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.     

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).     

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.     

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}}}} .     

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 .     

Comment on “Evaluation of concentration-depth profiles by sputtering in SIMS and AES” by S. Hofmann

The statistics of the sputtering process, which has been used to explain sputterbroadening effect due to surface roughness, has been treated with conditional probabilities. This results in the relationship, , instead of derived by S. Hofmann [Appl. Phys.9, 59 (1976)], where δz,z, and are the depth resolution, sputtered depth and sputtering yield, respectively.     

Creating large NOON states with imperfect phase control

Optical NOON states ${{\left( {\left| {\left. {N,0} \right\rangle + } \right|\left. {0,N} \right\rangle } \right)} \mathord{\left/ {\vphantom {{\left( {\left| {\left. {N,0} \right\rangle + } \right|\left. {0,N} \right\rangle } \right)} {\sqrt 2 }}} \right. \kern-\nulldelimiterspace} {\sqrt 2 }}${{\left( {\left| {\left. {N,0} \right\rangle + } \right|\left. {0,N} \right\rangle } \right)} \mathord{\left/ {\vphantom {{\left( {\left| {\left. {N,0} \right\rangle + } \right|\left. {0,N} \right\rangle } \right)} {\sqrt 2 }}} \right. \kern-\nulldelimiterspace} {\sqrt 2 }} are an important resource for Heisenberg-limited metrology and quantum lithography. The only known methods for creating NOON states with arbitrary N via linear optics and projective measurements seem to have a limited range of application due to imperfect phase control. Here, we show that bootstrapping techniques can be used to create high-fidelity NOON states of arbitrary size.     

Painlevé analysis and hamiltonian structure of a new space-dependent KdV equation

We deduce the Lax pair for a new space-dependent KdV equation, , via the technique of Painlevé analysis. From it, infinitely many conservation laws are deduced and the symplectic structure is obtained.     

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.     

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.     

Search for double electron capture of 106Cd

A search for double electron capture of ¹⁰⁶Cd was performed at the Modane Underground Laboratory (4800 m w.e.) using a low-background and high-sensitivity multidetector spectrometer TGV-2 (Telescope Germanium Vertical). New limits on β ⁺/EC, EC/EC decays of ¹⁰⁶Cd were obtained from preliminary calculations of experimental data accumulated for 4800 h of measurement of 10 g of ¹⁰⁶Cd with enrichment of 75%. They are > 9.1 × 10¹⁸ yr, > 1.9 × 10¹⁹ yr for transitions to the first 2⁺, 511.9 keV excited state of ¹⁰⁶Pd, and > 1.3 × 10¹⁹ yr, > 6.2 × 10¹⁹ yr for transitions to the ground 0⁺ state of ¹⁰⁶Pd. All limits are given at 90% C.L. The text was submitted by the authors in English.     

Quantum conformal superspace

For a compact connected orientablen-manifoldM, n 3, we study the structure ofclassical superspace ,quantum superspace ,classical conformal superspace , andquantum conformal superspace . The study of the structure of these spaces is motivated by questions involving reduction of the usual canonical Hamiltonian formulation of general relativity to a non-degenerate Hamiltonian formulation, and to questions involving the quantization of the gravitational field. We show that if the degree of symmetry ofM is zero, thenS,S ₀,C, andC ₀ areilh orbifolds. The case of most importance for general relativity is dimensionn=3. In this case, assuming that the extended Poincaré conjecture is true, we show that quantum superspaceS ₀ and quantum conformal superspaceC ₀ are in factilh-manifolds. If, moreover,M is a Haken manifold, then quantum superspace and quantum conformal superspace arecontractible ilh-manifolds. In this case, there are no Gribov ambiguities for the configuration spacesS ₀ andC ₀. Our results are applicable to questions involving the problem of thereduction of Einstein's vacuum equations and to problems involving quantization of the gravitational field. For the problem of reduction, one searches for a way to reduce the canonical Hamiltonian formulation together with its constraint equations to an unconstrained Hamiltonian system on a reduced phase space. For the problem of quantum gravity, the spaceC ₀ will play a natural role in any quantization procedure based on the use of conformal methods and the reduced Hamiltonian formulation.     

Anomalous temperature dependence of the order parameter of a superconductor with weakly correlated impurities

It is shown that weak correlations between pair-breaking impurities in superconductors influence the temperature dependence of the order parameter within the Ginzburg-Landau region if correlation radius of impurities R is greater than the coherence length of the superconductor ξ₀. The dependence of the square of the average order parameter on a temperature difference T _c − T changes its slope in a region $ \xi _0 \sqrt {{{T_c } \mathord{\left/ {\vphantom {{T_c } {\left( {T_c - T} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {T_c - T} \right)}}} \sim R $ \xi _0 \sqrt {{{T_c } \mathord{\left/ {\vphantom {{T_c } {\left( {T_c - T} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {T_c - T} \right)}}} \sim R . The influence of correlations of impurities on other thermodynamic properties of superconductors is discussed.     

Diffusion of proton in alumina-rich nonstoichiometric magnesium aluminate spinel

The phenomenon of the diffusion of proton and deuteron in a single crystal of magnesium aluminate spinel was studied by infrared absorption. The chemical diffusion coefficient of proton was determined by the relaxation time of the absorption intensity upon the substitution of deuteron with proton. The temperature dependence of the chemical diffusion coefficient of proton for was expressed as . The chemical diffusion coefficient of proton was found to be independent of the composition of spinel and of the atmosphere. Paper presented at the 11th Euro Conference on the Science and Technology of Ionics, Batz-sur-Mer, Sept. 9–15 2007.     

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.     

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.     

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 $$S_N = o\left( {\left[ {{{\log N} \mathord{\left/ {\vphantom {{\log N} {\log \log N}}} \right. \kern-\nulldelimiterspace} {\log \log N}}} \right]} \right)$$      

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.