Dielectron widths of the <Emphasis Type="Italic">S</Emphasis>-, <Emphasis Type="Italic">D</Emphasis>-vector bottomonium states

The dielectron widths of Y(nS)(n = 1, …, 7) and vector decay constants are calculated using the relativistic string Hamiltonian with a universal interaction. For Y(nS) (n = 1, 2, 3) the dielectron widths and their ratios are obtained in full agreement with the latest CLEO data. For Y(10580) and Y(11020) a good agreement with experiment is reached only if the 4S-3D mixing (with a mixing angle θ = 27°± 4°) and 6S-5D mixing (with θ = 40°±5°) are taken into account. The possibility to observe higher “mixed D-wave” resonances, $ \tilde \Upsilon $ \tilde \Upsilon (n ³ D ₁) with n = 3, 4, 5 is discussed. In particular, $ \tilde \Upsilon $ \tilde \Upsilon (≈11120), originating from the pure 5³ D ₁ state, can acquire a rather large dielectron width, ∼130 eV, so that this resonance may become manifest in the e ⁺ e ⁻ experiments. On the contrary, the widths of pure D-wave states are very small, Γ _ee (n ³ D ₁)≤ 2 eV.     

Localization of Surface Spectra

We study spectral properties of the discrete Laplacian H on the half-space with random boundary condition ; the V(n) are independent random variables on a probability space and λ is the coupling constant. It is known that if the V(n) have densities, then on the interval [-2(d+1), 2(d+1)] (=σ(H ₀), the spectrum of the Dirichlet Laplacian) the spectrum of H is P-a.s. absolutely continuous for all λ [JL1]. Here we show that if the random potential P satisfies the assumption of Aizenman–Molchanov [AM], then there are constants λ _d and Λ _d such that for |λ|<lambda; _d and |λ|> Λ _d the spectrum of H outside σ(H ₀) is P-a.s. pure point with exponentially decaying eigenfunctions. Received: 3 December 1998 / Accepted: 27 May 1999     

The Birth of the Infinite Cluster:¶Finite-Size Scaling in Percolation

We address the question of finite-size scaling in percolation by studying bond percolation in a finite box of side length n, both in two and in higher dimensions. In dimension d= 2, we obtain a complete characterization of finite-size scaling. In dimensions d>2, we establish the same results under a set of hypotheses related to so-called scaling and hyperscaling postulates which are widely believed to hold up to d= 6. As a function of the size of the box, we determine the scaling window in which the system behaves critically. We characterize criticality in terms of the scaling of the sizes of the largest clusters in the box: incipient infinite clusters which give rise to the infinite cluster. Within the scaling window, we show that the size of the largest cluster behaves like n ^d π _n , where π _n is the probability at criticality that the origin is connected to the boundary of a box of radius n. We also show that, inside the window, there are typically many clusters of scale n ^d π _n , and hence that “the” incipient infinite cluster is not unique. Below the window, we show that the size of the largest cluster scales like ξ ^d π_ξ log(n/ξ), where ξ is the correlation length, and again, there are many clusters of this scale. Above the window, we show that the size of the largest cluster scales like n ^d P _∞, where P _∞ is the infinite cluster density, and that there is only one cluster of this scale. Our results are finite-dimensional analogues of results on the dominant component of the Erdős–Rényi mean-field random graph model. Received: 6 December 2000 / Accepted: 25 May 2001     

On Two-Temperature Problem for Harmonic Crystals

We consider the dynamics of a harmonic crystal in d dimensions with n components, d,n≥1. The initial date is a random function with finite mean density of the energy which also satisfies a Rosenblatt- or Ibragimov–Linnik-type mixing condition. The random function is translation-invariant in x ₁,...,x _d?1 and converges to different translation-invariant processes as x _d →±∞, with the distributions μ _±. We study the distribution μ _t of the solution at time $t \in \mathbb{B}$ . The main result is the convergence of μ _t to a Gaussian translation-invariant measure as t→∞. The proof is based on the long time asymptotics of the Green function and on Bernstein's “room-corridor” argument. The application to the case of the Gibbs measures μ _±=g _± with two different temperatures T _± is given. Limiting mean energy current density is ?(0,...,0,C(T ₊?T _?)) with some positive constant C>0 what corresponds to Second Law.     

Zero-Temperature Dynamics of ±J Spin Glasses¶and Related Models

We study zero-temperature, stochastic Ising models σ ^t on Z ^d with (disordered) nearest-neighbor couplings independently chosen from a distribution μ on R and an initial spin configuration chosen uniformly at random. Given d, call μ type ℐ (resp., type ℱ) if, for every x in Z ^d , σ _x ^t flips infinitely (resp., only finitely) many times as t→∞ (with probability one) – or else mixed type ℳ. Models of type ℒ and ℳ exhibit a zero-temperature version of “local non-equilibration”. For d=1, all types occur and the type of any μ is easy to determine. The main result of this paper is a proof that for d=2, ±J models (where μ=αδ _J +(1-α)δ_{- J} ) are type ℳ, unlike homogeneous models (type ℐ) or continuous (finite mean) μ's (type ℳ). We also prove that all other noncontinuous disordered systems are type ℳ for any d≥ 2. The ±J proof is noteworthy in that it is much less “local” than the other (simpler) proof. Homogeneous and ±J models for d≥ 3 remain an open problem. Received: 3 November 1999 / Accepted: 10 April 2000     

Lattice Dislocations in a 1-Dimensional Model

The spectral properties of the Schr?dinger operator T(t)=−d ²/dx ²+q(x,t) in L ²(ℝ) are studied, where the potential q is defined by q=p(x+t), x>0, and q=p(x), x<0; p is a 1-periodic potential and t∈ℝ is the dislocation parameter. For each t the absolutely continuous spectrum σ _ac (T(t))=σ _ac (T(0)) consists of intervals, which are separated by the gaps γ _n (T(t))=γ _n (T(0))=(α _n ⁻,α _n ⁺), n≥1. We prove: in each gap γ _n ≠?, n≥ 1 there exist two unique “states” (an eigenvalue and a resonance) λ _n ^±(t) of the dislocation operator, such that λ _n ^±(0)=α _n ^± and the point λ _n ^±(t) runs clockwise around the gap γ _n changing the energy sheet whenever it hits α _n ^±, making n/2 complete revolutions in unit time. On the first sheet λ _n ^±(t) is an eigenvalue and on the second sheet λ _n ^±(t) is a resonance. In general, these motions are not monotonic. There exists a unique state λ₀(t) in the basic gap γ₀(T(t))=γ₀(T(0))=(−∞ ,α₀ ⁺). The asymptotics of λ _n ^±(t) as n→∞ is determined. Received: 5 April 1999 / Accepted: 3 March 2000     

Emission of light nuclei (<Emphasis Type="Italic">p,d, t</Emphasis>, α) in the process of annihilation of slow antiprotons in nuclear emulsion

The annihilation of slow (∼7 MeV) antiprotons in nuclear emulsion has been studied. The yields and energy spectra of p, d, t, and α particles in the evaporation region have been measured. The shape of the spectra of p, d, and t is in agreement with the Maxwell distribution and the excitation energy of a nucleus is consistent with a theoretical estimate for evaporation from the equilibrium state. The probability of the absorption of antiprotons inside the nucleus estimated from the multiplicity of h particles is ɛ = (2.0 ± 0.6) × 10⁻². The relative d/p yield coincides with a similar ratio appearing in the capture of slow π⁻ mesons by nuclei in the nuclear emulsion. The yields of t and α particles in the process of the annihilation of antiprotons are much higher than those in a similar process for pions. To identify g particles (0.29 < β < 0.70), energy losses dE/dx on ionization and multiple scattering have been measured. In this velocity region, the yields of p, d, t, and pions have been observed. The ratios (n _d /n _p ) _g , (n _d /n _p ) _b , and n _d /n _p measured in the capture of π⁻ mesons are almost the same. In this velocity range (g particles), α particles have not been observed.     

Structural properties of silver nanoparticle agglomerates based on transmission electron microscopy: relationship to particle mobility analysis

In this work, the structural properties of silver nanoparticle agglomerates generated using condensation and evaporation method in an electric tube furnace followed by a coagulation process are analyzed using Transmission Electron Microscopy (TEM). Agglomerates with mobility diameters of 80, 120, and 150 nm are sampled using the electrostatic method and then imaged by TEM. The primary particle diameter of silver agglomerates was 13.8 nm with a standard deviation of 2.5 nm. We obtained the relationship between the projected area equivalent diameter (d _pa) and the mobility diameter (d _m), i.e., d _pa = 0.92 ± 0.03 d _m for particles from 80 to 150 nm. We obtained fractal dimensions of silver agglomerates using three different methods: (1) D _f = 1.84 ± 0.03, 1.75 ± 0.06, and 1.74 ± 0.03 for d _m = 80, 120, and 150 nm, respectively from projected TEM images using a box counting algorithm; (2) fractal dimension (D _fL) = 1.47 based on maximum projected length from projected TEM images using an empirical equation proposed by Koylu et al. (1995) Combust Flame 100:621–633; and (3) mass fractal-like dimension (D _fm) = 1.71 theoretically derived from the mobility analysis proposed by Lall and Friedlander (2006) J Aerosol Sci 37:260–271. We also compared the number of primary particles in agglomerate and found that the number of primary particles obtained from the projected surface area using an empirical equation proposed by Koylu et al. (1995) Combust Flame 100:621–633 is larger than that from using the relationship, d _pa = 0.92 ± 0.03 d _m or from using the mobility analysis.     

Properties of the πη,$ \eta{^\prime}$,σ, f0(980) and a0(980) mesons and their relevance for the polarizabilities of the nucleon

The signs and values of the two-photon couplings F _Mγγ of mesons (M) and their couplings g_MNN to the nucleon as entering into the t -channel parts of the difference of the electromagnetic polarizabilities (α - β) and the backward angle spin polarizabilities γ_π are determined. The excellent agreement achieved with the experimental polarizabilities of the proton makes it possible to make reliable predictions for the neutron. The results obtained are α_n = 13.4±1.0 , β_n = 1.8±1.0 (10^-4fm^3), and γ⁽ⁿ⁾ _π = 57.6±1.8 (10^-4fm^4). New empirical information on the flavor wave functions of the f ₀(980) - and the a ₀(980) -meson is obtained.     

Construction of the Incipient Infinite Cluster for Spread-out Oriented Percolation Above 4 + 1 Dimensions

 We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ ^d × ℤ₊, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ ⁿ (E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n)  ℤ ^d × ℤ₊, summing this probability over x  ℤ ^d , and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ_∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n ⁻¹, we prove existence of a limiting measure ℚ_∞, with ℚ_∞ = ℙ_∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension of the cluster of the origin, under ℙ_∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented percolation to super-Brownian motion, for d+1 > 4+1. Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002 RID="*" ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl     

Quark momentum-space charge distribution in deuteron and neutron/proton structure functions ratio

The electromagnetic polarizabilities of the nucleon are shown to be essentially composed of the nonresonant α _p(E ₀₊) = + 3.2, α _n(E ₀₊) = + 4.1, the t-channel α ^t _{p, n} = - β ^t _{p, n} = + 7.6 and the resonant β _{p, n}(P ₃₃(1232)) = + 8.3 contributions (in units of 10^-4fm^3). The remaining deviations from the experimental data Δα _p = 1.2±0.6, Δβ _p = 1.2±0.6, Δα _n = 0.8±1.7 and Δβ _n = 2.0±1.8 are contributed by a larger number of resonant and nonresonant processes with cancellations between the contributions. This result confirms that dominant contributions to the electric and magnetic polarizabilities may be represented in terms of two-photon coupling to the σ-meson having the predicted mass m _σ = 666MeV and two-photon width Γ _γγ = 2.6keV.     

On the asymptotical normality of statistical solutions for harmonic crystals in half-space

We consider the dynamics of a harmonic crystal in the half-space with zero boundary condition. It is assumed that the initial date is a random function with zero-mean, finite-mean energy density which also satisfies a mixing condition of Rosenblatt or Ibragimov type. We study the distribution μ _t of the solution at time t ∈ ℝ. The main result is the convergence of μ _t as t → ∞ to a Gaussian measure which is time stationary with a covariance inherited from the initial measure (non-Gaussian in general). Supported partly by research grant of RFBR (06-01-00096).     

1H NMR relaxation investigation of herbicides interacting with photosystem II preparations fromSpinacia oleracea L.

The interaction of three common herbicides, paraquat, acifluorfen and alachlor, with spinach chloroplast photosystem II (PS II) was investigated by measuring¹H nuclear magnetic resonance spin-lattice relaxation rates, transient nuclear Overhauser effect (NOE) and NOE spectroscopy (NOESY) spectra. Binding to PS II was detected by (i) the enhancement of single-selective relaxation rates and (ii) the decrease in the optimal mixing time providing maximal cross-peak intensity in NOESY spectra. Titration of relaxation enhancements was used to calculate the dissociation constants (K _d) from the bound state for paraquat (K _d = 292 ± 71 μM⁻¹) and acifluorfen (K _d = 311 ± 58 μM⁻¹). A similarK _d was apparent for alachlor. Double-selective relaxation rates allowed the isolation of dipolar relaxation terms between selected proton pairs wherefrom dynamic features of the bound state were evaluated. In all cases the motional correlation time of bound herbicide (τ_c = 0.1−0.4 ns at 300 K) was found two orders of magnitude slower than in the free-solution state. In the case of alachlor the E and Z isomers were observed to bind differently to PS II and a change in conformation could be hypothesized.     

Quasi-free Compton scattering and the polarizabilities of the neutron

Differential cross-sections for quasi-free Compton scattering from the proton and neutron bound in the deuteron have been measured using the Glasgow/Mainz photon tagging spectrometer at the Mainz MAMI accelerator together with the Mainz [48]cm ;SPMOslash; × [64]cm NaI(Tl) photon detector and the G?ttingen SENECA recoil detector. The data cover photon energies ranging from [200]MeV to [400]MeV at θ^LAB _γ = 136.2^°. Liquid deuterium and hydrogen targets allowed direct comparison of free and quasi-free scattering from the proton. The neutron detection efficiency of the SENECA detector was measured via the reaction p(γ,π⁺ n). The “free” proton Compton scattering cross-sections extracted from the bound proton data are in reasonable agreement with those for the free proton which gives confidence in the method to extract the differential cross-section for free scattering from quasi-free data. Differential cross-sections on the free neutron have been extracted and the difference of the electromagnetic polarizabilities of the neutron has been determined to be α_n - β_n = 9.8±3.6(stat)^+2.1 _-1.1(syst)±2.2(model) in units of [10^-4]fm ³. In combination with the polarizability sum α_n + β_n = 15.2±0.5 deduced from photoabsorption data, the neutron electric and magnetic polarizabilities, α_n = 12.5±1.8(stat)^+1.1 _-0.6(syst)±1.1(model) and β_n = 2.7±1.8(stat)^+0.6 _-1.1(syst)±1.1(model) are obtained. The backward spin polarizability of the neutron was determined to be γ⁽ⁿ⁾ _π = (58.6±4.0)×10^-4 fm ⁴. Received: 21 August 2002 / Accepted: 16 October 2002 / Published online: 11 February 2003 RID="a" ID="a"Part of the Doctoral Thesis. RID="b" ID="b"Present address: Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig. RID="a" ID="a"Part of the Doctoral Thesis. RID="b" ID="b"Present address: Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig. RID="c" ID="c"Part of the Habilitation Thesis. RID="d" ID="d"e-mail: schumacher@physik2.uni-goettingen.de Communicated by Th. Walcher     

Lagrangian instanton for the Kraichnan model

We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism, we find the scaling exponents ζ_n of the structure functions S _n for n≫1 under the additional condition dζ₂≫1 (where d is the dimensionality of space).At n<n _c (where n _c =dζ₂/[2(2−ζ₂)]) the exponents are ζ_n=(ζ ₂/4)(2n−n ²/n _c ), while at n>n _c they are n-independent: ζ _n=ζ₂ n _c /4. We also estimate the n-dependent factors in S _n . Pis’ma Zh. éksp. Teor. Fiz. 68, No. 7, 588–593 (10 October 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Strain-induced photoreflectance spectra in the vicinity of the E 0 transition in GaAs/Si and InP/Si heterostructures

A study is reported of the structure of photoreflectance (PR) spectra in the vicinity of the E ₀ transition from thin (d=1–5 μm) n-GaAs and n-InP films (n=10¹⁶–10¹⁷ cm⁻³) grown epitaxially on Si(001) substrates. A quantitative analysis of the spectra involving multi-component fitting shows that the electronic optical transition from the {3/2;±1/2} subband provides a dominant contribution to the intermediate-field electromodulation component in both systems. The splitting observed in the GaAS/Si PR spectra near the main peak are accounted for not by the strain-induced valence-band splitting but rather by a spectral superposition of the intermediate-field component due to the {3/2;±1/2} subband with a low-energy excitonic component. The analytically established transition energy E ₀ ^3/2;±1/2 is used to calculate biaxial strains in epitaxial films. Fiz. Tverd. Tela (St. Petersburg) 41, 725–731 (April 1999)     

Determination of the 1S0 neutron-neutron scattering length in the nd breakup reaction at energies in the range En = 40?60 MeV

The first results are obtained in a kinematically complete experiment devoted to measuring the n + d → p + n + n reaction yield at energies in the range E _n = 40−60 MeV and various angles of divergence of two neutrons (Δθ = 4°, 6°, and 8°) in the geometry of neutron-neutron final-state interaction. The ¹ S ₀ neutron-neutron scattering length a _nn is determined by comparing the experimental energy dependence of the reaction yield with the results of a simulation in the Watson-Migdal approximation, which depend on a _nn . For E _n = 40 MeV and Δθ = 6° (the best statistics in the experiment), the value a _nn = −17.9 ± 1.0 fm was obtained. A further improvement of the experimental accuracy will make it possible to remove the existing disagreement of the results from different experiments.     

Inclusive production of neutral vector mesons in hadronic Z decays

A data sample of about 3.0 million hadronicZ decays collected by the ALEPH experiment at LEP in the years 1991 through 1994 is used to make an inclusive selection of B hadron events. In this event sample 4227±140±252B* mesons in the decayB*→Bγ and 1944±108±161B** _u,d mesons decaying into a B meson and a charged pion are reconstructed. Here and in the followingB** _u,d denotes the eightL=1(bū) and (bd) states and their charge conjugate. For the well establishedB* meson the following quantities are obtained:ΔM=M _B*−M_B=(45.30±0.35±0.87) MeV/c² andN _B*/(N _B+N _B*)=(77.1±2.6±7.0)%. The angular distribution of the photons in theB* rest frame is used to measure the relative contribution of longitudinalB* polarization states to beσ _L/(σ _L+σ _T)=(33±6±5)%.     

The quenching of nucleon yields in the nonmesonic weak decay of Λ -hypernuclei and the three-body weak decay process

Recent exclusive coincidence measurements of non-mesonic weak decays (NMWD) reported for the ratio of the partial decay width of neutron-induced-to-proton-induced NMWD, Γ_n/Γ_p , values of 0.45±0.11±0.03 and 0.51±0.13±0.04 for 5lam and ¹² _Λ C , respectively. These observations agree well with the improved theoretical Γ_n/Γ_p ratios which are in the range of 0.3-0.7. It appears that the long-standing discrepancy between the experimental and theoretical values of Γ_n/Γ_p has finally been solved. However, when compared to the results of intra-nuclear cascade (INC) calculations, the observed numbers of both single nucleons and coincident nucleon pairs are strongly quenched. The quenching of the proton yield observed previously has been interpreted as an increase of the Γ_n/Γ_p ratio. On the other hand, significant contributions from the two-nucleon-induced three-body process ΛNN → nNN are predicted. Indeed, the angular correlation of the emitted nucleon pairs in the NMWD of ¹² _Λ C showed not only decay events in back-to-back kinematics, but also events with non-back-to-back kinematics. In this paper we show that the difficulties to extract the correct Γ_n/Γ_p ratio from the proton spectra is related to the three-body weak-interaction process which strongly quenches the nucleon yields.     

Scaling of Loop-Erased Walks in 2 to 4 Dimensions

We simulate loop-erased random walks on simple (hyper-)cubic lattices of dimensions 2, 3 and 4. These simulations were mainly motivated to test recent two loop renormalization group predictions for logarithmic corrections in d=4, simulations in lower dimensions were done for completeness and in order to test the algorithm. In d=2, we verify with high precision the prediction D=5/4, where the number of steps n after erasure scales with the number N of steps before erasure as n∼N ^D/2. In d=3 we again find a power law, but with an exponent different from the one found in the most precise previous simulations: D=1.6236±0.0004. Finally, we see clear deviations from the naive scaling n∼N in d=4. While they agree only qualitatively with the leading logarithmic corrections predicted by several authors, their agreement with the two-loop prediction is nearly perfect.