Coherent pion production in neutrino and antineutrino interactions on nuclei of heavy freon molecules

Studying the coherent diffractive production of pions in neutrino and antineutrino scattering off the nuclei of freon molecules we have observed for the first time in one experiment all three states of the isospin triplet of the axial part of the weak charged and neutral currents. For the corresponding cross sections we derive $$\begin{array}{*{20}c} {\sigma _{coh}^v (\pi ^ + ) = (106 \pm 16) \cdot 10^{ - 40} {{cm^2 } \mathord{\left/ {\vphantom {{cm^2 } {\left\langle {nucl.} \right\rangle }}} \right. \kern-\nulldelimiterspace} {\left\langle {nucl.} \right\rangle }}} \\ {\sigma _{coh}^{\bar v} (\pi ^ - ) = (113 \pm 35) \cdot 10^{ - 40} {{cm^2 } \mathord{\left/ {\vphantom {{cm^2 } {\left\langle {nucl.} \right\rangle }}} \right. \kern-\nulldelimiterspace} {\left\langle {nucl.} \right\rangle }}and} \\ {\sigma _{coh}^v (\pi ^0 ) = (52 \pm 19) \cdot 10^{ - 40} {{cm^2 } \mathord{\left/ {\vphantom {{cm^2 } {\left\langle {nucl.} \right\rangle }}} \right. \kern-\nulldelimiterspace} {\left\langle {nucl.} \right\rangle }}} \\ \end{array} $$ . Comparing our data with theoretical predictions based on the standard model of weak interactions we find reasonable agreement. Independently from any model of coherent pion production we determine the isovector axial vector coupling constant to be |β|=0.99±0.20.     

A measurement of the branching ratio∑ +→pγ/∑ +→pπ 0⋆

In an experiment performed in the CERN SPS hyperon beam we have obtained a value for the branching ratio $${{\Sigma ^ + \to p\gamma } \mathord{\left/ {\vphantom {{\Sigma ^ + \to p\gamma } {\Sigma ^ + \to p\pi }}} \right. \kern-\nulldelimiterspace} {\Sigma ^ + \to p\pi }}^0 of\left( {2.46_{ - 0.35}^{ + 0.30} } \right) \times 10^{ - 3} ,$$ corresponding to a branching ratio $${{\Sigma ^ + \to p\gamma } \mathord{\left/ {\vphantom {{\Sigma ^ + \to p\gamma } {\Sigma ^ + \to all}}} \right. \kern-\nulldelimiterspace} {\Sigma ^ + \to all}}of\left( {1.27_{ - 0.18}^{ + 0.16} } \right) \times 10^{ - 3} .$$ This result is discussed in the context of present understanding of hyperon radiative decays.     

On (n,p) cross sections for 14 MeV neutrons

Using older compilations and recent data the (n, p) cross sections for neutron energies between 14 and 15 MeV have been collected and revised critically. The experimental data can be represented phenomenologically by the formula $$\log _{10} ({{\sigma _{np} } \mathord{\left/ {\vphantom {{\sigma _{np} } {mb}}} \right. \kern-\nulldelimiterspace} {mb}}) = 0.2 + 0.4A^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} - 4.6{{(N - Z)} \mathord{\left/ {\vphantom {{(N - Z)} {A^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} }}} \right. \kern-\nulldelimiterspace} {A^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} }}$$ . The compound part of the (n, p) reactions is described by a statistical model; the direct reactions are taken into account semiempirically.     

Der Einfluß der Wärmebewegung auf die Breite einer Mössbauerlinie über den Dopplereffekt zweiter Ordnung

AtT=0 a perfect Mössbauer line has natural line widthΓ=?/τ _n . However, with rising temperature the width increases. The reason of the line broadening is the second order Doppler effect which causes a stochastic frequency modulation of theγ-radiation, reflecting the thermal motion of the Mössbauer atom. Following Josephson in treating the second order Doppler shift as a mass changeΔM=E _n/c² of theγ-emitting atom caused by the loss of nuclear excitation energy E _n , and using the well known relaxation formalism for calculating theγ-frequency spectrum, the line broadeningΔ Γ is evaluated within the framework of harmonic lattice theory. For a parabolic lattice frequency spectrum with Debye-temperature Θ one obtains $$\Delta {\Gamma \mathord{\left/ {\vphantom {\Gamma \Gamma }} \right. \kern-\nulldelimiterspace} \Gamma } = \left( {{{\tau _n } \mathord{\left/ {\vphantom {{\tau _n } {\tau _c }}} \right. \kern-\nulldelimiterspace} {\tau _c }}} \right) \cdot \left( {{{E_n } \mathord{\left/ {\vphantom {{E_n } {Mc^2 }}} \right. \kern-\nulldelimiterspace} {Mc^2 }}} \right) \cdot F\left( {{T \mathord{\left/ {\vphantom {T \Theta }} \right. \kern-\nulldelimiterspace} \Theta }} \right),where\tau _c = {{\rlap{--} h} \mathord{\left/ {\vphantom {{\rlap{--} h} k}} \right. \kern-\nulldelimiterspace} k}\Theta $$ is the correlation time of the lattice vibrations. The functionF(T/Θ) may be expanded in powers ofT/Θ, yielding $$F\left( {{T \mathord{\left/ {\vphantom {T \Theta }} \right. \kern-\nulldelimiterspace} \Theta }} \right) = 9720\pi \left( {{T \mathord{\left/ {\vphantom {T \Theta }} \right. \kern-\nulldelimiterspace} \Theta }} \right)^7 forT<< \Theta $$ and $$F\left( {{T \mathord{\left/ {\vphantom {T \Theta }} \right. \kern-\nulldelimiterspace} \Theta }} \right) = 2.7\pi \left( {{T \mathord{\left/ {\vphantom {T \Theta }} \right. \kern-\nulldelimiterspace} \Theta }} \right)^2 forT > > \Theta $$ , respectively. Although unavoidable, the line broadening is obviously too small to be observable by means of the present experimental technique.     

Laser-Rf double-resonance studies of the hyperfine structure of metastable atomic states of55Mn

The hyperfine structure (hfs) of the metastable atomic states 3d⁶4s⁶ D _{1/2, 3/2, 5/2, 7/2, 9/2} of⁵⁵Mn was measured using theABMR- LIRF method (atomicbeammagneticresonance, detected bylaserinducedresonancefluorescence). The hfs constantsA andB, corrected for second order hfs perturbations, could be derived from these measurements. The theoretical interpretation of these correctedA- andB-factors was performed in the intermediate coupling scheme taking into account the configurations 3d ⁵4s ², 3d ⁶4s and 3d ⁷. Examining the influence of the composition of the eigenvectors on the hfs parameters \(\left\langle {r^{ - 3} } \right\rangle ^{k_s k_l } \) it was found, that for the configuration 3d ⁶4s the two-body magnetic interaction should be considered in the calculation of the eigenvectors. Investigating second order electrostatic configuration interactions and relativistic effects and using calculated relativistic correction factors we obtained for the nuclear quadrupole moment of the nucleus⁵⁵Mn a value ofQ=0.33(1) barn, which is not perturbed by a shielding or antishielding Sternheimer factor. The following hfs constants have been obtained: $$\begin{gathered} A\left( {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 882.056\left( {12} \right)MHz \hfill \\ A\left( {{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 469.391\left( 7 \right)MHzB\left( {{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = - 65.091\left( {50} \right)MHz \hfill \\ A\left( {{5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 436.715\left( 3 \right)MHzB\left( {{5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = - 46.769\left( {30} \right)MHz \hfill \\ A\left( {{7 \mathord{\left/ {\vphantom {7 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 458.930\left( 3 \right)MHzB\left( {{7 \mathord{\left/ {\vphantom {7 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 21.701\left( {40} \right)MHz \hfill \\ A\left( {{9 \mathord{\left/ {\vphantom {9 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 510.308\left( 8 \right)MHzB\left( {{9 \mathord{\left/ {\vphantom {9 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 132.200\left( {120} \right)MHz \hfill \\ \end{gathered} $$      

Study of the mechanisms of pre-equilibrium nuclear reactions in the microscopic approach

The mechanisms of pre-equilibrium nuclear reactions are investigated within the Statistical Multistep Direct Process (SMDP) + Statistical Multistep Compound Process (SMCP) formalism. It has been shown that from an analysis of linear part in such dependences as $$\ln \left[ {{{\frac{{d^2 \sigma }}{{d\varepsilon _b d\Omega _b }}} \mathord{\left/ {\vphantom {{\frac{{d^2 \sigma }}{{d\varepsilon _b d\Omega _b }}} {\varepsilon _b^{1/2} }}} \right. \kern-\nulldelimiterspace} {\varepsilon _b^{1/2} }}} \right]upon\varepsilon _b $$ and $$\ln \left[ {{{\frac{{d\sigma ^{SMDP \to SMCP} }}{{d\varepsilon _b }}} \mathord{\left/ {\vphantom {{\frac{{d\sigma ^{SMDP \to SMCP} }}{{d\varepsilon _b }}} {\frac{{d\sigma ^{SMDP} }}{{d\varepsilon _b }}}}} \right. \kern-\nulldelimiterspace} {\frac{{d\sigma ^{SMDP} }}{{d\varepsilon _b }}}}} \right]upon{{U_B } \mathord{\left/ {\vphantom {{U_B } {\left( {E_a - B_b } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {E_a - B_b } \right)}}$$ one can extract information about the type of mechanism (SMDP, SMCP, SMDP→SMCP) and the number of stages of the multistep emission of secondary particles. In the above approach, we have discussed the experimental data for a broad class of reactions in various entrance and exit channels.     

Asymptotic behavior of Mayer cluster sums for the one-dimensional Ising model

The properties of the high-field polynomialsL _n (u) for the one-dimensional spin 1/2 Ising model are investigated. [The polynomialsL _n (u) are essentially lattice gas analogues of the Mayer cluster integralsb _n (T) for a continuum gas.] It is shown thatu ^?1 L _n (u) can be expressed in terms of a shifted Jacobi polynomial of degreen?1. From this result it follows thatu ^?1 L _n (u); n=1, 2,... is a set of orthogonal polynomials in the interval (0, 1) with a weight functionω(u)=u, andu ^?1 L _n (u) hasn?1 simple zerosu _n (v); v=1, 2,...,n?1 which all lie in the interval 0<u<1. Next the detailed behavior ofL _n (u) asn→∞ is studied. In particular, various asymptotic expansions forL _n (u) are derived which areuniformly valid in the intervalsu<0, 0<u<1, andu>1. These expansions are then used to analyze the asymptotic properties of the zeros {u _n (v); v=1, 2,...,n?1}. It is found that $$\begin{array}{*{20}c} {u_n (v) \sim \tfrac{1}{4}({{j_{1,v} } \mathord{\left/ {\vphantom {{j_{1,v} } n}} \right. \kern-\nulldelimiterspace} n})^2 [1 - ({{j_{1,v}^2 } \mathord{\left/ {\vphantom {{j_{1,v}^2 } {12}}} \right. \kern-\nulldelimiterspace} {12}})n^{ - 1} + ({{j_{1,v}^2 } \mathord{\left/ {\vphantom {{j_{1,v}^2 } {700)( - 3 + 2j_{1,v}^2 )n^{ - 4} }}} \right. \kern-\nulldelimiterspace} {700)( - 3 + 2j_{1,v}^2 )n^{ - 4} }}} \\ { + ({{j_{1,v}^2 } \mathord{\left/ {\vphantom {{j_{1,v}^2 } {20160)(40 + 4j_{1,v}^2 - j_{1,v}^4 }}} \right. \kern-\nulldelimiterspace} {20160)(40 + 4j_{1,v}^2 - j_{1,v}^4 }})n^{ - 6} + \cdot \cdot \cdot ]} \\ {u_n (n - v) \sim 1 - ({{j_{0,v}^2 } \mathord{\left/ {\vphantom {{j_{0,v}^2 } 4}} \right. \kern-\nulldelimiterspace} 4})n^{ - 2} + ({{j_{0,v}^2 } \mathord{\left/ {\vphantom {{j_{0,v}^2 } {48)( - 2 + j_{0,v}^2 )n^{ - 4} }}} \right. \kern-\nulldelimiterspace} {48)( - 2 + j_{0,v}^2 )n^{ - 4} }}} \\ { + ({{j_{0,v}^2 } \mathord{\left/ {\vphantom {{j_{0,v}^2 } {2880)(2 + 9j_{0,v}^2 - 2j_{0,v}^4 )n^{ - 6} + \cdot \cdot \cdot }}} \right. \kern-\nulldelimiterspace} {2880)(2 + 9j_{0,v}^2 - 2j_{0,v}^4 )n^{ - 6} + \cdot \cdot \cdot }}} \\ \end{array} $$ asn→∞v fixed, wherej _k,v denotes thevth zero of the Bessel functionJ _k(^z)     

Light quark masses in quantum chromodynamics and chiral symmetry breaking

We derive model independent lower bounds for the sums of effective quark masses \(\bar m_u + \bar m_d \) and \(\bar m_u + \bar m_s \) . The bounds follow from the combination of the spectral representation properties of the hadronic axial currents two-point functions and their behavior in the deep euclidean region (known from a perturbative QCD calculation to two loops and the leading non-perturbative contribution). The bounds incorporate PCAC in the Nambu-Goldstone version. If we define the invariant masses \(\hat m\) by $$\bar m_i = \hat m_i \left( {{{\frac{1}{2}\log Q^2 } \mathord{\left/ {\vphantom {{\frac{1}{2}\log Q^2 } {\Lambda ^2 }}} \right. \kern-\nulldelimiterspace} {\Lambda ^2 }}} \right)^{{{\gamma _1 } \mathord{\left/ {\vphantom {{\gamma _1 } {\beta _1 }}} \right. \kern-\nulldelimiterspace} {\beta _1 }}} $$ and <F ²> is the vacuum expectation value of $$F^2 = \Sigma _a F_{(a)}^{\mu v} F_{\mu v(a)} $$ , we find, e.g., $$\hat m_u + \hat m_d \geqq \sqrt {\frac{{2\pi }}{3} \cdot \frac{{8f_\pi m_\pi ^2 }}{{3\left\langle {\alpha _s F^2 } \right\rangle ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} }}} $$ ; with the value <α _u F ²?0.04GeV⁴, recently suggested by various analysis, this gives $$\hat m_u + \hat m_d \geqq 35MeV$$ . The corresponding bounds on \(\bar m_u + \bar m_s \) are obtained replacingm _π ² f _π bym _K ² f _K . The PCAC relation can be inverted, and we get upper bounds on the spontaneous masses, \(\hat \mu \) : $$\hat \mu \leqq 170MeV$$ where \(\hat \mu \) is defined by $$\left\langle {\bar \psi \psi } \right\rangle \left( {Q^2 } \right) = \left( {{{\frac{1}{2}\log Q^2 } \mathord{\left/ {\vphantom {{\frac{1}{2}\log Q^2 } {\Lambda ^2 }}} \right. \kern-\nulldelimiterspace} {\Lambda ^2 }}} \right)^d \hat \mu ^3 ,d = {{12} \mathord{\left/ {\vphantom {{12} {\left( {33 - 2n_f } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {33 - 2n_f } \right)}}$$ .     

Absence of long-range order in one-dimensional spin systems

For a one-dimensional Ising model with interaction energy $$E\left\{ \mu \right\} = - \sum\limits_{1 \leqslant i< j \leqslant N} {J(j - i)} \mu _\iota \mu _j \left[ {J(k) \geqslant 0,\mu _\iota = \pm 1} \right]$$ it is proved that there is no long-range order at any temperature when $$S_N = \sum\limits_{k = 1}^N {kJ\left( k \right) = o} \left( {[\log N]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } \right)$$ The same result is shown to hold for the corresponding plane rotator model when $$S_N = o\left( {\left[ {{{\log N} \mathord{\left/ {\vphantom {{\log N} {\log \log N}}} \right. \kern-\nulldelimiterspace} {\log \log N}}} \right]} \right)$$      

Weber potential from finite velocity of action?

The Weber potential energy U for charges q and q' separated by the distance R is U = (qq'/R)[1 – (dR/dt)²/2c²]. If this potential arises from a finite velocity c of energy transfer Q', where the retarded rate of transfer from q' to q is dQ(t-R/c)/dt = Q'[1 – (dR/dt)/c] and where the advanced rate from q to q' is dQ(t+R/c)/dt = Q'[1 + (dR/dt)/c], then the resultant time-average root-mean-square action is given by . Identifying Q' with the Coulomb potential energy qq'/R, the Weber potential is obtained. Using the same argument, Newtonian gravitation yields a corresponding Weber potential energy, qq'/R being replaced by ( - Gmm'/R).     

Self-diffusion in α-Fe2O3 natural single crystals

Measurements of¹⁸O self-diffusion in hematite (Fe₂O₃) natural single crystals have been carried out as a function of temperature at constant partial pressure a_{O 2}=6.5·10^?2 in the temperature range 890 to 1227 °C. The a_{O 2} dependence of the oxygen self-diffusion coefficient at fixed temperature T=1150 °C has also been deduced in the a_{O 2} range 4.5·10^?4 - 6.5·10^?1. The concentration profiles were established by secondary-ion mass spectrometry; several profiles exhibit curvatures or long tails; volume diffusion coefficients were computed from the first part of the profiles using a solution taking into account the evaporation and the exchange at the surface. The results are well described by $$D_O \left( {{{cm^2 } \mathord{\left/ {\vphantom {{cm^2 } s}} \right. \kern-\nulldelimiterspace} s}} \right) = 2.7 \cdot 10^8 a_{O_2 }^{ - 0.26} \exp \left( { - \frac{{542\left( {{{kJ} \mathord{\left/ {\vphantom {{kJ} {mol}}} \right. \kern-\nulldelimiterspace} {mol}}} \right)}}{{RT}}} \right)$$ From fitting a grain boundary diffusion solution to the profile tails, the oxygen self-diffusion coefficient in sub-boundaries has been deduced. They are well described by $$D''_O \left( {{{cm^2 } \mathord{\left/ {\vphantom {{cm^2 } s}} \right. \kern-\nulldelimiterspace} s}} \right) = 3.2 \cdot 10^{25} a_{O_2 }^{ - 0.4} \exp \left( { - \frac{{911\left( {{{kJ} \mathord{\left/ {\vphantom {{kJ} {mol}}} \right. \kern-\nulldelimiterspace} {mol}}} \right)}}{{RT}}} \right)$$ Experiments performed introducing simultaneously¹⁸O and⁵⁷Fe provided comparative values of the self-diffusion coefficients in volume: iron is slower than oxygen in this system showing that the concentrations of atomic point defects in the iron sublattice are lower than the concentrations of atomic point defects in the oxygen sublattice. The iron self-diffusion values obtained at T>940 °C can be described by $$D_{Fe} \left( {{{cm^2 } \mathord{\left/ {\vphantom {{cm^2 } s}} \right. \kern-\nulldelimiterspace} s}} \right) = 9.2 \cdot 10^{10} a_{O_2 }^{ - 0.56} \exp \left( { - \frac{{578\left( {{{kJ} \mathord{\left/ {\vphantom {{kJ} {mol}}} \right. \kern-\nulldelimiterspace} {mol}}} \right)}}{{RT}}} \right)$$ The exponent - 1/4 observed for the oxygen activity dependence of the oxygen self-diffusion in the bulk has been interpreted considering that singly charged oxygen vacancies V _O ^? are involved in the oxygen diffusion mechanism. Oxygen activity dependence of iron self-diffusion is not known accurately but the best agreement with the point defect population model is obtained considering that iron self-diffusion occurs both via neutral interstitals Fe _x ⁱ and charged ones.     

Superconductive superheating field for finiteκ

We have calculated analytically the superheating fieldH _sh for bulk superconductors, correct to second order in. We find , which agrees well with numerical computations for<0.5. The surface order parameter is , and the penetration depth is .     

Universal estimate of the gap for the Kac operator in the convex case

The aim of this paper is to prove that ifV is a strictly convex potential with quadratic behavior at ∞, then the quotient μ₂/μ₁ between the largest eigenvalue and the second eigenvalue of the Kac operator defined on L²(? ^m ) by exp ?V(x)/2 · exp Δ_x · exp ?V(x)/2 where Δ_x is the Laplacian on ? ^m satisfies the condition: $${{\mu _2 } \mathord{\left/ {\vphantom {{\mu _2 } {\mu _1 {{ \leqslant \exp - \cosh ^{ - 1} (\sigma + 1)} \mathord{\left/ {\vphantom {{ \leqslant \exp - \cosh ^{ - 1} (\sigma + 1)} {2,}}} \right. \kern-\nulldelimiterspace} {2,}}}}} \right. \kern-\nulldelimiterspace} {\mu _1 {{ \leqslant \exp - \cosh ^{ - 1} (\sigma + 1)} \mathord{\left/ {\vphantom {{ \leqslant \exp - \cosh ^{ - 1} (\sigma + 1)} {2,}}} \right. \kern-\nulldelimiterspace} {2,}}}}$$ where σ is such that HessV(x)≥σ>0.     

O(G μ 2 m t 4 ) electroweak radiative corrections to theZb \bar b vertex

The leading heavy-top two-loop corrections to theZb \(\bar b\) vertex are determined from a direct evaluation of the corresponding Feynman diagrams in the largem _t limit. The leading one-loop top-mass effect is enhanced by \([{{1 + G_\mu m_t^2 ({{9 - \pi ^2 } \mathord{\left/ {\vphantom {{9 - \pi ^2 } 3}} \right. \kern-0em} 3})} \mathord{\left/ {\vphantom {{1 + G_\mu m_t^2 ({{9 - \pi ^2 } \mathord{\left/ {\vphantom {{9 - \pi ^2 } 3}} \right. \kern-0em} 3})} {(8\pi ^2 \sqrt 2 )}}} \right. \kern-0em} {(8\pi ^2 \sqrt 2 )}}]\) . Our calculation confirms a recent result of Barbieri et al..     

Empirical two-point correlation functions

Let A ₁ , A ₂ , A ₃ A ₄ be four observables, the compatible observables among them being (A ₁ , A ₃ ), (A ₁ , A ₄ ), (A ₂ , A ₃ ), (A ₂ , A ₄ ). In order that the empirical data be reproducible by a quantum or a classical theory, the two-point correlation functions $$\{ C_{ij} = \left\langle {A_i A_j } \right\rangle :i,j a compatible pair\} $$ must necessarily satisfy $$|X_{13} X_{14} - X_{23} X_{24} | \leqslant \left( {1 - X_{13} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {1 - X_{14} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + \left( {1 - X_{23} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {1 - X_{24} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} (*)$$ where X_ij=C_ijC _ii ^?1/2 C _jj ^?1/2 . In the case ofGaussian data, this inequality is alsosufficient; If (*) holds, there is a Gaussian joint distribution for A ₁ , A ₂ , A ₃ , A ₄ which reproduces the Gaussian data for compatible pairs. It follows that Bell's inequality is satisfied by all true-false propositions about the Gaussian data. A further consequence of the analysis is thatquantum Gaussian fields satisfy Bell's inequality for all true-false propositions aboutfield measurements. The maximum violation of (*) corresponds to Rastall's example in the case of two-valued observables.     

Upper bound on the decay of correlations in the plane rotator model with long-range random interaction

We give an upper bound on the decay of correlation function for the plane rotator model with Hamiltonian $$ - \frac{1}{2}\mathop \sum \limits_{xy} \frac{{J_{xy} \cos (\theta _x - \theta _y )}}{{\| {x - y} \|^{({3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2} + \varepsilon )^d } }}$$ in dimensiond=1 andd=2 when (J _xy are independent random variables with mean zero.     

Er-Yb Codoped Ferroelectrics for Controlling Visible Upconversion Emissions

Under a 980 nm laser pumping, quenching of green upconversion (UC) emission accompanied with enhancement of red UC emission observed was dominated by the energy back-transfer (EBT) process in Er³⁺ and Yb³⁺ co-doped PbTiO₃, BaTiO₃, and SrTiO₃ polycrystalline powders. The efficiency of the EBT process depends not only on Yb³⁺ concentration but also on level match of the doped Er³⁺ and Yb³⁺ ions caused by the crystal fields with different symmetries. Our UC emission spectra and X-ray diffraction confirm that the centrosymmetric crystal field arising from reducing tetragonality causes level match of transition of Er³⁺ and of Yb³⁺. This level match is responsible for enhancing red UC emission.     

Al,F-doped new perovskite lithium fast ion conductor Li3x La2/3−x□1/3−2x Ti1−y Al y O3−y F y (x=0.11)

Al, F-doped new perovskite lithium ion conductors (x=0.11) have been prepared by solid state reaction. It is found that a pure perovskite-structured phase with space group of P4mm(99) exits in the composition range of 0<y≤0.10. The sample with y=0.02 possesses the highest ionic conductivity of 1.06×10⁻³ S/cm at room temperature, and its decomposing voltage is 2.3 V. The factors affecting the conductivity of this system are discussed.