On surface layers on BaTiO3 single crystals

The possibility of explaining the existence of a surface layer on BaTiO₃ crystals by the presence of Schottky defects in the crystal is investigated. The magnitude of the potential difference between the surface and the interior of the crystal and the thickness of the surface layer, which at temperatures of over 400°C agrees with the measured values, are calculated for the cubic phase from a simplified ionic model.

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BaTiO₃

iO₃ . , 400° .

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In conclusion the author would like to thank Dr. M. Trlifaj and V. Janovec, candidates of physics and mathematics, for valuable remarks.     

Instability in degenerate two-photon running wave laser

The stability of the homogeneously broadened and degenerate two-photon running wave laser is analysed by using the full set of matter-field equations. The stability depends on the relative size of the relaxation constants. For 2k>1+r(k=/,r=/; is the cavity loss of the field and , are the longitudinal and transversal decay constants, respectively) no stable lasing state exists. Forr<k<(1+r)/2 an instability occurs. With the decrease in pumping the stable lasing state loses its stability due to Hopf-bifurcation.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

Spin manifolds,killing spinors and universality of the Hijazi inequality

In terms of the Dirac operator P, we introduce on any field a first-order operator D and show that the operator (–) on the spinors (=(n/4(n–1))R; dim W=n) is positive. By means of a universal formula, we show that, on a compact spin manifold of dimension 3, the Hijazi inequality [8] holds for every spinor field such that (P, P) = ²(, ) (=const.). In the limiting case, the manifold admits a Killing spinor which can be evaluated in terms of . Different properties of spin manifolds admitting Killing spinors are proved. D is nothing but the twistor operator.     

A contribution to direct processes in the Co59(p,n) reaction forE p ∼ 6·5 MeV

Nuclear emulsions were used to study the energy spectrum and forward-backward asymmetry of neutrons from the Co⁵⁹(p,n) reaction forE _p 6·5 MeV. It was found that the decay of the compound nucleus makes a maximum contribution of 50% to the reaction yield. Energies of some excited states of the Ni⁵⁹ nucleus were also determined.

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Co⁵⁹(p,n) E _p 6,5 MeV

- Co⁵⁹(p,n) E _p 6,5 MeV. , 50%. , Ni⁵⁹.

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The authors would like to thank all those who helped in this work, particularly all members of the cyclotron group of the Nuclear Research Institute of the Czechoslovak Academy of Sciences, who so willingly helped with the irradiation, and H. Koutová from the Faculty of Technical and Nuclear Physics, who carefully measured the emulsions. Our thanks are also due to R. Krejová from the Faculty of Technical and Nuclear Physics for developing the emulsions and J. Kopecký from the Nuclear Research Institute for providing the cobalt target.     

Determination of accuracy in measuring the parameters of tetragonal and hexagonal lattices

The procedure for determining the accuracy when measuring the parameters of tetragonal and hexagonal lattices is described. The accuracy can easily be calculated for all common methods by means of graphically represented functions. The relations derived can be used as quantitative criteria for the suitability of the combination of lines from which the lattice parameters are to be determined.

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. , . , .

     

Characterization of the Weyl solutions

For the Weyl solutions(z, x) of the Schrödinger and Dirac equations, asymptotics for |z| are obtained. This gives a possibility of selecting Weyl solutions by their behaviour when |z| . Some applications are given.     

ВОЗНИКНОВЕНИЕ КАТОД НЫХ ПЯТЕН И РАСПРЕДЕЛЕНИЕ ПЛОТ НОСТИ ТОКА В КАТОДНЫХ ПЯТНАХ СИЛНОТОЧНОГО ЭЛЕКТРИЧЕСКОГО РАЗР ЯДА

. , 760 mm . .

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Formation of cathode spots and current density distribution in cathode spots of short-time high-intensity electric discharge

The connection between the current density distribution in a spot and the vapour jets was found for a short-time high-intensity electric discharge by studying the structure of partial cathode traces and measuring the current density on the cathode. The variation of the current density on the spot with the current gradient was also found and the etching of the cathode surface with ionic bombardment at a pressure of 760 mm Hg was observed.

     

Solar wind protons,alpha particles and electrons in the shock wave and the potential barrier (The intershock project)

The paper discusses the dynamics of solar wind proton,-particle and electron fluxes near the Earth's bow shock front. In subsequently developed events, deceleration and deflection of ion components and electron heating are observed. The velocity distributions of protons and-particles behind the shock front have a strongly inhomogeneous structure that is gradually smoothing out in the magnetosheath. Unlike protons,-particles behind the front do not generate beams with energy exceeding that of the solar wind.Presented at the Colloquium on Plasma physics Topics Common to the Laboratory and the Space Plasma Research, September 21–25, 1987, Skalsky Dvr, Czechoslovakia.     

Influence of relative humidity on surface conductivity of germanium

A study was made of the influence of the relative humidity (from 0.5–90%) on the surface conductivity of bothp- andn-type germanium having differing resistivity. It was. found that the range of changes in the surface potential did not depend on the volume properties of germanium. An analysis of the experimental results shows that the surface potential has values approximately in the range from _s =–3kT/q to _s =+5kT/q for a change in humidity from 0.5 to 90%. Assuming that the Fermi level changes on the outer side of the oxide layer by approximately the same value as on the germaniumgermanium oxide boundary as a result of the increase and decrease of slow states, it follows that the levels of the slow centres are considerably distant from the Fermi level during the whole humidity range. It is also shown that on the first monomolecular layer of adsorbed water there is an increment of (7.5±0.8) x 10¹⁰ donor levels per cm². This increase in levels either decreases with the number of adsorbed monomolecular layers of water and for 90% humidity has approximately the value 2×10¹⁰ cm^–2 or remains almost unchanged with the number of layers, if it is assumed that for _s =6.0kT/q the Fermi level passes through the centres of adsorbed water.

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0,5 90% p n. . , _s =– 3kT/q _s =+ 5kT/q 0,5 90%. , - , , . , (7,5 ±0,8). 10¹⁰ cm². 90% . 2. 10¹⁰ cm^–2 , , , _s =6,0kT/q .

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In conclusion the author thanks Dr. J. Taue for instigating this work and S. Koc, C. Sc., for remarks and the interest with which he followed the work. He also thanks A.Müller for measuring the Hall constant in the samples.     

ИжМЕРЕНИЕ пОльРИжАц ИИ пРОтОНОВ пРИ УпРУг ОМ РАссЕьНИИ НА УглЕРОД Е

, . 6,5 . 3,6–4,52 :P(40 ) = 0,30±+ 0,05;P(45/)=0,36±0,07;P(50/)=0,33±0,06;P(60/)=0,20±0,05. , , .

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The measurement of the polarization of protons scattered elastically on carbon

The polarization of protons scattered elastically on carbon was measured by means of a cyclotron proton beam accelerated to 6.5 MeV. The following angular distribution was found in the energy interval from 3.60 to 4.52 MeV:P(40 _lab )=0.30±0.05;P(45 _lab ^o )=0.36±0.07;P(50 _lab )=0.33±0.06;P(60 _lab )=0.20±0.05. The results were compared with calculations given in the literature.

     

Radiation effects in the production and decay of ψ mesons by leptons

A new expression _e is obtained for resonance in the reaction e⁺e^– ar ^+– with allowance for the radiative corrections, which also contain the emission of hard photons by the final leptons and the final value of the energy resolution E. An expression is obtained for the total probability of radiative lepton decay. A numerical analysis of the experimental data is made for the reaction ^+–, and the parameters e⁺e^– (3, 1) e⁺e^–, and _e ² /, _e, and are determined for (3, 1) resonance-with allowance for the radiative corrections.This paper was read (November 17–21, 1975) at a session on high-energy physics of the Department of Nuclear Physics of the Academy of Sciences of the USSR.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 29–34, March, 1977.     

The spectrum of a Schrödinger operator inL p ℝ v isp-independent

LetH _p =–1/2+V denote a Schrödinger operator, acting inL _p ^v , 1p. We show that (H _p )=(H ₂) for allp[1, ], for rather general potentialsV.     

Radiative decays of the Z boson

We calculate the Stokes parameters of the photons produced in the decays of neutral vector bosons Z, Z 1+¯1+ and Z q+¯q+, wherel=e, , or , and q is a quark. In the decays of unpolarized Z bosons (with the production of unpolarized leptons or quarks) the nonzero Stokes parameters for ₂ (circularly polarized photons) and ₃ (linearly polarized photons). The magnitude of ₃ does not depend on the parameters of the netural weak current of the leptons and the quarks (if their mass is neglected). The anomalous magnetic moment of the Z boson is studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 38–43, February, 1986.     

Slow non-exponential changes oe surface conductivity of germanium

A study was made of slow relaxation effects produced during changes in the external d-c electric field above the oxided surface of germanium and an empirical relation was found to describe their time dependence. It is seen that the activation energy of the control process, which is about 0·4 eV, can be determined from the temperature dependence of slow effects.

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, , , . , , 0,4 eV.

     

К СПЕКТРУ ПОГЛОЩЕНИЯ АМОРФНОГО СЕЛЕНА В ИНФРАКРАСНОЙ ОБЛАС ТИ

0,6 25 . , , . , 13,4 20,4 , , , . . , . .

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A contribution to the absorption spectrum of amorphous selenium in the infra-red region

The absorption spectrum of amorphous selenium was measured in the region of 0·6 to 25 on samples of high purity and homogeneity. The absorption bands of amorphous and liquid sulphur were also measured in the same wave-length region. The measurements showed that the absorption bands 13·4 and 20·4 , appearing in the spectrum of amorphous selenium, are its intrinsic absorption bands and are not caused by impurities, as some authors think. The similarity between the infra-red spectra of selenium and sulphur is shown.

     

Representations of state space transformations by Markov kernels

Every convex subset of a locally convex Hausdorff space (X, ) is equipped with the (-algebra generated by its-relatively open subsets. Within the set () of probability measures on two particular convex subsets are considered: (a) the set ^s () of probability measures with a separable support, and (b) the set ^c () of probability measures with a compact convex support. If is the base of a cone inX, then there exists an affine barycenter map from ^c () onto whose composition with the natural embedding of in ^c () yields the identity map on , and every-continuous affine transformation of can be represented by an affine transformation of ^c () that is induced by a Markov kernel. If (X, ) is a Banach space and is a closed, bounded, generating cone base inX that is contained in a hyperplane, then analogous results are obtained with respect to ^s (). Since the state spaces considered in noncommutative measure theory are cone bases and every change in time of an empirical system can be thought of as an affine transformation of the associated state space (Schrödinger picture), the existence of these representation theorems implies that the time evolution of general empirical systems can be described by dynamical concepts borrowed from classical probability theory.     

Calculation of the dispersion of the third-order optical nonlinearity in C60 films

Using wave functions determined from ground-state local-density calculations, we have calculated the wave-dispersed free response of the optical nonlinear polarizability ⁽³⁾(–3;,,), for the C₆₀ molecule and ⁽³⁾(–3;,,) i.e. Third-Harmonic Generation (THG) for films using a sum-over-states approach. The influence of screening was determined by applying an external static electric field in separate selfconsistent calculations to evaluate induced dipole moments which was used to determine the static linear and nonlinear polarizabilities. The polarizabilities calculated in the static limit were used to determine an effective screening parameter which was, in turn, used together with an RPA approach to calculate screened wave-dispersed, third-order nonlinear optical properties such as ⁽³⁾(–3;,,) and ⁽³⁾(–3;,,). Comparing evaluated polarizabilities with experimental values we found that the non-resonant free polarizability compares well in absolute magnitude with experimental results. Inclusion of screening results in a polarizability about two orders of magnitude below the experimental values.Paper presented at the 129th WE-Heraeus-Seminar on Surface Studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994     

Zum Problem der Exoelektronenemission

Zusammenfassung Es werden die zwei einfachsten Fälle der Exoelektronenemission untersucht und auf Grund dessen geeignete Verfahren zur Verarbeitung der Versuchsergebnisse vorgeschlagen.

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ВЛИЯНИЕ ДАВЛЕНИЯ НА Ч УВСТВИТЕЛЬНОСТЬ ФОТОГРАФИЧЕСКОЙ ЭМУ ЛЬСИИ

- gr, -, . - , - . , , .