ИспОльжОВАНИЕ ФлУОР ЕсцЕНтНОгО РЕНтгЕНО ВскОгО ИжлУЧЕНИь Дль кОНтАк тНОИ МИкРОРАДИОгРАФ ИИ

( )K- Fe, Ti Ca . , , , . , , , K- , .

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The use of fluorescent X-rays for contact microradiography

The possibilities of using fluorescentK-radiation of the elements Fe, Ti and Ca for contact microradiography of thin, little absorbing samples were studied and a simple set-up for carrying out this method, which uses a common type of microstructural X-ray tube as a source of the exciting radiation, was proposed. The experiments performed showed that if large magnifications are not required secondary-excitedK-radiation of the above-mentioned elements can be advantageously used for contact microradiography without the exposure times becoming impracticably long.

     

О взаимодействии экс итонов с колебаниями кристаллической реш етки

, - . : - . - .     

An interpretation of the conditions for the existence of Shockley surface states

A study is made of the Shockley surface states in a linear chain of equal atoms, joined by alternately strong bonds. If the simple MO LCAO method is used, which considers the exchange integrals between nearest neighbours and next nearest neighbours, we get the surface states for a semi-infinite chain if the stronger bond is interrupted. The connection between Shockley and Tamm surface states is shown and the hypothesis is put forward that the condition for the existence of Shockley surface states has a generally simple physical interpretation, the validity of which is proved on the models of a semi-infinite crystal studied up to now.

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, . MO LCAO, , , . , , , .

     

Rate equations in the hopping transport

The usual kinetic equations for the site occupation probabilities in an external field are solved exactly in a simple one-dimensional periodic model with two kinds of atoms using a) free boundary conditions and order of limitsN, 0 needed for a proper treatment of the dc conductivity here b) boundary conditions with metallic contacts and order of limitsN, 0 and c) the same boundary conditions but reversed order of limiting processes 0,N typical of e.g. numerical and percolation treatments. (N and are the number of sites and frequency.) It is demonstrated that though the bulk dc conductivity is the same in all three cases, local bulk properties of the material are strongly dependent on the régime used. The role of the order of all three limiting processes 0,N+ andn+ (N–n+) for local shifts of the chemical potential _n in the dc limit is examined (n is the number of the relevant site calculated from a boundary of the chain). It is shown especially that the rate equation treatment (régime a) on the one hand and numerical or percolation treatments (régime c) on the other hand never yield the same bulk values of _r.     

Two-barrier detector

The paper describes the principle of a detector with two opposite surface barriers and the experimental verification of its functioning. The detector permits double the effective depth to be attained on the material with a given bias voltage. The principle of opposite barriers also permits a reduction in the system of dE/dx andE detectors to one detector.

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. . dE/dx E .

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The authors thank A. Irra for carefully preparing the plates, K. Putz and J. imková for very effective help in measuring on the cyclotron and the members of of the cyclotron staff for their cooperation.     

On the Hamiltonian interpolation of near-to-the identity symplectic mappings with application to symplectic integration algorithms

We reconsider the problem of the Hamiltonian interpolation of symplectic mappings. Following Moser's scheme, we prove that for any mapping , analytic and -close to the identity, there exists an analytic autonomous Hamiltonian system, H such that its time-one mapping _H differs from by a quantity exponentially small in 1/. This result is applied, in particular, to the problem of numerical integration of Hamiltonian systems by symplectic algorithms; it turns out that, when using an analytic symplectic algorithm of orders to integrate a Hamiltonian systemK, one actually follows exactly, namely within the computer roundoff error, the trajectories of the interpolating Hamiltonian H, or equivalently of the rescaled Hamiltonian K=^-1H, which differs fromK, but turns out to be ⁵ close to it. Special attention is devoted to numerical integration for scattering problems.     

Wave chaos in quantum systems with point interaction

We study perturbations of the quantized version ₀ of integrable Hamiltonian systems by point interactions. We relate the eigenvalues of to the zeros of a certain meromorphic function . Assuming the eigenvalues of ₀ are Poisson distributed, we get detailed information on the joint distribution of the zeros of and give bounds on the probability density for the spacings of eigenvalues of . Our results confirm the wave chaos phenomenon, as different from the quantum chaos phenomenon predicted by random matrix theory.SFB 237 Essen-Bochum-Düsseldorf     

Rigorous Spectral Analysis of the Metal–Insulator Transition in a Limit-Periodic Potential

We consider the limit-periodic Jacobi matrices associated with the real Julia sets of f (z)=z ²– for which [2, ) can be seen as the strength of the limit-periodic coefficients. The typical local spectral exponent of their spectral measures is shown to be a harmonic function in decreasing logarithmically from 1 to 0.     

Unmixing of binary alloys by a vacancy mechanism of diffusion: a computer simulation

The initial stages of phase separation are studied for a model binary alloy (AB) with pairwise interactions _AA , _AB , _BB between nearest neighbors, assuming that there is no direct interchange of neighboring atoms possible, but only an indirect one mediated by vacancies (V) occurring in the system at a concentrationc _v and which are strictly conserved, as are the concentrationsc _A andc _B of the two species.A-atoms may jump to vacant sites with jump rate _A , B-atoms with jump rate _B (in the absence of interactions). Particular attention is paid to the question to what extent nonuniform distribution of vacancies affects the unmixing kinetics. Our study focuses on the special case _A = _B on a square lattice, considering three different choices of interactions with the same = _AB – ( _AA + _BB )/2: (i) _AB =, _AA = _BB = 0; (ii) _AA = 0, _AA = _BB ; = ; (iii) _AB = _BB = 0, _AA = –2. We obtain both the time evolution of the structure factorS(k,t) following a quench from infinite temperature to the considered temperature, and the timedependence of the mean cluster size and the various neighborhood probabilities of a vacancy. While in case (i) forc _V 0.16 the distribution of vacancies in the system stays nearly random, in case (ii) the vacancies cluster in theA-B interfacial region, and in case (iii) they get nearly completely expelled from theA-rich regions. While phase separation proceeds in case (i) only slightly faster than in case (ii), a significant slowing down of the relaxation is observed for case (iii), which shows up in a strong reduction of the effective exponents describing the growth.     

Long-Time tails in a random diffusion model

Letw = {w(x)xZ^d} be a positive random field with i.i.d. distribution. Given its realization, letX _t be the position at timet of a particle starting at the origin and performing a simple random walk with jump rate w^–1(X_t). The processX={X _t:t0} combined withw on a common probability space is an example of random walk in random environment. We consider the quantities _t =(d/dt) E (X _t ² –M ^–1 t and _t(w) = (d/dt)E_w(X _t ² – M^– 1t). Here E_w. is expectation overX at fixedw and E = E_w (dw) is the expectation over bothX andw. We prove the following long-time tail results: (1) lim_t t^d/2_t= V²M^d/2–3(d/2)^d/2 and (2) lim_t t^d/4 _st(w)= Z_s weakly in path space, with {Z_s:s>0} the Gaussian process with EZ_s=0 and EZ_rZ_s= V²M^d/2–4(d)^d/2 (r + s)^–d/2. HereM and V² are the mean and variance of w(0) under . The main surprise is that fixingw changes the power of the long-time tail fromd/2 tod/4. Since , with ₀ the stationary measure for the environment process, our result (1) exhibits a long-time tail in an equilibrium autocorrelation function.     

Energy level crossings in quantum mechanics

From the eigenvalue equationH \ _n () =E _n ()\ _n () withH H ₀ +V one can derive an autonomous system of first order differential equations for the eigenvaluesE _n () and the matrix elementsV _mn () where is the independent variable. To solve the dynamical system we need the initial valuesE _n ( = 0) and \ _n ( = 0). Thus one finds the motion of the energy levelsE _n (). We discuss the question of energy level crossing. Furthermore we describe the connection with the stationary state perturbation theory. The dependence of the survival probability as well as some thermodynamic quantities on is derived. This means we calculate the differential equations which these quantities obey. Finally we derive the equations of motion for the extended caseH =H ₀ +V ₁ + ² V ₂ and give an application to a supersymmetric Hamiltonian.     

Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

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A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

Mikrophy'sikalische Vorgänge,die die Entstehung der Schnellen Schichtungswellen in der Neonglimmentladung bedingen

Zusammenfassung Im nachstehenden Artikel werden mikrophysikalische Vorgänge behandelt, die das Auftreten schneller Schichtungswellen in Neonglimmentladungen veranlassen können. Es werden sowohl die qualitativen Abhängigkeiten, als auch die ziffernmäigen Werte der Parameter der Schichtungswellen mit den charakteristischen Gröenwerten der in diesem Entladungstypus vor sich gehenden Vorgänge verglichen. Auf Grund der vorgenommenen Vergleiche kann gesagt werden, da die Relaxationszeiten der schnellen Wellen durch die Diffusionslebensdauer der atomaren, bzw. molekularen Ionen gegeben sind.

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, . , . , , .

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Zum Schlu danken wir F. Kroupa und V. Krejí für die aufmerksame Lesung der Arbeit und wertvolle Hinweise.     

ВОЗМОЖНОСТЬ ИССЛЕДО ВАНИЯ ХОДА ИСКАЖЕНИЙ РЕШЕТКИ В КРИСТАЛЛИКАХ ПРИ ПО МОЩИ РЕНТГЕНОВСКИХ Л УЧЕЙ РАЗНОЙ ДЛИНЫ ВОЛНЫ

, . , (K , , ), - , -. -, 25 a 1956.     

Spin-orbit coupling in the chlorobenzene molecule

The possible ways of drawing of the intensity of the S₀ T* transition in the chlorobenzene molecule are investigated. The effective spin-orbit coupling of either S* or S* states with the T* state leads to the out-of-plane polarized component of phosphorescence in the chlorobenzene. The in-plane polarized component cannot be explained by the mechanism under consideration — by drawing of intensity of the S₀ S₀* transitions through spin-orbit coupling of first order.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 134–138, August, 1974.     

On the Effect of Increasing the Radiative-Transition Rate Near a Nanosize Point

A short review of theoretical and experimental studies concerning the photoexcited florescence and Raman scattering of light for a substance in a space containing small material bodies is presented. Calculations of the radiativetransition probability for atoms (molecules) in the vicinity of bodies with a size much smaller than the light wavelength are performed. The probabilities of the singlephoton and doublephoton transitions are shown to increase by factors of 9 and 81 in the vicinity of a nanosize sphere with dielectric constant ||\ 1. The probability of a radiative transition in the vicinity of the vertex of a conic needle bearing up against a plane (both with || 1) increases by factors of (/R _in)² and (/R _in)⁴ for singlephoton and doublephoton transitions, respectively (R _in is the curvature radius for the needle vertex). This theoretical result is suggested as an explanation of the effect of increasing the radiation process intensity in the experiments carried out in the studies cited below.     

Power law growth for the resistance in the Fibonacci model

Many one-dimensional quasiperiodic systems based on the Fibonacci rule, such as the tight-binding HamiltonianH(n)=(n+1)+(n–1)+v(n) (n),n,l ²(),, wherev(n)=[(n+1)]–[n],[x] denoting the integer part ofx and the golden mean , give rise to the same recursion relation for the transfer matrices. It is proved that the wave functions and the norm of transfer matrices are polynomially bounded (critical regime) if and only if the energy is in the spectrum of the Hamiltonian. This solves a conjecture of Kohmoto and Sutherland on the power-law growth of the resistance in a one-dimensional quasicrystal.     

Polarization of photo-luminescence of ZnS: Cu monocrystals

Different models of luminescence centres are discussed on the basis of measurements of the composition of ZnS monocrystal photo-luminescence in different polarizations and temperature dependence of the degree of polarization. Those of the models submitted by Birman, which assume the polarization to be due to the different force of the oscillators for transitions withEc andEc, or models assuming luminescence polarization to be due to the orientation of the luminescence centres, agree with the results of experiments, i.e. the temperature independence of the degree of polarization and the conformable spectral composition of both polarizations. It is also shown that measurements made up to now of the degree of polarization must be taken as orientational as a consequence of the depolarizing influence of the diffused rays of luminescence on its value.

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ZnS: Cu

ZnS , . , . . , , , E E, , . , , - .

     

Thermostimulierte Exoemission und Lumineszenz von MgO und CaO

Ohne Zusammenfassung

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MgO CaO

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Ich danke bestens Frau K. Listoová für die sorgfältige Durchführung der Versuchsreihen und Ing. S. urovi und Dr. A. Bergstein für das liebenswürdige Überlassen der Präparate.     

Long-time tails in lattice Lorentz gases

We consider a Lorentz gas on a square lattice with a fraction c of scattering sites. The collision laws are deterministic (fixed mirror model) or stochastic (with transmission, reflection, and deflection probabilities ,, and respectively). If all mirrors are parallel, the mirror model is exactly solvable. For the general case a self-consistent ring kinetic equation is used to calculate the longtime tails of the velocity correlation function (0) (t) and the tensor correlation Q(0)Q(t) withQ= _{x y} . Both functions showt ^–2 tails, as opposed to the continuous Lorentz gas, where the tails are respectivelyt ^–2 andt ^–3. Inclusion of the self-consistent ring collisions increases the low-density coefficient of the tail in (0)(t) by 30–100% as compared to the simple ring collisions, depending on the model parameters.