ГАЛЬВАНОМАГНИТНЫЙ Э ФФЕКТ В ОБЛАСТИ ТЕМПЕРАТУРЫ КЮРИ

. - II- . .     

Long-wave optical absorption in electron-bombarded GaAs

The absorption spectra of n- and p-type GaAs bombarded with 2-MeV electrons at T=300K were studied in the spectral range from 0.2 eV to Eg. It was found that shallow radiation-defect levels E_c – 0.01 eV and E_c + (0.06–0.1) eV were formed. The structureless character of the absorption in the region h < Eg in electron-bombarded gallium arsenide specimens was shown to be due to the distinctive features of photoionization of deep levels and the strong electron-phonon interaction in this material.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 93–97, July, 1981.     

БЕТАТРОННЫЕ КОЛЕБАН ИЯ В УСКОРИТЕЛЕ С ОБЩИМ ПОЛЕМ I

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Betatron oscillations in an accelerator with a general field I

The paper gives a linear theory of equilibrium trajectories in an accelerator with a generalized magnetostatic field, the components of which are defined on a general rotation surface. Equations of motion of the particles in natural coordinates are derived with respect to the change in energy and dissipative force. A system of equilibrium trajectories is found in the general form. Conditions for the field components on the reference surface, necessary for the existence of equilibrium trajectories, for the conservation of their geometric similarities and for maintaining the constancy of the frequencies of the betatron oscillations, are derived. A condition is also derived which must be satisfied by the reference surface in order to conserve constant circular frequency of the particles. It is seen that it is not possible to find a field for an accelerator with an exactly constant circular frequency and with constant frequencies of the betatron oscillation in the relativistic energy region. An ultra-relativistic cyclotron with such properties is realizable.

     

Approximate calculation of frequencies of localized vibrations

An exact calculation of the frequencies of localized vibrations in a crystal with defects meets with considerable difficulties and therefore only the simplest cases have been calculated [9, 10]. An approximate calculation is confined to computing the frequencies of a system composed of several atoms in the neighbourhood of the defect. The interaction between this system and the other atoms of the lattice, which however are immobile in this approximation, is taken into consideration. Since the analytical estimate of the approximation is very rough, the approximate and exact calculations have been compared for some concrete cases (Fig. 1, 2). It is clear from these calculations that the use of the proposed approximation leads to good results.

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The energy of periodic surface structures in ferromagnetism

The periodic domain structures on unfavourably oriented surface layers of ferromagnetic materials were studied both experimentally and theoretically. The connection between the surface structure and the crystallographic orientation of the crystals was confirmed. All the terms contributing to the total energy of the surface layer were calculated. A general solution of the potential problem is given for arbitrary periodic distribution of the charges.

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On the electroluminescence of powdered zinc sulphide layers

The experimental study of the dependence of the electroluminescence brightness on the voltage confirms the correctness of the mechanism of electroluminescence, based on impact ionization in parts of the crystal where the electric field is concentrated. A study of the photoluminescent and electroluminescent spectra of phosphors containing two activators (copper and an element of rare earth) permits the determination of the magnitude of the volume of the crystal in which electroluminescence occurs. A study of the influence of the stored light sum on the brightness of electroluminescence and a study of the rate of growth of the variable and constant components of electroluminescence point to the fact that the excitation is transferred from the region of field concentration to the whole volume of the crystal.

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The semi-conducting properties of CdSnAs2

The paper gives the results of measuring the temperature dependence of the electrical conductivity(T), the Hall coefficientR _H (T) and the magnetic susceptibility(T) forn-type CdSnAs₂. The effective mass of the electrons was determined by analysis of the measured dependences on the basis of the simple theory for an isotropic non-degenerate semi-conductor. It was found to bem _n /m ₀=2×10^–2 in the intrinsic region and does not depend on the temperature; the energy gap ise _g ⁰=0·26 eV and the molar susceptibility of the CdSnAs₂ lattice _G ^mol=–112× ×10^–6. The mobility of the electrons in the intrinsic region reaches a value of _n =25 000 cm²V^–1sec^–1 at 500°K and decreases exponentially _n T ^–1.67 with rising temperature. The density of CdSnAs₂ was determined pyknometrically,g9=5·35 g cm^–3. The measurements were made on ann-type polycrystalline sample consisting of crystals a few millimetres in diameter, which at a temperature of 100°K had a free electron concentration ofn _s =6×10¹⁶ cm^–3.

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CdSnAs₂

(T), R _H (T) (T) CdSnAs₂ . m _n /m ₀= =2.10^–2, ; E _G ⁰=0,26 eV, CdSnAs_{2 G} ^mol= =–112.10^–6. 500°K _n =25 000 cm²V^–1sec^–1 , _n T ^–1,67. CdSnAs₂ =5,35 g cm^–3. , , 100°K n _s =6.10¹⁶cm^–3.

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The authors would like to thank Mr. P. Jansa for help in measuring the temperature dependence of the magnetic susceptibility.     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.     

ВлИьНИЕ стАцИОНАРНО гО РАсслОЕНИь НА ДВИж УЩИЕсь слОИ В тлЕУЩЕМ РАжРьД Е B Ne

The paper describes a new experimentally found phenomenon of the effect of standing stratification on the parameters of moving striations in the positive column of a glow discharge.

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. . M. Hobaky      

The physical nature of the production of moving striations in a d-c discharge plasma

The physical nature of the stratification of the d-c discharge plasma is found and physically interpreted. The interpretation is based on the mathematical expression of the production of periodic structure in plasma after an aperiodic disturbance, derived from an extremely simplified system of equations. Only three basic phenomena occurring in the plasma of each d-c discharge are included: a) the dependence of the rate of ionization on the electron temperature and hence on the electric field, b) the production of space charges due to the different rates of diffusion of the electrons and ions, c) the creation of additional electric fields due to the creation of space charges. The interactions of these phenomena gives rise to a chain, expanded in time and space, which leads to the production of moving striations. In agreement with experiment this structure is developed only on the side towards the anode from the place where the equilibrium state is disturbed.

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In conclusion the authors thank J. Fousek, J. Kaczér and M. Novák for carefully reading this paper and for valuable remarks, and J. Holub for carrying out the numerical and graphical work.     

СЕРНИСТЫЙ ТЕЛЛУР — ПО ЛУПРОВОДИОЕ СОЕДИНЕ НИЕ

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A contribution to the theory of ferromagnetic resonance at high power levels

The instability of spin waves at ferromagnetic resonance is discussed. An equation of the stationary state of spin wavesk0 is derived by means of the quantum theory of spin waves. It is shown when discussing this equation that the concept of the critical uniform precession angle may be obtained when using an approximation which neglects the action of spin wavesk0 backward on their own excitation. We believe we are justified in supposing that, due to this effect, a stable stationary state can exist even above the critical amplitude of uniform precession, given by theories up to now.

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In conclusion the author thanks G. A. Smolenskij for enabling him to carry out this work in his laboratory. Thanks also go to the theoretical staff of the Institute of Semi-conductors of Acad. Sci. USSR in Leningrad for valuable discussions, especially to A. I. Anselm, V. L. Gurevic and J. A. Firsov.     

The S-matrix for abstract scattering systems

Let S() be the S-matrix at energy for an abstract scattering system. We derive a bound, in terms of the interaction, on integrals of the form h () S()- _HS ² d, where denotes the Hilbert-Schmidt norm.Supported by the Swiss National Science Foundation.     

КОРРЕКЦИОННЫЕ ФАКТО РЫ ПРИ АБСОЛЮТНОЙ ДОЗ ИМЕТРИИ ПЛОСКИХ ИСТОЧНИКОВβ-ИЗЛУЧЕНИЯ С ПОМОЩЬЮ СЧЕТЧИКА ГЕЙГЕРА-МЮЛ ЛЕРА

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Quantitative method for determination of fibre texture in wires I. Principle of method and analytical expression of absorption factor

An X-ray diffraction method is described for the quantitative determination of the fibre texture in cylindrical specimens (wires), which does not require specimen preparation. The integrated intensity of the diffracted radiation from a certain atomic plane is measured in the direction parallel to the plane determined by the axis of the wire and by the direct beam for different orientations of the axis of the wire. These measurements can be carried out in practice using an X-ray counter diffractometer or Weissenberg goniometer. The pole figure is determined from the dependence of the diffracted intensity on the orientation of the wire after correcting the intensities for the absorption of radiation in the specimen. The geometric arrangement enables the absorption factor to be calculated analytically. Its form was verified experimentally by measuring the dependence of the intensity of the 220 reflection on the orientation of the axis of a cylindrical specimen of Al containing randomly oriented crystals.

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The author wishes to thank Z. iký for help in carrying out the measurements and calculations.     

Positivity of entropy production in nonequilibrium statistical mechanics

We analyze different mechanisms of entropy production in statistical mechanics, and propose formulas for the entropy production ratee() in a state . When is steady state describing the long term behavior of a system we show thate()0, and sometimes we can provee()>0.     

Unbounded derivations and invariant states

Let be a von Neumann algebra with a cyclic and separating vector . Let =i[H, ·] be the spatial derivation implemented by a selfadjoint operatorH, such thatH=0. Let be the modular operator associated with the pair (, ). We prove the equivalence of the following three conditions:1)H is essential selfadjoint onD(), andH commutes strongly with .2) The restriction ofH toD() is essential selfadjoint onD(^1/2) equipped with the inner product(|)_#=(|)+(^1/2|^1/2), , D(^1/2).3) exp (itH) exp (–itH)= for anyt.We show by an example, that the first part of 1),H is essential selfadjoint onD(), does not imply 3). This disproves a conjecture due to Bratteli and Robinson [3].Part of this work was done while O.B. was a member of Zentrum für interdisziplinäre Forschung der Universität Bielefeld     

Strong coupling expansion for classical statistical dynamics

We discuss the simple, randomly driven systemdx/dt = –x –x³ +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)ⁿ, whereR is the internal Reynolds number ()^1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp ²/2 +m ² x ²/2 +vx ⁴ +x ⁶/2, we evaluate the path integral on a lattice by assuming that thex ⁶ term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)^1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy.     

The spectrum of a quasiperiodic Schrödinger operator

The spectrum (H) of the tight binding Fibonacci Hamiltonian (H _mn= _m,n+1+ _m+1,n + _m,n v(n),v(n)= ((n–1)), 1/ is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any , and (H) is a Cantor set for 4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for 16.On leave from the Central Research Institute for Physics, Budapest, Hungary     

Systematic study of muon transfer to sulphur dioxide

In a systematic study of the transfer process to sulphur dioxide, in seven different H₂ + SO₂ gas mixtures, the time spectra of the muonic sulphur X-rays yield muon transfer rates to the SO₂ molecule, deduced from the lifetimes of the p atoms, which agree all well with each other. The muonic oxygen time spectra show an additional structure as if p atoms of another kind were present. Reduced transfer rates_O are reproducible if one uses the model of ephemeral p atoms. The intensity ratios between the different kinds of p atoms are also discussed in the framework of this model and the one of black and white p atoms.