Effect of the three-body force on trinucleon bound systems consideringS andS′-state admixture

We report the calculation of binding energy, charge form factor and point-like proton density of both³H and³He by the hyperspherical harmonics method with the inclusion of two-pion exchange three-nucleon force (Fujita-Miyazawa type). For the two-body force theN-N Afnan-Tang S-3 potential is taken. Coulomb and three-body forces are treated nonperturbatively. In this calculation the mixed symmetryS′-state of the trinucleon ground state is considered along with the space totally symmetricS-state.     

Trinucleon system with Reid soft core potential by hyperspherical harmonics expansion method

The hyperspherical harmonics expansion method has been used to solve the trinucleon system where the nucleons interact through Reid soft core potential. The binding energy of triton, both for extreme adiabatic approximation and uncoupled adiabatic approximation, and theS-state,S′-state andD-state probabilities are calculated and compared with the results by the Faddeev method.     

Natural origin of SO3-spinors in an eight-dimensional Kaluza theory exhibiting an additional U1×SU2 internal symmetry

The higher-dimensional spaceM ₄×S ₁×S ₃ (M ₄ = Minkowski space) is assumed. The symmetry group ofS ₃ isSO ₄ SU ₂×SU₂ Gravitational waves produce a symmetry breaking so thatSO ₃, rotations inM ₄ are linked with one of theSU ₂. Certain components of the metrical tensor ofM ₄×S ₁×S ₃, appear then as spinor fields.     

Crystal structure of the ceramic superconductor BaPb0.75Bi0.25O3

The ceramic superconductor BaPb_0.75Bi_0.25O₃ is monoclinic atT<430 K with space groupI2/m. Lattice constants and the atomic coordinates result from 20 reflection groups (12<2<120°, =1.1267 Å) collected with a high resolution powder diffractometer using a synchrotron radiation source and a full neutron powder pattern (6<2<140, =1.909 Å). Synchrotron and neutron data were simtultaneously refined with SIMREF, a new profile refinement program, based on the Rietveld method. Group theoretical analysis of the distortion field leading from the ideal perovskite structure toI2/m exhibitsR ₄ ⁺ symmetry. A comparison is made with the corresponding distortions in nonsuperconducting BaBiO₃ where three different symmetry types are identified. The space groupI2/m found for BaPb_0.75Bi_0.25O₃ allows only one type of averaged (Pb/Bi)O₆ octahedron in the structure: this may support valence fluctuations and hence contribute to the mechanism of superconductivity in this particular compound.     

The Flavor Physics in Unified Gauge Theory from an S3 × P Discrete Symmetry

We investigate the phenomenological implication of the discrete symmetry S₃ × P on flavor physics in SO(10) unified theory. We construct a minimal renormalizable model which reproduce all the masses and mixing angle of both quarks and leptons. As usually the SO(10) symmetry gives up to relations between the down sector and the charged lepton masses. The underlining discrete symmetry gives a contribution (from the charged lepton sector) to the PMNS mixing matrix which is bimaximal. This gives a strong correlation between the down quark and charged lepton masses, and the lepton mixing angles. We obtain that the small entries V _ub, V _cb, V _td, and V _ts in the CKM matrix are related to the small value of the ratio δ m² _solΔ m² _atm: they come from both the S₃×P structure of our model and the small ratio of the other quark masses with respect to m _t. Wonderfully, with our model, we fit 17 experimental data %with only 13 free relevant combinations of vevs.     

Effect of two body core on the charge form factor of3He including three body force and meson exchange current

We compare the effect of two body core on the charge form factor of³He by the hyperspherical harmonics expansion method using various 2BF potentials with the inclusion of three body force. We also include the meson exchange current contribution to the CFF for the same potentials in addition to the 3BF. The results indicate that the combined effect of 3BF and MEC (i) movesq _min ² (the first diffraction minimum) appreciably to the left, amount of shift depends on the 2BF atr ₁₂∼0.7 fm and (ii) enhancesF _max (the height of the secondary maximum of CFF) by an appreciable amount, the increment in general increases with the repulsive core of 2BF (r⩽0.1 fm).     

Controllable generation of harmonics by means of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7 − <Emphasis Type="Italic">x</Emphasis></Subscript> superconductors

The nonlinear magnetic properties of YBa₂Cu₃O_{7 − x} high-temperature superconducting polycrystals are investigated. Using the results of investigations as a basis, a method for controlling the amplitudes of generated magnetization harmonics is worked out and a controllable harmonic generator is devised. The amplitudes of the harmonics are controlled by means of a permanent magnetic field or current. The use of YBa₂Cu₃O_{7 − x} polycrystals makes it possible to produce a spectrum with offering a large number of higher harmonics. An YBa₂Cu₃O_{7 − x} -based device has a wide dynamic range; its design is simple and reliable in a wide interval of the amplitudes of an input signal.     

Non-symmetrized Basis Function for Identical Particles

We propose to use the hyperspherical harmonics (HH) basis to solve the A-body system problem without explicit symmetrization or anti-symmetrization of the basis functions as required by the statistic of the system. Therefore, the HH basis set is expressed with respect to a given ordering of the A particles. However, after diagonalization, the eigenvectors reflect the symmetries of the Hamiltonian, and it is possible to identify the physical states having the expected symmetry under particle permutation. As an example we study the case of four particles interacting through a short-range spin-dependent interaction and the Coulomb potential.     

Local versus hyperspherical modes of formaldehyde

Near-degenerate local versus hyperspherical modes of H₂CO are evaluated as vibrationally highly excited H₂C-stretches coupled to cold CO-bonds, for the electronic ground state (S ₀). Similar to isolated CH₂ fragments, the wavefunctions of local modes have frontier lobes pointing towards the two equivalent H·+·HCO radical product configurations. In contrast, the wavefunctions of hyperspherical modes extend approximately along arcs on spheres around the four-atom-coincidence. The wavefunctions are represented by reduced linear combinations of symmetry-adapted products of Morse times harmonic oscillator wavefunctions (LCSPM-HO). The dominant basis functions constituting the molecular vibrational states are selected by an efficient reduction technique.     

Relativistic Landau levels in a hyperspherical finite cavity

We consider a Dirac electron in the hyperspherical cavityS ³. A uniform magnetic field is applied, and the electron is given an arbitraryg-factor. By exploiting the symmetry properties of the hypersphere, we obtain closed-form expressions for the energy levels. This will allow the rigorous analysis of infrared behaviour. The correspondence between hyperspherical states and ordinary quantum numbers is discussed. We also show that the infinite-volume limit reduces to the proper result for ordinary flat space. In the presence of a magnetic field, however, the rate at which the limit is approached depends on theg-factor anomaly as well as on an auxiliary parameter which occurs in the hyperspherical Dirac equation.This work was supported by the U.S. Dept. of Energy under contract DE-AC02-76ER-03066.     

Invariant states in statistical mechanics

Mathematically we consider aC*-algebra , acted upon by the groupT of space-translations, which has an asymptotic abelian property. We analyse invariant states over . Physically this programme can be considered as a kinematical study of equilibrium states in statistical mechanics. Each invariant state can be uniquely decomposed into elementary invariant states (E-states). These elementary states have, amongst other characteristics, the physical property that space-averages of local observables are constants in the corresponding representations. In anE-state the discrete spectrum S _D of space-translations is additive which gives rise to the classificationE _I,E _II, andE _III corresponding to the three possibilities that S _D contains one point, a lattice of points, or a set with accumulation points. AnE _II-state can be uniquely decomposed into states (L-states) having a symmetry with respect to a closed subgroupT _L of (S _D and T _L are reciprocal lattices).L-states have properties with respect toT _L analogous to the properties ofE _I-states with respect toT. The decomposition intoL-states is the inverse process of homogenizing a lattice state by smearing it over a lattice distance. The mathematical methods which we employ have more general applications.     

State sum models and simplicial cohomology

We study a class of subdivision invariant lattice models based on the gauge groupZ _p , with particular emphasis on the four dimensional example. This model is based upon the assignment of field variables to both the 1- and 2-dimensional simplices of the simplicial complex. The property of subdivision invariance is achieved when the coupling parameter is quantized and the field configurations are restricted to satisfy a type of mod-p flatness condition. By explicit computation of the partition function for the manifoldRP ³×S ¹, we establish that the theory has a quantum Hilbert space which differs from the classical one.Supported by Stichting voor Fundamenteel Onderzoek der Materie (FOM)     

The generalization of the Schwarzschild solution in quasi-Riemannian theories

We discuss the generalization of the Schwarzschild solution of General Relativity to an (N + M)-dimensional quasi-Riemannian theory with tangent space groupSO(1,N–1)×SO(M). We find some regular blackhole solutions whose horizon has a topologySN–2×S ^M, but which are not asymptotically flat. We also discuss the dimensional reduction of the theory     

Supersymmetric preon models with three-fermion generations

A class of supersymmetric preon models is considered in which the hypercolour groupG _HC and the unbroken flavour groupG _f anomalies are zero without needing spectators. It is shown that forG _HC=SU(2) and SU(3) quarks and leptons as composites can be obtained satisfying ’t Hooft’s anomaly matching conditions. For the case ofG _HC=SU(3),G _f can accommodate a horizontal symmetry group to describe just three generations.     

Hyperspherical harmonics and the nuclear four-body problem

A method proposed earlier by Aguilera, Moshinsky, and Kramer, for adapting a system of translationally invariant four-particle harmonic oscillator functions to the symmetry of the permutation group S(4), is applied to hyperspherical harmonic functions depending on three relative vectors. Except for a few cases in which diagonalization of matrices is required, the method gives closed formulas for orthonormal sets of harmonic functions with good permutational symmetry. The matrix elements of S(4) permutations with respect to the harmonic functions are obtained.     

The first order of the hyperspherical harmonic expansion method

The hyperspherical harmonic expansion method is studied in this work. Our attention is focused on the properties of the L_m-approximation in which only the hyperspherical harmonics of minimal order are taken into account. Exact solutions of the Schrödinger equation for a few simple hyperspherical potentials are given. Recipes for constructing antisymmetric hyperspherical harmonics for fermions are investigated, and various procedures to derive the effective potential in the L_m-approximation are discussed. The method is applied to the calculation of ground state and hyperradial excited states (which are identified as the breathing modes) of doubly-magic nuclei. Finally, the energy per particle is derived in the L_m-approximation with Skyrme like forces for an infinitely heavy self-conjugate nucleus.     

Quantum deformation of lorentz group

A one parameter quantum deformationS _μ L(2,ℂ) ofSL(2,ℂ) is introduced and investigated. An analog of the Iwasawa decomposition is proved. The compact part of this decomposition coincides withS _μ U(2), whereas the solvable part is identified as a Pontryagin dual ofS _μ U(2). It shows thatS _μ L(2,ℂ) is the result of the dual version of Drinfeld's double group construction applied toS _μ U(2). The same construction applied to any compact quantum groupG _c is discussed in detail. In particular the explicit formulae for the Haar measures on the Pontryagin dualG _d ofG _c and on the double groupG are given. We show that there exists remarkable 1-1 correspondence between representations ofG and bicovariant bimodules (“tensor bundles”) overG _c . The theory of smooth representations ofS _μ L(2,ℂ) is the same as that ofSL(2,ℂ) (Clebsh-Gordon coefficients are however modified). The corresponding “tame” bicovariant bimodules onS _μ U(2) are classified. An application to 4D ₊ differential calculus is presented. The nonsmooth case is also discussed.     

A basis-free approach to time-reversal for symmetry groups

We develop a basis-free approach to time-reversal for the quantal angular momentum group,SU2, and apply these methods to the physical symmetrySU2_isospin,SU3_flavor,SU3_nuclear and the nuclear collective symmetry groupSL(3,R) of Gell-Mann and Tomonaga.     

Chemical bath deposition of Bi2S3 films by a novel deposition system

Bismuth sulfide (Bi₂S₃) films were chemically deposited by a novel deposition system in which ammonium citrate was used as the chelating reagent. Two sulfur source thioacetamide (TA) and sodium thiosulfate (Na₂S₂O₃) were used to prepare Bi₂S₃ films. Both the as-prepared films have amorphous structure. However, annealing can improve the crystallization of the films. The composition of the films prepared by TA and Na₂S₂O₃ are all deviate from the stoichiometric ratio of Bi₂S₃. The Bi₂S₃ films are all homogeneous and well adhered to the substrate. The optical properties of the Bi₂S₃ films are studied. The electrical resistivity of the as-prepared films are all around 7 × 10³ Ω cm in dark, which decreases to around 1 × 10³ Ω cm under 100 mW/cm² tungsten-halogen illumination. After the annealing, the dark resistivity of the Bi₂S₃ film prepared by TA decreases by four magnitudes. In contrast, the dark resistivity of the Bi₂S₃ film prepared by Na₂S₂O₃ only decreases slightly.     

Field theory onR×S 3 topology. II: The Weyl equation

A Weyl-type equation onR×S ³ topology is derived, as a generalization to previously obtained Klein-Gordon- and Schrödinger-type equations for the same topology. The general solution of the new equation is given as an expansion in the matrix elements of the irreducible representations of the groupSU ₂. The properties of the solutions are discussed.Supported in part by the Colgate Research Council.