Λ _Λ ⁵ He system is similar to neutron scattering on a deuteron.     

Calculation of the fine structure of the level in Rydberg state of lithium

The level shift and level formula of lithium atom in Rydberg states are achieved by means of the calculation of polarization of the atomic core （including the contribution of dipole moment, quadrupole moment and octupole moment） ; meanwhile, the effect of relativity theory, the orbital angular momentum L and the spin angular momentum S coupling （IS coupling）, and high order correction of the effective potential are considered. Thesome fine structures （N = 5- 12, L = 4-9, J = L ± 1/2） and the corresponding level intervals in Rydberg statescan be calculated by the above-mentioned level formula and compared with correlated experimental data.     

Calculation of the fine structure of the level in Rydberg state of lithium

The level shift and level formula of lithium atom in Rydberg states are achieved by means of the calculation of polarization of the atomic core (including the contribution of dipole moment, quadrupole moment and octupole moment);meanwhile, the effect of relativity theory, the orbital angular momentum L and the spin angular momentum S coupling (LS coupling), and high order correction of the effective potential are considered. The some fine structures (N=5～12,L=4～9,J=L±1/2) and the corresponding level intervals in Rydberg states can be calculated by the above-mentioned level formula and compared with correlated experimental data.     

Orbital Relaxation Effects in the Calculation of Aluminum Kα Absorptions

A recent experimental Kα transmission spectrum of an Muminum plasma is theoretically studied by a detailed level accounting model. It is found that the orbital relaxation effects of the K- and L-shell orbitals should be considered to calculate accurate line positions and strengths. To do this the initial and the final radial wave functions of Kα lines are respectively optimized by solving the full relativistic Dirac-Fock equation. Extensive configuration interaction calculations are performed to obtain the energy levels and the oscillator strengths. It is shown that both the line positions and the line strengths agree quite well with experiment when the orbital relaxations are considered.     

Solving Linear Systems of Equations by Using the Concept of Grover’s Search Algorithm: an IBM Quantum Experience

International Journal of Theoretical Physics - Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here,...     

Three-Body Calculation of the 4He（aH,γ）7Li and 4He（aHe,γ）7Be Reactions and Structure of the 7Li and 7Be at Solar Energies

The two 3H＋4He and 3He＋4He fusion reactions at low energies are usually viewed as an approximate external capture process. We study the 4He（3H,γ）rLi and 4He（SHe,γ）7Be reactions in a cluster model, which can take into account two- and three-body electromagnetic currents, using minimal substitution in the explicit momentum dependence of the two- and three-cluster interactions. Our main goal is to explore how the cross section of the low-energy 3H＋4He or 3He＋4He capture reactions depends on energy. The astrophysical S-factors for these reactions are calculated at very low energies. We construct the conserved realistic Argonne v18 for two nucleons and Urbana IX or Tucson-Melbourne three-cluster interactions, which are considered for calculation. We also calculate the binding energies and the structural properties of a Hq-4He or 3He＋4 He systems. The binding energies are found to be -37.72 （-36.32） MeV and -39.35 （-37.43） MeV, with （without） three-body interactions for 7Be and 7 Li, in satisfactory agreement with other theoretical results and experimental data, respectively.     

Applications of the modified Faddeev equations: t + dμ-

We present calculations of the cross-sections for elastic as well as for muon transfer in t + dμ^- collisions below the tμ^-(n = 2) threshold. The appropriate mass-scaled Jacobi coordinates are used in the direct and rearrangement channels. The K-matrix elements are obtained from the solution of multichannel Faddeev equations in the configuration space formulation. A bipolar expansion and spline representation are used in the numerical solution of the modified Faddeev equations. This revised version was published online in August 2006 with corrections to the Cover Date.     

On an Essential Spectrum of the Random p-Adic Schrödinger-type Operator in the Anderson Model

The random p-adic Schrödinger-type operators are considered. The p-adic analogue of the Anderson model is defined for these operators and the spectral properties of this model are investigated.     

Can the Highly Symmetric SU(4) Spin—Orbital Model Be Realized in α-ZrCl3?

JETP Letters - We study physical properties of layered α-ZrCl3 as a potential candidate for the physical realization of the SU(4) spin—orbital model. Both DFT and DFT + U + SOC...