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.     

The electrochemical properties of LaAl12O18N

The ceramic material LaAl₁₂O₁₈N which adopts the magnetoplumbite type structure was prepared by a high temperature sintering technique from La₂O₃, α-Al₂O₃ and AlN powders under a controlled atmosphere. Phase purity was confirmed by powder XRD and IR spectroscopy. Impedance spectroscopy data from a ceramic disc of LaAl₁₂O₁₈N revealed an intra-granular ionic (La³⁺) conductivity (≈3×10^?5 Scm^?1 at 1540 K) with an activation energy E_a=1.6 eV and a dielectric constant ?=56. The ionic conductivity at 1540 K is comparable to an extrapolated value for the divalent material; Sr-Li-β-alumina. Since LaAl₁₂O₁₈N can be considered as a quasi-binary compound (LaN·6Al₂O₃), it was shown to act simultaneously as an electrolyte and a nitrogen-sensing phase at high temperature. The key electrochemical reaction in terms of dinitrogen gas is: $$La^{3 + } \left( {LaAl_{12} O_{18} N} \right) + 3e^ - + {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}N_2 \left( g \right) + 6\alpha - Al_2 O_3 \to LaAl_{12} O_{18} N.$$ . Positive e.m.f. measurements at high temperature across the following cell: $$Nb,Nb_2 N,\alpha - Al_2 O_3 \left| {LaAl_{12} O_{18} N} \right|\alpha - AL_2 O_3 ,Nb_2 N,Nb_4 N_3 ,$$ , were in agreement withP _N2(Nb₂N,Nb₄N₃)>P _N2(Nb, Nb₂N) for the idealised cell reaction; Nb₄N₃+ 2Nb → 3Nb₂N, thus demonstrating the nitrogen-sensing property of this cell. The e.m.f. for a variety of cells with electrodes containing the sub-nitrides of vanadium, niobium, tantalum and titanium were consistent with the predicted equilibrium nitrogen partial pressures.     

Non-Faradaic electrochemical modification of the catalytic activity of Pt using a CaZr0.9In0.1O3-α proton conductor

The effect of non-Faradaic electrochemical modification of catalytic activity (NEMCA) was investigated for the case of C₂H₄ oxidation on a Pt polycrystalline catalyst film also acting as a working electrode in a galvanic cell of the type: $$C_2 H_4 ,O_2 ,CO_2 ,H_2 O,Pt|CaZr_{0.9} In_{0.1} O_{3 - \alpha } |Au,C_2 H_4 , O_2 ,CO_2 ,H_2 O$$ In addition to proton conduction, CaZr_0.9In_0.1O_3-α is known to exhibit oxygen and hole conduction. Proton conduction predominates over the temperature range, 380 to 460 °C, of the present investigation. It was found that negative current application, i.e. proton supply to the Pt catalyst film causes up to 500% reversible enhancement to the rate of C₂H₄ oxidation. The catalytic rate increase is up to 20,000 higher than the rate, -I/F, of proton supply to the catalyst. The observed phenomena are discussed within the framework of previous electrochemical promotion (NEMCA) studies.     

In situ controlled promotion of catalyst surfaces via solid electrolytes: Ethylene oxidation on Rh and propylene oxidation on Pt

The kinetics of C₂H₄ oxidation on Rh and C₃H₆ oxidation on Pt were investigated on polycrystalline metal films interfaced with ZrO₂(8mol%Y₂O₃) solid electrolyte in galvanic cells of the type:

Neutrino production of dimuons

Neutrino interactions with two muons in the final state have been studied using the Fermilab narrow band beam. A sample of 18v _μ like sign dimuon events withP _μ>9 GeV/c yields 6.6±4.8 events after backgroud subtraction and a prompt rate of (1.0±0.7)×10^?4 per single muon event. The kinematics of these events are compared with those of the non-prompt sources. A total of 437v _μ and 31 \(\bar v_\mu \) opposite sign dimuon events withP _μ>4.3 GeV/c are used to measure the strange quark content of the nucleon: \(\kappa = {{2s} \mathord{\left/ {\vphantom {{2s} {\left( {\bar u + \bar d} \right) = 0.52_{ - 0.15}^{ + 0.17} \left( {or\eta _s \frac{{2s}}{{u + d}} = 0.075 \pm 0.019} \right) for 100< E_v< 230 GeV\left( {\left\langle {Q^2 } \right\rangle = {{23 GeV^2 } \mathord{\left/ {\vphantom {{23 GeV^2 } {c^2 }}} \right. \kern-0em} {c^2 }}} \right)}}} \right. \kern-0em} {\left( {\bar u + \bar d} \right) = 0.52_{ - 0.15}^{ + 0.17} \left( {or\eta _s \frac{{2s}}{{u + d}} = 0.075 \pm 0.019} \right) for 100< E_v< 230 GeV\left( {\left\langle {Q^2 } \right\rangle = {{23 GeV^2 } \mathord{\left/ {\vphantom {{23 GeV^2 } {c^2 }}} \right. \kern-0em} {c^2 }}} \right)}}\) using a charm semileptonic branching ratio of (10.9±1.4)% extracted from measurements ine ⁺ e ^? collisions and neutrino emulsion data.     

Mössbauer study of the (Ru1-xFex)Sr2GdCu2O8-δ system and two of its possible impurities: SrRuO3 and Gd2CuO4

Mössbauer spectra of a series of samples of the weak ferromagnetic $ {\left( {Ru_{{1 - x}} Fe_{x} } \right)}Sr_{2} GdCu_{2} O_{{8 - \delta }} M?ssbauer spectra of a series of samples of the weak ferromagnetic system reveal the existence of three dissimilar sites where the Fe atoms can go into the structure. The M?ssbauer parameters of the three observed quadrupole doublets, together with the relative population on each site, allow the following site assignment for the iron atoms: Fe³⁺ in four-fold planar coordination at Ru sites; Fe³⁺ in five-fold pyramidal coordination also at Ru sites and Fe²⁺ or Fe³⁺ in five-fold coordination at Cu sites. This assignment implies the formation of oxygen-vacancies at the charge reservoir (the RuO₂ planes) that affect the structure and the superconducting and magnetic properties of the undoped system. Moreover, a close correlation between the oxygen content, calculated through the M?ssbauer data, and the measured cell volume is established. We also report the M?ssbauer spectra of two compounds (SrRu_0.95Fe_0.05O₃ and Gd₂Cu_0.95Fe_0.05O₄) that could be formed as impurities during the synthesis of our samples.     

Oxygen ion transport numbers: assessment of combined measurement methods

Several modifications of the faradaic efficiency and electromagnetic field (EMF) methods, taking electrode polarisation resistance into account, were considered based on the analysis of ion transport numbers and p-type electronic conductivity of ceramics at 973–1,223 K. In air, the activation energies for p-type electronic and oxygen ionic transport are 115 ± 9 and 71 ± 5 kJ/mol, respectively. The oxygen ion transference numbers vary in the range 0.992–0.999, increasing when oxygen pressure or temperature decreases. The apparent electronic contribution to the total conductivity, estimated from the classical faradaic efficiency and EMF techniques was considerably higher than true transference numbers due to a non-negligible role of interfacial exchange processes. The modified measurement routes give reliable and similar results when p(O₂) values at the electrodes are high enough, whilst decreasing the oxygen pressure leads to a systematic error for all techniques associated with measurements of concentration cell EMF. This effect, presumably due to diffusion polarisation, increases with decreasing temperature. The most reliable results in the studied p(O₂) range were provided by the modified faradaic efficiency method.     

Gluon condensate and the effective gluon mass

Using massive gauge invariant QCD we show explicity how power like corrections to \(\Pi _{\mu v} \left( q \right) = i\int {dx} e^{iq'x} \left\langle {0\left| {j_\mu ^{em} \left( x \right)\bar j_v^{em} \left( 0 \right)} \right|0} \right\rangle \) arise. Using our result for the 1/q ⁴ contribution, a one to one correspondence is made between the gluon condensate and the effective gluon mass. By relating this mass to, \(\langle 0|\frac{{\alpha _s }}{\pi }G_{\mu v}^2 |0\rangle \) a value ofm _gluon=750 MeV is found at ?q ²=10 GeV². In addition, within the context of dimensional regularization, a new technique for evaluating two loop momentum integrals with massive propagators is introduced. This method is a derivative of the Mellin transform technique that was applied to ladder diagrams in the days of Reggeisation.     

A new method for calculating three-particle interaction in the theory of modulus elasticity

We propose a new method for calculating the potential of multiparticle interaction. Our method considers the energy symmetry for clusters that contain N identical particles with respect to permutation of the number of atoms and free rotation in three-dimensional space. As an example, we calculate moduli of third-order rigidity for copper considering only the three-particle interaction. We analyze nine models of energy dependence on the polynomials that form the integral rational basis of invariants (IRBI) for the group G ₃ = O(3) ? P ₃. In this work, we use only the simplest relation between energy and the invariants forming the IRBI: \(\varepsilon \left( {\left. {i,k,l} \right|j} \right) = \sum\nolimits_{i,k,l} {\left[ { - A_1 r_{ik}^{ - 6} + A_2 r_{ik}^{ - 12} + Q_j I_j^{ - n} } \right]}\), where I _j is the invariant number j (j = 1, 2,..., 9). The results are in good agreement with the experimental values. The best agreement is observed at n = 2, j = 4: \(I_4 = \left( {\vec r_{ik} \vec r_{kl} } \right)\left( {\vec r_{kl} \vec r_{li} } \right) + \left( {\vec r_{kl} \vec r_{li} } \right)\left( {\vec r_{li} \vec r_{ik} } \right) + \left( {\vec r_{li} \vec r_{ik} } \right)\left( {\vec r_{ik} \vec r_{kl} } \right)\).     

Hyperfine structure,g j factors and lifetimes of excited2 P 1/2 states of Rb

The hyperfine structure of the 6² P _1/2 and 7² P _1/2 state of⁸⁵Rb and⁸⁷Rb and of the 6² P _3/2 state of⁸⁷Rb has been investigated with optical double resonance at intermediate magnetic fields. The magnetic interaction constants,g _j factors and lifetimes are: $$\begin{gathered} 6^2 P_{1/2} state: A\left( {^{85} Rb} \right) = 39.11\left( 3 \right) MHz,A\left( {^{87} Rb} \right) = 132.56 \left( 3 \right)MHz, \hfill \\ g_j = 0.6659\left( 3 \right), \tau = 1.14\left( {13} \right) \cdot 10^{ - 7} \sec , \hfill \\ 7^2 P_{1/2} state: A\left( {^{85} Rb} \right) = 17.68\left( 8 \right)MHz,A\left( {^{87} Rb} \right) = 59.92\left( 9 \right)MHz, \hfill \\ g_j = 0.6655\left( 5 \right), \hfill \\ 6^2 P_{3/2} state: g_j = 1.3337\left( {10} \right), \tau = 1.12\left( 8 \right) \cdot 10^{ - 7} \sec for ^{87} Rb. \hfill \\ \end{gathered} $$ From the hfs coupling constants of then ² P multiplets a 11.5% core polarization contribution to the magnetic hfs of then ² P _3/2 states is obtained, which is found to be independent from the main quantum numbern. The expectation values <r ^?3> _j for thenp valence electrons corrected for core polarization are compared with those derived from the² P fine structure separation. Good agreement is achieved for allnp levels with the choice ofZ _i =Z?3=34 for the effective nuclear charge number. The nuclear quadrupole moments of⁸⁵Rb and⁸⁷Rb are rederived on the basis of this more improved treatment for thep-electron-nucleus interaction yielding $$\begin{gathered} Q_N \left( {^{85} Rb} \right) = + 0.274\left( 2 \right) \cdot 10^{ - 24} cm^2 \hfill \\ Q_N \left( {^{85} Rb} \right) = + 0.132\left( 1 \right) \cdot 10^{ - 24} cm^2 \hfill \\ \end{gathered} $$ where the error does not include the remaining theoretical uncertainty of about 10%.     

Measurements of the electronic conductivities of In-doped CaZrO<Subscript>3</Subscript> by a DC polarization technique

The following hydrogen and oxygen concentration cells using the oxide protonic conductors, \textCaZ\textr_0.98\textI\textn_0.02\textO_{3 - d} {\text{CaZ}}{{\text{r}}_{0.98}}{\text{I}}{{\text{n}}_{0.02}}{{\text{O}}_{3 - \delta }} and \textCaZ\textr_0.9\textI\textn_0.1\textO_{3 - d} {\text{CaZ}}{{\text{r}}_{0.{9}}}{\text{I}}{{\text{n}}_{0.{1}}}{{\text{O}}_{{3} - \delta }} , as the solid electrolyte were constructed, and their polarization behavior was studied,

More corrections to the sixth-order anomalous magnetic moment of the muon

The contribution to the sixth-order muon anomaly from second-order electron vacuum polarization is determined analytically to orderm _e/m _μ. The result, including the contributions from graphs containing proper and improper fourth-order electron vacuum polarization subgraphs, is $$\begin{gathered} \left( {\frac{\alpha }{\pi }} \right)^3 \left\{ {\frac{2}{9}\log ^2 } \right.\frac{{m_\mu }}{{m_e }} + \left[ {\frac{{31}}{{27}}} \right. + \frac{{\pi ^2 }}{9} - \frac{2}{3}\pi ^2 \log 2 \hfill \\ \left. { + \zeta \left( 3 \right)} \right]\log \frac{{m_\mu }}{{m_e }} + \left[ {\frac{{1075}}{{216}}} \right. - \frac{{25}}{{18}}\pi ^2 + \frac{{5\pi ^2 }}{3}\log 2 \hfill \\ \left. { - 3\zeta \left( 3 \right) + \frac{{11}}{{216}}\pi ^4 - \frac{2}{9}\pi ^2 \log ^2 2 - \frac{1}{9}log^4 2 - \frac{8}{3}a_4 } \right] \hfill \\ + \left[ {\frac{{3199}}{{1080}}\pi ^2 - \frac{{16}}{9}\pi ^2 \log 2 - \frac{{13}}{8}\pi ^3 } \right]\left. {\frac{{m_e }}{{m_\mu }}} \right\} \hfill \\ \end{gathered} $$ . To obtain the total sixth-order contribution toa _μ?a _e, one must add the light-by-light contribution to the above expression.     

Structures of distorted phases and critical and noncritical atomic displacements of elpasolite Rb<Subscript>2</Subscript>KInF<Subscript>6</Subscript> during phase transitions

The structures of all three phases of the Rb₂KInF₆ crystal have been determined from the experimental X-ray diffraction data for the powder sample. The refinement of the profile and structural parameters has been carried out by the technique implemented in the DDM program, which minimizes the differences between the derivatives of the calculated and measured X-ray intensities over the entire profile of the X-ray diffraction pattern. The results obtained have been discussed using the group-theoretical analysis of the complete order-parameter condensate, which takes into account the critical and noncritical atomic displacements and permits the interpretation of the experimental data obtained previously. It has been reliably established that the sequence of changes in the symmetry during phase transitions in Rb₂KInF₆ can be represented as $ Fm\bar 3m\xrightarrow[{0,0,\phi }]{{11 - 9\left( {\Gamma _4^ + } \right)}}{{I114} \mathord{\left/ {\vphantom {{I114} {m\xrightarrow[{\left( {\psi ,\phi ,\phi } \right)}]{{11 - 9\left( {\Gamma _4^ + } \right) \oplus 10 - 3\left( {X_3^ + } \right)}}{{P12_1 } \mathord{\left/ {\vphantom {{P12_1 } {n1}}} \right. \kern-\nulldelimiterspace} {n1}}}}} \right. \kern-\nulldelimiterspace} {m\xrightarrow[{\left( {\psi ,\phi ,\phi } \right)}]{{11 - 9\left( {\Gamma _4^ + } \right) \oplus 10 - 3\left( {X_3^ + } \right)}}{{P12_1 } \mathord{\left/ {\vphantom {{P12_1 } {n1}}} \right. \kern-\nulldelimiterspace} {n1}}}} $ Fm\bar 3m\xrightarrow[{0,0,\phi }]{{11 - 9\left( {\Gamma _4^ + } \right)}}{{I114} \mathord{\left/ {\vphantom {{I114} {m\xrightarrow[{\left( {\psi ,\phi ,\phi } \right)}]{{11 - 9\left( {\Gamma _4^ + } \right) \oplus 10 - 3\left( {X_3^ + } \right)}}{{P12_1 } \mathord{\left/ {\vphantom {{P12_1 } {n1}}} \right. \kern-\nulldelimiterspace} {n1}}}}} \right. \kern-\nulldelimiterspace} {m\xrightarrow[{\left( {\psi ,\phi ,\phi } \right)}]{{11 - 9\left( {\Gamma _4^ + } \right) \oplus 10 - 3\left( {X_3^ + } \right)}}{{P12_1 } \mathord{\left/ {\vphantom {{P12_1 } {n1}}} \right. \kern-\nulldelimiterspace} {n1}}}} .     

Structural properties of TiO2 nanocrystallites condensed in vapor-phase for photocatalyst applications

We have synthesized titanium dioxide (TiO₂) nanocrystallites by pulsed laser ablation (PLA) in oxygen (O₂) background gas for photocatalyst applications. Varying O₂ background gas pressure \( \left( {P_{{{\text{O}}_{ 2} }} } \right) \) or substrate target distance (D _TS), it was possible to change weight fraction of anatase phase in the anatase/rutile mixture from 0.2 to 1.0. Porosity of the deposited TiO₂ films increased with increasing \( \left( {P_{{{\text{O}}_{ 2} }} } \right) \) and D _TS. Relation between the process parameters and the formed crystal phases was explained from the point of cooling process in vapor-phase. Furthermore, rapid thermal annealing (RTA) was performed as post-annealing, suppressing sintering of the nanocrystallites. Photocatalytic activities of the TiO₂ nanocrystallites depended on the RTA temperature and following crystallinity restoring as well as the crystal phase: anatase or rutile.     

Three-loop relation of quark\overline {MS} and pole masses

We calculate, exactly, the next-to-leading correction to the relation between the \(\overline {MS} \) quark mass, \(\bar m\) , and the scheme-independent pole mass,M, and obtain $$\begin{gathered} \frac{M}{{\bar m(M)}} \approx 1 + \frac{4}{3}\frac{{\bar \alpha _s (M)}}{\pi } + \left[ {16.11 - 1.04\sum\limits_{i = 1}^{N_F - 1} {(1 - M_i /M)} } \right] \hfill \\ \cdot \left( {\frac{{\bar \alpha _s (M)}}{\pi }} \right)^2 + 0(\bar \alpha _s^3 (M)), \hfill \\ \end{gathered} $$ as an accurate approximation forN _F?1 light quarks of massesM _i <M. Combining this new result with known three-loop results for \(\overline {MS} \) coupling constant and mass renormalization, we relate the pole mass to the \(\overline {MS} \) mass, \(\bar m\) (μ), renormalized at arbitrary μ. The dominant next-to-leading correction comes from the finite part of on-shell two-loop mass renormalization, evaluated using integration by parts and checked by gauge invariance and infrared finiteness. Numerical results are given for charm and bottom \(\overline {MS} \) masses at μ=1 GeV. The next-to-leading corrections are comparable to the leading corrections.     

The shrinkage of the diffraction peak of the bare pomeron in QCD

The new parameterQ ₀ is introduced in our integration over transverse momentaq _t in perturbative QCD to avoid infrared divergencies. Consideringq _t >Q ₀, the distribution of wee partons in impact parameter (b _t ) and the mean radius of interaction are calculated in the framework of the leading logarithmic approximation (LLA) of perturbative QCD. It is shown that the slope of the elastic amplitude increases as \(B \propto {{\sqrt {\alpha _s In s} } \mathord{\left/ {\vphantom {{\sqrt {\alpha _s In s} } {Q_0^2 }}} \right. \kern-0em} {Q_0^2 }}\) .     

Role of Fe,Mn, and Zn ions as dopants on the electrical conductivity behavior of sodium phosphate glass

Sodium phosphate glass undoped and doped with different concentrations of chlorides of iron, manganese, and zinc were prepared by melt quenching. The synthesized glasses were characterized by elemental analysis, X-ray diffraction, infrared (IR) spectroscopy, differential scanning calorimetry, and electrical conductivity studies. The undoped sodium phosphate glass (Na₂O–P₂O₅) has low electrical conductivity σ compared to all doped glasses except for 10% FeCl₃-doped samples for which σ is found to be the lowest, and the trend is

Influence of dephasing on the entanglement teleportation via a two-qubit Heisenberg XYZ system

We study the entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system in the presence of intrinsic decoherence. The usefulness of such a system for performance of the quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation protocol T₁\mathcal{T}_1 is also investigated. The results depend on the initial conditions and the parameters of the system. The roles of system parameters such as the inhomogeneity of the magnetic field b and the spin-orbit interaction parameter D, in entanglement dynamics and fidelity of teleportation, are studied for both product and maximally entangled initial states of the resource. We show that for the product and maximally entangled initial states, increasing D amplifies the effects of dephasing and hence decreases the asymptotic entanglement and fidelity of the teleportation. For a product initial state and specific interval of the magnetic field B, the asymptotic entanglement and hence the fidelity of teleportation can be improved by increasing B. The XY and XYZ Heisenberg systems provide a minimal resource entanglement, required for realizing efficient teleportation. Also, in the absence of the magnetic field, the degree of entanglement is preserved for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.. The same is true for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right., in the absence of spin-orbit interaction D and the inhomogeneity parameter b. Therefore, it is possible to perform quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation T₁\mathcal{T}_1, with perfect quality, by choosing a proper set of parameters and employing one of these maximally entangled robust states as the initial state of the resource.     

g-factors of rotational states in176Hf,177Hf,and180Hf

g-factors of rotational states in¹⁷⁶Hf and¹⁸⁰Hf were measured with the twelve detector IPAC-apparatus of our laboratory [1]. The natural radioactivity 3.78·10¹⁰y¹⁷⁶Lu and the 5.5 h isomer^180mHf were used which populate the ground-state rotational bands of¹⁷⁶Hf and¹⁸⁰Hf. The integral rotations ofγ-γ directional correlations in strong external magnetic fields and in static hyperfine fields of (Lu→Hf)Fe₂ and HfFe₂ were observed. The following results were obtained: $$\begin{array}{l} ^{176} Hf: g\left( {4_1^ + } \right) = + 0.334\left( {38} \right) \\ ^{180} Hf: g\left( {2_1^ + } \right) = + 0.305\left( {14} \right) \\ g\left( {4_1^ + } \right) = + 0.358\left( {43} \right) \\ {{ g\left( {6_1^ + } \right)} \mathord{\left/ {\vphantom {{ g\left( {6_1^ + } \right)} {g\left( {4_1^ + } \right)}}} \right. \kern-\nulldelimiterspace} {g\left( {4_1^ + } \right)}} = + 0.95\left( {12} \right) \\ \end{array}$$ . The hyperfine field in (Lu→Hf)Fe₂ was calibrated by observing the integral rotation of the 9/2^? first excited state of¹⁷⁷Hf populated in the decay of 6.7d¹⁷⁷Lu. Theg-factor of this state was redetermined in an external magnetic field as $$^{177} Hf: g\left( {{9 \mathord{\left/ {\vphantom {9 {2^ - }}} \right. \kern-\nulldelimiterspace} {2^ - }}} \right) = + 0.228\left( 7 \right)$$ . Finally theg-factor of the 2 ₁ ⁺ state of¹⁷⁶Hf was derived from the measuredg(2 ₁ ⁺ ) of¹⁸⁰Hf by use of the precisely known ratiog(2 ₁ ⁺ ,¹⁷⁶Hf)/g(2 ₁ ⁺ ,¹⁸⁰Hf) [2] as $$^{176} Hf: g\left( {2_1^ + } \right) = + 0.315\left( {30} \right)$$ .     

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 $$\left\langle {\bar \psi \psi } \right\rangle \left( {Q^2 } \right) = \left( {{{\frac{1}{2}\log Q^2 } \mathord{\left/ {\vphantom {{\frac{1}{2}\log Q^2 } {\Lambda ^2 }}} \right. \kern-\nulldelimiterspace} {\Lambda ^2 }}} \right)^d \hat \mu ^3 ,d = {{12} \mathord{\left/ {\vphantom {{12} {\left( {33 - 2n_f } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {33 - 2n_f } \right)}}$$ .