Rapid graphical determination of the radial intensity distribution of the small-angle scattering of X-rays from the measured data

The radially symmetrical small-angle scattering pattern (which would be obtained by the use of a direct beam having a point-like cross section) is in practice distorted, especially by the beam height. To eliminate this distortion the integration of a set of curves based on the derivative of the measured intensity distribution is required to derive the true radial intensity distribution. A rapid graphical method of plotting these curves is described and its accuracy is proved on an example. It is further shown that the radial intensity distribution can be determined in principle using the values of the measured curve instead of its derivative.

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( ) . , . . . , .

     

Zero measure spectrum for the almost Mathieu operator

We study the almost Mathieu operator: (H _{, ,} u)(n)=u(n+1)+u(n-1)+ cos (2n+)u(n), onl ² (Z), and show that for all ,, and (Lebesgue) a.e. , the Lebesgue measure of its spectrum is precisely |4–2|. In particular, for ||=2 the spectrum is a zero measure cantor set. Moreover, for a large set of irrational 's (and ||=2) we show that the Hausdorff dimension of the spectrum is smaller than or equal to 1/2.Work partially supported by the GIF     

Influence of temperature on integrated intensity of (200) reflection of pure Al

The temperature dependence of the intensity and reflecting range of the (200) reflection of X-rays on an aluminium crystal exhibiting strong primary extinction was studied. It was found that the observed temperature dependence cannot be even approximately expressed by the Debye-Waller factor. The reversible change in the system of imperfections in the crystal is suggested and discussed as a mechanism qualitatively explaining the observed phenomena.

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(200) A1

(200) , . , , , -. , .

     

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.     

Investigation of the excitation of nitrogen molecules in the positive column of a discharge in a mixture of CO2 and N2

The absolute populations of the electron states of the nitrogen molecule C³_u and B³_g in the positive column of a discharge in a mixture of CO₂ and N₂ at an overall pressure of 2.5 mm Hg, a ratio of the components of 11, and a current of 60 mA, are determined. An estimate is made of the possibility of exciting the electron state C³_u by direct electron collision and by multistage excitation from the electron state B³_g. It is suggested that the most probable process by which the electron state C³_u is excited is multistage excitation from vibrational levels of the electron state B³_g.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 49–52, October, 1972.     

Химическая сенсиБил изация фотографичес кой эмульсии

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Chemical sensiblilisation of photographic emulsion

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, 7. V. 1953 .     

Embedding of posets into lattices in quantum logic

It has been proposed that some posets of quantum logic could be embedded into lattices in order to recover the lattice structure avoiding the introduction of ad hoc axioms. We consider here the embedding _s of any posetS into the complete lattice _s of its closed ideals (normal embedding ofS) and show that _s can be characterized (up to a lattice isomorphism) either by means of a density property or by means of a minimality property. Both of these suggest that the normal embedding satisfies some intuitive conditions which make it preferable with respect to other possible embeddings ofS. We consider the poset of all the effects associated to yes-no experiments and briefly comment on the application of the normal embedding in this case. The possibility of giving a physical interpretation to the elements of is also discussed.Research sponsored by CNR and INFN (Italy).     

Spectral superbroadening of self-focused picosecond laser pulses in D2O

Intense picosecond light pulses of a mode-locked Nd: glass laser at _L =1054 nm (fundamental wavelength) and _SH =527 nm (second harmonic wavelength) are passed through a sample of D₂O under self-focusing conditions. Spectrally structured superbroadened, spatially bell-shaped emission in the forward direction is obtained. Primary generation processes are pump-pulse-degenerate stimulated parametric four-photon interaction (₁ + _{1 3} + ₄) and stimulated Raman scattering (_{1 R} + ), which occur concurrently (₁= _L or _SH angular pump frequency, #x03C9; _R first Stokes frequency, #x03C9; signal frequency, #x03C9;₃ signal frequency, #x03C9;₄ idler frequency). The parametric four-photon interaction occurs under collinear non-phase-matched conditions and under longitudinally phase-matched, transversally non-phase-matched (erenkov-like) conditions. Subsequent interaction processes are pump-pulse-nondegenerate four-photon interaction of the type ₁ + _{R 3} + ₄, coherent antiStokes Raman scattering (CARS, ₁ + ₁ – _{4 3}), inverse Raman scattering ( _A + ₁ + ), and cascading light up-conversion of the type ₁ + _(i) – _{R (i+1)}.     

On the basic laws of reaction kinetics

The paper gives the basic laws necessary and in principle sufficient for constructing a system of differential equations for any reaction kinetic process. A new and more exact formulation of two of the basic laws (the principle of superposition of partial reaction velocities and the Guldberg-Waage law) is made possible by an exact definition of the important quantities of this subject. In conclusion the paper points out the difference between the general form of the differential equations for concentrations of components expressed in moles per unit weight and that for concentrations of components expressed in moles per unit volume.

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On the lunar variation of cosmic radiation

The paper investigates the lunar variation of the intensity of cosmic radiation as assumed by E. Bagge and O. Binder. By evaluating the data of two stations on the same meridian circle (Rome and Makapuu Point) we reach the conclusion that this lunar variation is only apparent. The result obtained by E. Bagge and O. Binder could be caused by a small difference between the diurnal period and the assumed lunar variation. This statement is demonstrated by searching for variations with periods 22, 23, 24, 25 and 26 hours which also differ little from the 24-hour period of the diurnal variation. For these calculations the data of the station Mt. Norikura were used.

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, . . . , ( ), , . , . . , . 22, 23, 24, 25 26 , 24 . . .

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In conclusion the authors wish to express their thanks to J. Sláma for his valuable help in the numerical calculations.     

Radiation damping of waves in a cold magnetized two-component plasma

It is shown in this paper that the damping decrements of electromagnetic waves with right circular polarization and the decrements of plasma oscillations near the cyclotron and hybrid frequencies in a strong magnetic field _eBpe are proportional to the square of the cyclotron frequencies _eB and _iB. In a weak magnetic field _eBpe the damping decrements of all modes are proportional to the square of the plasma oscillation frequencies _pe, _pi. Taking account of ions results in a nonzero damping decrement for electromagnetic waves with left circular polarization.Deceased.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, p. 8–11, October, 1982.In conclusion, I am grateful to L. S. Kuz'menkov and P. Polyakov for constant attention to the research and for useful remarks.     

The distribution of neutron density in the vicinity of a partly inserted black rod in two-group approximation

The neutron density in the vicinity of a black cylindrical rod partly inserted in a bare reactor is calculated and illustrated by a numerical example. The starting point is a two-group diffusion theory approximation. While the dependence of the effect of the rod on the insertion depth can be calculated simply by means of perturbation theory, the question of the neutron density estimate in the vicinity of the rod is considerably more difficult and in some considerations the estimate of the neutron density caused by the presence of the rod is indispensable. The method makes it possible to determine the reactivity value of the rod in dependence on the insertion depth and especially the neutron density deformation in the vicinity of the rod.

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()

. , . , , . , . [1] . .

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In conclusion the author thanks J. Svato for help in carrying out the numerical calculations.     

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.

     

Normalization in the Spinor Strong Interaction Theory and Strong Decay of Vector Meson V → PP

The meson wave function in the spinor stronginteraction theory is uniquely normalized on dimensionalgrounds, thus bypassing the fundamental problems in thenormalization of Klein-Gordon (KG) and Bethe-Salpeter amplitudes for mesons. While the KG amplitudeis proportional to 1/E, the present meson wavefunction is not and is thus flavor-independent. Theconfinement term is inactive for free mesons, but isactivated when interacting with another hadron or chargedlepton. The theory is applied to the strong decay of atwo-quark vector meson into two pseudoscalar mesons V PP. The so-obtained and estimated decay rates are consistent with data, as are the ratios ofthese rates to the corresponding radiative decay V P rates. These decay rates indicate apossible connection of the strong quark-quark coupling_s with the electromagnetic coupling alpha via_s = ^1/4 = 0.2923.Contrary to the standard electroweak model (SM), theelectromagnetic and weak couplings are detached fromeach other in connection with the absence of Higgs bosons,without altering the main results of the SM.     

Elimination of variables in simple laser equations

The usual way of obtaining rate equations (RE) and a single equation for the field amplitude (EFA) from the semiclassical laser equations (Lorenz-Haken model) is reexamined by undertaking a systematic elimination procedure developed in synergetics. The RE and EFA are justified in the case 1 (, ) and case 2 (, ), respectively. We show that, because the eliminated variable happens to contain a considerable contribution from an unstable mode, the usual elimination technique in the case 3 (, ) leads to an inconsistency. As important by-products we obtain the RE and EFA for arbitrary cavity relaxation constant (). Some remarks are given on the direct elimination technique in the non-diagonal representation in the study of instabilities.     

СЕРНИСТЫЙ ТЕЛЛУР — ПО ЛУПРОВОДИОЕ СОЕДИНЕ НИЕ

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A theory of 1/f noise

Letu() be an absolutely integrable function and define the random process where thet _i are Poisson arrivals and thes _i, are identically distributed nonnegative random variables. Under routine independence assumptions, one may then calculate a formula for the spectrum ofn(t), S _n(), in terms of the probability density ofs, p_s(). If any probability density p_s() having the property p_s() I for small is substituted into this formula, the calculated S_n() is such that S_n() 1 for small . However, this is not a spectrum of a well-defined random process; here, it is termed alimit spectrum. If a probability density having the property p_s() for small , where > 0, is substituted into the formula instead, a spectrum is calculated which is indeed the spectrum of a well-defined random process. Also, if the latter p_s is suitably close to the former p_s, then the spectrum in the second case approximates, to an arbitrary, degree of accuracy, the limit spectrum. It is shown how one may thereby have 1/f noise with low-frequency turnover, and also strict 1/f ^1– noise (the latter spectrum being integrable for > 0). Suitable examples are given. Actually, u() may be itself a random process, and the theory is developed on this basis.     

Soliton mass and surface tension in the (λ|Ø|4)2 quantum field model

The spectrum of the mass operator on the soliton sectors of the anisotropic (|ø|⁴)₂—and the (ø⁴)₂—quantum field models in the two phase region is analyzed. It is proven that, for small enough >0, the mass gapm _s() on the soliton sector is positive, andm _s()=0(^–1). This involves estimatingm _s() from below by a quantity () analogous to the surface tension in the statistical mechanics of two dimensional, classical spin systems and then estimating () by methods of Euclidean field theory. In principle, our methods apply to any two dimensional quantum field model with a spontaneously broken, internal symmetry group.A Sloan Foundation Fellow; Research supported in part by the U.S. National Science Foundation under Grant No. MPS 75-11864.Supported in part by the National Science Foundation under Grant No. PHY 76-17191     

The thickness dependence of the permittivity of barium titanate single crystals

A thickness dependence of the permittivity ofc-domain barium titanate single crystals was found. The experimental results were explained by means of a model of a dielectric with surface layers. The thickness of the layer and the permittivity of the surface layer and bulk of the crystal were determined.

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iO₃

iO₃, -. . , .

     

Spectral asymptotics for the Schrödinger operator with potential which steadies at infinity

We consider the discrete spectrum of the selfadjoint Schrödinger operatorA _h =–h ² +V defined inL ²(^m) with potentialV which steadies at infinity, i.e.V(x)=g+|x|^– f(1+o(1)) as |x| for>0 and some homogeneous functionsg andf of order zero. Let _h (),0, be the total multiplicity of the eigenvalues ofA _h smaller thanM–, M being the minimum value ofg over the unit sphereS ^m–1 (hence,M coincides with the lower bound of the essential spectrum ofA _h ). We study the asymptotic behaviour of ₁() as0, or of _h () ash0, the number0 being fixed. We find that these asymptotics depend essentially on the structure of the submanifold ofS ^m–1, where the functiong takes the valueM, and generically are nonclassical, i.e. even as a first approximation (2) ^m _h () differs from the volume of the set {(x, )^2m:h ²||²+V(x)<M–}.Partially supported by Contract No. 52 with the Ministry of Culture, Science and Education