Monte Carlo optimisation of correlated wave functions for normal two-electron systems

A simple, new type of correlated wave function is proposed for the studies of normal two-electron atomic systems: ψ(r₁, r₂) = Σc_mΦ_m(r₁, r₂) with Φ_m(r₁, r₂) = exp[−(r₁ + r₂)]/(br₁₂ + a)^m, where , a, b are non-linear variational parameters. A notable feature of this basis function is that only three terms are required within the framework of the Raleigh-Ritz variational principle to obtain fairly accurate energy eigenvalues and satisfactory cusp conditions. The non-linear variational parameters are optimised by using the Monte Carlo technique.     

Measurement of the slope parameter for the neutral pion spectrum in KL → πππ decay

The π⁰ spectrum in the K_L⁰ → 3π decay was measured using a wire chambers magnetic spectrometer. In the usual approximation, the matrix element can be expressed as: M² ≈ 1 + 2a₀(M_K/M_π²)(2T_π⁰−T_π⁰max) + a₁(M_K²/M_π⁴)(2T_π⁰−T_π⁰max)². We obtained a₀ = −0.282 ± 0.011 and a₁ consistent with zero.     

Entropy of planar random surfaces on the lattice

We study planar random surfaces on a hypercubic lattice in two and three dimensions by Monte Carlo techniques. Our data are consistent with the formula n₀(A;C) A^b₀A, where n₀(A;C) is the number of planar random surfaces with area A and boundary C. We find b₀ = −1.4 ± 0.2, = 5.31 ± 0.03 (for d = 2) and b₀ = −1.5 ± 0.2, = 7.13 ± 0.05 (for d = 3). The values of b₀ disagree with those obtained from the Polyakov string model.     

A new measurement of the weak magnetism term in the betaspectra of B and N

The betaspectra of ¹²B and ¹²N have been measured with a NaI crystal as spectrometer. Assuming a shape correction factor 1 + aW + bW² and b₋ = 1.106 × 10⁻⁴ MeV⁻², b₊ = −1.397 × 10⁻⁴ MeV⁻², the spectra yield a₋ = (+0.91 ± 0.11) × 10⁻² MeV⁻¹ and a₊ = (−0.07 ± 0.09) × 10⁻² MeV⁻. the a₋ − a₊ = (+0.98 ± 0.09) × 10⁻² MeV⁻¹ is in agreement with the weak magnetism prediction.     

Gauge coupling unification with extra dimensions and correction due to higher dimensional operators

We study the gauge coupling unification with extra dimensions. We take into account corrections due to the higher dimensional operators. We show the prediction of ₃(M_Z) is sensitive to such corrections, even if cΦ/M=O(0.01). We also discuss the b−τ Yukawa unification.     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.     

核磁共振碳谱研究:烷烃化学位移和(CSS)与分子路径指数矢量(VPM)

系统研究了核磁共振碳谱和化学位移规律及其定量构谱关系(QSSR).本文研究了一组十元素分子路径指数矢量VPM,并发现它与烷烃化学位移和CCS有良好线性相关性.采用多元线性回归进行准确估计与预测,结果优良.     

Interactions between a tetraanionic porphyrin and the methylviologen dication in methanol studied by fluorescence quenching reaction

Fluorescence decay curves for 5,10,15,20-tetrakis(4-sulfonatophenyl)-21H,23H-porphine tetraanion (TPPS⁴⁻) have been measured in the absence and presence of the methylviologen dication (MV²⁺) with various ionic strengths in methanol. In the presence of MV²⁺ the fluorescence decays can be expressed by a double exponential function, I(t = I₁exp(−t/τ₁) + I₂exp(−t/τ₂). The contribution by the faster decay component to the total fluorescence signal increases with increasing MV²⁺ concentration. The faster decay process is attributed to fluorescence from the excited state of a solvent-separated ion pair (SSIP) formed between TPPS⁴⁻ and MV²⁺, and the slower process is attributed to fluorescence from free TPPS⁴⁻ ions in the solution. Rate constants for the quenching of fluorescence from free TPPS⁴⁻ by MV²⁺ (k_q) and formation constants for the SSIP (K_SSIP) were calculated and both are found to decrease with increasing ionic strength. The decrease in k_q and K_SSIP values can be interpreted in terms of the shielding of electrostatic attraction between the ions.     

In-band M1 and E2 transition rates and collective structures in Ba

Subpicosecond mean lifetimes of eight excited states in ¹²⁸Ba populated via the ⁹⁶Zr(³⁶S,4n) reaction were measured by the Doppler-shift attenuation (DSA) technique using a line-shape analysis. The differential decay-curve method (DDCM) was applied for the lifetime determination. The B(E2) values in the yrast band indicate that the first band-crossing is with a proton S-band. The configuration πh_11/2d_5/2 of the negative-parity semi-decoupled bands is confirmed by the measured B(E2, I → I − 2) and B(M1, I → I − 1) transition strengths. The higher-lying “dipole” band in ¹²⁸Ba can be described as a high-K four-quasiparticle band built on the prolate configuration (πh_11/2d_5/2) (νh_11/2g_7/2).     

Search for narrow NNπ resonances in exclusive pp→ppππ measurements

Narrow structures in the range of a few MeV have been searched for in ppπ⁺ and ppπ⁻ invariant mass spectra (M_ppπ⁺ and M_ppπ⁻) obtained from exclusive measurements of the pp→ppπ⁺π⁻ reaction at T_p=725,750 and 775 MeV using the PROMICE/WASA detector at CELSIUS. The selected reaction is particularly well suited for the search for dibaryon resonances decoupled from NN and/or NΔ. In the mass range 2020 MeV/c²<m_dibaryon<2085 MeV/c² no narrow structures could be identified on the 3σ level of statistical significance neither in M_ppπ⁻ nor in M_ppπ⁺ giving an upper limit (95% C.L.) for dibaryon production in this reaction of σ<20 nb.     

Compton scattering by the proton through θcms = 75° and 90° in the Δ-resonance region

Differential cross sections for Compton scattering by the proton have been measured in the energy interval between 200 and 500 MeV at scattering angles of θcms = 75° and θcms = 90° using the CATS, the CATS/TRAJAN, and the COPP setups with the Glasgow Tagger at MAMI (Mainz). The data are compared with predictions from dispersion theory using photo-meson amplitudes from the recent VPI solution SM95. The experiment and the theoretical procedure are described in detail. It is found that the experiment and predictions are in agreement as far as the energy dependence of the differential cross sections in the Δ-range is concerned. However, there is evidence that a scaling down of the resonance part of the M1+3/2 photo-meson amplitude by (2.8 ± 0.9)% is required in comparison with the VPI analysis. The deduced value of the M1+3/2-photoproduction amplitude at the resonance energy of 320 MeV is: |M1+3/2| = (39.6 ± 0.4) × 10−3 mπ+−1.     

The crystallographic symmetries of single BaPb1−xBixO3 crystals grown from BaCO3-PbO2-Bi2O3 solutions

Single crystals of Perovskite-type oxide BaPb_1−xBi_xO₃ are grown from BaCO₃-PbO₂-Bi₂O₃ solutions which are weighed in two kinds of mixing ratios: X/2 mol % BaCO₃ − (100−X) mol % PbO₂ − X/2 mol % Bi₂O₃ and (10+X/2) mol % BaCO₃ − (90−X) mol % PbO₂ − X/2 mol % Bi₂O₃ These room temperature crystal structures are examined by using an X-ray powder diffraction method. The crystals grown from X/2−(100−X)−X/2 mol % solutions are orthorhombic at room temperature, while the structures are tetragonal with crystals grown from relatively Ba rich and Pb poor ( (10+X/2)−(90−X)−X/2 mol % ) solutions. This result indicates that the difference in the mixing ratio of the initial materials brings about a drastic structural change. The orthorhombic and the tetragonal crystals of x0.25 exhibit superconducting transition at 10K and 12K, respectively. The transition temperature in the latter is 2K higher than the former. In the light of this result, some difference between orthorhombic and tetragonal crystals is considered to influence superconductivity in this system.     

Effect of Sn doping on the magnetic and transport properties of LaMnO3+δ

We report the influence of the Sn doping on the magnetotransport properties of the LaMnO_3+δ perovskite. Two series of samples with nominal LaSn_xMn_1−xO_3+δ (I series) and La_{(1−x)/(1+x)}Sn_xMn_1−xO_3+δ (II series) compositions (x=0, 0.025, 0.05 and 0.10) were prepared at T_s=750°C. The M(T) data under 0.01 and 0.5 T for the I series reveal a depressed magnetization as the Sn content increases suggesting the presence of magnetic clusters with a superparamagnetic behavior. Resistivity measurements indicate an insulator material for all Sn content independently of the applied magnetic field. On the contrary, for the II series the M(T) and M(H) data reveal FM behavior and an improvement of the magnetization as Sn increases. These samples show magnetoresistance. The magnetotransport properties are discussed in terms of the presence of A-site cation vacancies.     

Mössbauer investigations on Np3S5

The 59.5 keV Mössbauer resonance of ²³⁷Np has been measured in Np₃S₅ at 77 and 4.2 K. At 77 K, two different quadrupolar splittings are observed. The first one (δ₁ = −5(1) mm sec⁻¹/NpAl₂) is assigned to the Np⁴⁺ ions and the second one (δ₂ = 28(1) mm sec⁻¹/NpAl₂) is assigned to the Np³⁺ ions. At 4.2 K the spectrum gives a ratio of areas S(Np³⁺)/S(Np⁴⁺) of 2.0. These results clearly confirm the crystallographic data of this mixed-valence material.     

Anomalous magnetotransport phenomena in θ-(BEDT-TTF)2I3

Anomalous magnetotransport phenomena have been observed in θ-(BEDT-TTF)₂I₃ crystals at temperatures below 15 K. The magnetoresistance M : (1) is a linear function of the magnetic field H, (2) is not affected by the angle between the electric current and the magnetic field, (3) but depends on the magnetic field orientation with respect to the crystal axis. Magnetoresistance is expressed as M = (aH²_a + bH²_b + cH²_c)₀^-3/2/H in terms of H = (H_a, H_b, H_c), the zero field resistivity ₀, and parameters a, b, and c which are independent of temperature and magnetic field. We have found that b a > c. Magnetoresistance up to 40 is observed for H = 7T along the b-axis at T = 1.5K.     

Distance functions and statistics

This paper proves that the Riemannian distance function is maximal in the class of distance functions associated with the Riemannian metric tensor.

Secondly, it is proven that there exists a unique minimum of

on a complete Riemannian surface (M,g) with small curvature, small curvature change and injectivity radius +∞. Here p_iM and γ_v is the maximal geodesic with initial velocity v and 0<t₁<<t_m.     

1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.     

A new upper bound formula for the ground state energies of N-boson systems

The energy E_N of an N-body system of pairwise interacting bosons is shown to satisfy the inequality, E_N < [N(N − 1)/n(n − 1)] E_n, where N > n 2. This inequality generalizes the Bruch-Sawada result, E₃ < 3E₂, and is superior in its predictive ability to Lim et al.'s .     

Synthesis and electrophysical properties of novel lithium ion conducting oxides

Novel lithium ion conducting oxides with perovskite structure have been synthesized and studied. It has been found that the La_2/3−xLi_3xTiO₃ and La_2/3−xLi_3xNb₂O₆ compounds have a perovskite structure at 1/24 < x < 1/6 and 0 < x < 3/10, respectively. The results of investigating the electrical properties of both groups of perovskites indicate a high lithium ion conductivity.     

Two separate Li ionic motions observed by Li and B NMR in xLi2S + (1 − x)B2S3 glassy fast ionic conductors

Studies of ion dynamics in the highly conductive glassy fast ionic conductor (FIC) xLi₂S + (1 − x)B₂S₃ (x = 0.65 and 0.70) were made with NMR nuclear spin lattice relaxation (NSLR) R₁(ω, T) of both mobile ⁷Li and immobile ¹¹B ions, and ⁷Li NMR line narrowing δν(T). The possible dependence of ion dynamics on the short range order structures (SRO) and the distribution of activation energies (DAE) in this highly conductive FIC was investigated. Two Gaussian DAE were employed to fit ⁷Li NSLR data, where each Gaussian DAE was correlated to a separate ¹¹B NSLR in a BS₃ and in a BS₄ group. The long range diffusion of Li ions among BS₃ groups and a seemingly localized ionic hopping motion around BS₄ group is suggested as a microscopic model for the ion dynamics in thioborate glasses, namely a ‘two channel relaxation’.