Bounds to the differential cross-section for the processes p¯p→π+ −

Using scattering data, the integrated cross-section for p¯p^+–, and unitarity, we derive upper bounds to the differential cross-section for p¯p^{+ –}. Comparison with experimental data shows that in general the bounds are several times larger than the measured value, but that at certain points this factor is only about two or three.Presented at the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975.I would like to thank Dr. A. K.Common for useful discussions and collaboration in the early stages of this work.     

тЕМпЕРАтУРНАь жАВИс ИМОсть ЁФФЕктА ДЕМБЕ РА НА AgCl

AgCl . –190C +20C. –60C . T–130°C, . .

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The temperature dependence of the Dember effect on AgCl

The condenser method was used to study the temperature dependence of the Dember effect on monocrystalline plates of AgCl when illuminating with ultra-violet light. The dependence was studied from –190C up to room temperature. At approximately –60C a change in the effect from negative to positive was found. At temperatures around –130C there was a maximum the magnitude of which changed when the measurement was repeated. A possible interpretation of the experiments is put forward.

     

Mössbauer hyperfine interactions in thermally treated iron-yttrium oxide systems

Iron-yttrium mixed oxides in varying ratios (YFe 91, 31, 11, 12, 13, and 19) annealed to different temperatures (850, 1000 and 1250 C) have been investigated by Mössbauer spectroscopy down to 85 K. The Mössbauer spectra are complex in nature, showing up to three magnetically split hyperfine patterns in iron-rich (Y Fe 11, 12, 13 and 19) samples; these three components are attributed to characteristic YFeO₃, Y₃Fe₅O₁₂ and hematite. The yttrium-rich samples (YFe 91, 31) show only one six-line spectrum of YFeO₃.     

μSR studies in heavily doped GaAs

Transverse-field (TF) and longitudinal-field (LF) ⁺ SR measurements have been made on conducting GaAsSi (n-type 10¹⁸ cm^–3) and GaAsZn (p-type 10¹⁹ cm^–3) from 20 mK to 200 K. At low temperatures in GaAsSi, the frequency spectra show a large diamagnetic signal as well as broad lines due to bond-centered muonium (Mu _BC ). This broadening is attributed to spin exchange interactions with charge carriers in impurity bands. Only the diamagnetic signal is observed in GaAsZn. The field dependence of the TF diamagnetic relaxation rate at 5 K can be explained by the combined electric quadrupolar and Zeeman interaction between the muon and the surrounding nuclei and the temperature scan at TF=1.5 T indicates that the mechanisms responsible for the broadening are temperature independent. The candidates for the diamagnetic species are discussed in view of these results.This work is partially supported by the Natural Sciences and Engineering Research Council of Canada, the Welch Foundation (C-1048 [TLE], D-1053 [RLL]) and the U.S. National Science Foundation (DMR-8917639 [TLE, BH]).     

Electrooptical parameters of uniaxial crystals

For the linear effect in classes 4, ¯4, 42, 4 · m, 6, 62, and 6 m, one of the optic axes always coincides with the high-order symmetry axis c when the electric field e lies in a plane perpendicular to that axis, while the other describes a circular cone around c as e rotates in that plane. The same rotation in classes 3, 32, 3 · m, 3 m, and m · 3 m causes both optic axes to deviate from c to opposite sides by equal angles, both describing circular cones. One of the optic axes always coincides with c for any direction of e in classes 42 and 62, while the other axis describes an elliptic cone around c as e rotates in a plane inclined to c. Both optic axes describe an elliptic cone in classes 3 m, 32, and m · 3 m.     

Superstability estimates for anharmonic systems

We consider an anharmonic crystal described by variablesS _x ,x ^d ,S _x , with one-body interaction ¦S _x ¦ and nearest neighbor (n.n.) two body interaction ¦S _x –S _y ¦. We prove that, for ^d bounded, , where is the correlation function for the free boundary condition Gibbs state in ,>0 and are suitable constants independent of and . This generalizes previous results obtained in the case.Research partially supported by Consiglio Nazionale delle Ricerche.     

π0 → γγ in the Spinor Strong Interaction Theory

An expression for the decay rate (⁰ ) has been derived in the frameworkof the spinor strong interaction theory, a first-principles strong interaction theoryproposed some years ago as an alternative to low-energy QCD. The startingpoint is the SO(3) gauge-invariant action for two quark mesons which has beensuccessful in accounting for confinement, ^{+ +} , e⁺, and ⁰ e⁺, nonexistenceof the Higgs boson, and other low-energy mesonic phenomena. The quasi-four-quarkmeson equations developed for the decay of a vector meson into twopseudoscalar mesons V PP has been taken over here to apply to P(⁰) VV(^{+ –}) (plus ⁺ and ^– which annihilate each other). This mechanismin principle agrees with that of the assumption of vector meson dominance inthe literature. It, together with the effect of form factors, arises naturally in theformalism and need not be assumed. Equations for the perturbed vector mesonwave functions cannot be simply solved and an assumption has been made toobtain an estimate of their magnitude. Together with a constant associated withthe strong coupling obtained earlier from V() PP(K⁺K^–), the estimated decayrate is 19.2 eV, in order-of-magnitude agreement with data (7.74 eV).     

The Statistics of the Trajectory of a Certain Billiard in a Flat Two-Torus

We consider a billiard in the punctured torus obtained by removing a small disk of radius >0 from the flat torus ², with trajectory starting from the center of the puncture. In this case the phase space is given by the range of the velocity only. Let (), and respectively R(), denote the first exit time (length of the trajectory), and respectively the number of collisions with the side cushions when ² is being identified with [0,1)². We prove that the probability measures on [0, ) associated with the random variables and R are weakly convergent as 0⁺ and explicitly compute the densities of the limits. Research partially supported by ANSTI grant C6189/2000.     

R andRτ ratios at the five-loop level of perturbative QCD

We study perturbative QCD at the five-loop level. In particular we considerR = _tot(e ⁺ e ^– hadrons)/(e ⁺ e ^{– + –}) andR = ( v+hadrons)/( ev). We use our method to estimate the five-loop coefficients. As a result, we obtain _s (M _z ) = 0.1186(11) and _s (34 GeV) = 0.1396(16), which are accurate at the 1% level. We also findR = 3.8350(18), which is consistent withR and is accurate to 0.05%.     

Study of magnetic after-effect in magnesium manganese ferrites

The magnetic after-effect caused by the diffusion of electrons was studied in detail in MnMg ferrites of the series Mg _x Mn_1.15–x Fe_1.85O₄₊ ; the comparative measurements were also carried out on a sample of MgFe₂O₄₊₍<0). By combining the two methods, (a) investigation of the disaccommodation of initial permeability at different temperatures and (b) measurement of the displacement of the maximum of the temperature dependence tan with the frequency, it was possible to study the relaxation processes whose time constants lay between 0.5 sec and several hours, or between 10^–4 to 10^–7 sec. It was found that the processes taking place at low temperatures and studied by method (a) differ from those observed at high temperatures by method (b), particularly in the lower activation energies and greater dispersion of the time constants. In addition to these two main relaxation processes a weak relaxation superposed over the main disaccommodation was found in ferrites with non-zero content of manganese. An analysis of the intensity of different relaxation effects showed the participation of Mn ions in these relaxation effects and it was found that both main relaxations are probably equivalent as regards the final steady state, to the creation of which they lead; they differ however in the mechanism of electron diffusion by which this state is realized. The main features of the different diffusion mechanisms are discussed.

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, , MnMg Mg _x Mn_1.15–x Fe_1.85O₄₊ . MgFe₂O_{4+ (}<0). ()- , () tg , , 0,5 sec , 10^–4–10^–7 sec. , , () , , (), , , . , . Mn , , , , , ; , , , . .

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In conclusion the author thanks Dr. J. Bro and K. Závta for valuable discussion and F. Vilím for carefully carrying out the measurements.     

ИССЛЕДОВАНИЕ ЭРОЗИЙ НОГО ДЕЙСТВИЯ ИМПУЛЬ СНЯХ ЭЛЕКТРИЧЕСКИХ РАЗРЯ ДОВ С СЛАБЫМ ТОКОМ

50–100 , 1–2 1–10 . - . - . , , - . -.     

Birefringence in YAlO3∶Ce between 2–5 eV

This contribution presents birefringence spectra for orthorhombic YAlO₃Ce single crystal in the region 2–5 eV. The spectra were measured by means of a reflection method of null ellipsometry and were compared with spectra of YAlO₃:Nd determined from values measured in the region of lower energies (1·1–2·2 eV). We have found that there are differences between the spectra of YAlO₃Nd and YAlO₃:Ce which are most pronounced in thea-axis direction.The author is most grateful to Ing. . Viovský CSc. for helpful discussions during the course of this work and to Monokrystaly Turnov for preparation of the samples.     

Four-wave mixing in CO via the C 1Σ+ (υ′=0) state

Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (_VUV=2₁–₂) of pulsed dye laser radiation in carbon monoxide (CO). The frequency ₁ was tuned to the C ¹⁺(=0)X ¹⁺(=0) two-photon transition, while the dye laser frequency ₂ was scaned around 17650 cm^–1 which corresponds to the A ¹(=7)«C ¹⁺(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A ¹(=7) state and (ii) that the off-resonance excitation in the C ¹⁺(=0)X ¹⁺(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed.     

ВЛИЯНИЕ СОДЕРЖАНИЯ К ИСЛОРОДА НА ЭЛЕКТРИЧЕСКИЕ И ТЕ РМОЭЛЕКТРИЧЕСКИЕ СВОЙСТВА ТРОЙНОЙ СИС ТЕМЫ Вi2Те3−x Sе x

, Bi₂Te_3–x Se _x . , , . , , . .

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Influence of oxygen content on electric and thermoelectric properties of ternary system Bi₂Te_3–x Se _x

A study is made of the influence of oxygen, contained in the semi-conducting system Bi₂Te_3–x Sé _x , on the electric and thermoelectric properties. It is shown that the addition of oxygen to the prepared samples Bi₂Te_2.4Se_0.6 causes a decrease in electric conductivity while the thermoelectric force remains unchanged. This influence is connected with a decrease in the mobility of the electrons but their concentration is not influenced by the presence of oxygen. Conclusions are reached as to the influence of oxygen on the efficiency of the conversion of thermal energy into electric energy and vice versa.

     

Theory of the singular quantum oscillator

We propose a number of arguments in favor of reevaluating the theory of a quantum oscillator described by the Hamiltonian H=–d²/dx² + 2²x² + x^–2(=2m=1). We propose that functions ₊(x) which continuously reduce to even harmonic oscillator solutions in the 0 limit be taken as the even solutions of the Hamiltonian in the –1/4 < < 3/4 range. In this scheme the problem becomes truly one-dimensional such that even and odd parity energy levels alternate, whereas the usual approach leads to parity degeneracy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 85–89, October, 1989.     

ГАЛЬВАНОМАГНИТНЫЙ Э ФФЕКТ В ОБЛАСТИ ТЕМПЕРАТУРЫ КЮРИ

. - II- . .     

Über die an „Schwachen“ Grenzflächen Entstehenden Kopfwellen

Zusammenfassung In der vorliegenden Arbeit werden die Kopfwellen untersucht, die beim Auffallen einer harmonischen Schall-Kugelwelle auf die Ebene Grenzfläche zwischen zwei flüssigen Medien entstehen. Vorausgesetzt wird, daß die Grenzfläche schwach ist, d. h. daß die Geschwindigkeit der Schallwellen im Medium mit der Erregungsquelle nur um weniges kleiner ist als die Geschwindigkeit der Schallwellen im Medium ohne die Quelle.

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, . , , . . .

     

Schrödinger Operators with Empty Singularly Continuous Spectra

Let H be a semibounded perturbation of the Laplacian H ₀ in L ²( ^d ). For an admissible function sufficient conditions are given for the completeness of the scattering system (H), (H ₀). If is the exponential function and if e^{– H} is an integral operator we denote the kernel of the difference D = e^{– H} – e^{– H} ₀ by D (x, y), > 0. The singularly continuous spectrum of H is empty if^d dx ^d dy |D(x,y)| (1 + |y|²)< for some > 1. This result is applied to potential perturbations and to perturbations by imposing Dirichlet boundary conditions.     

An investigation of finite-size scaling for systems with long-range interaction: The spherical model

A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr ^{–d –} , whered is the space dimensionality and>0. It allows for a unified treatment of short-range (=2) and long-range (<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL ^d–d× ^d subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd, 0d. It is shown that the-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities.     

Asymptotic behaviour of spin-momentum distribution observables for fermion fields with cut-off self-coupling

In a previous paper asymptotic creation and annhilation operatorsa _± ^# have been constructed by the Kato-Mugibayashi method from the creation and annihilation operatorsa ^# for spin 1/2 fields with an interaction Hamiltonian density which is an evendegree polynomial in the field with ultra-violet cut-off and its derivatives. For any eigenvector of the total HamiltonianH=H ₀+H _I partial isometries _± have been defined so thata _± ^# equal _± a ^# *_± on the ranges _± of _±. Since the existence of a groundstate ofH has been proved, the existence of at least one pair _± follows. The purpose of this paper is to show that for any _± orthogonal to the distribution of spins and momenta of the interacting Schrödinger states exp[–itH]_± approaches fort the distributions of spins and momenta of the free state exp[–itH ₀] if a wave-amplitude renormalization is carried out in _±. This is achieved by studying the expectation values of the operators in themaximally abelian W*-algebra generated by operators of the form a*a, in terms of whichany information about spins and momenta can be expressed.Supported in part by the National Research Council of Canada.