Mathematical models for quantum point-contact spectroscopy

We sketch here two mathematical models intended to describe the point-contact spectroscopical experiments. A new item is added to the list of recently discovered applications of the self-adjoint extensions theory.The paper represents an extended version of the lecture given by one of the authors at the 8th Congress of IAMP, Marseille, July 1986.On leave of absence fromNuclear Physics Institute, Czechosl. Acad. Sci., 250 68 e near Prague, Czechoslovakia.On leave of absence fromNuclear Centre, Charles University, V Holeovikách 2, 180 00 Prague, Czechoslovakia.     

ПЛОТНОСТЬ ТОКА В АНОД НЫХ ПЯТНАХ ИСКРОВЫХ РАЗРЯДОВ В ВОЗДУХЕ ПР И АТМОСФЕРНОМ ДАВЛЕН ИИ

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BЛИЯHИE CBETA HA MOHOКPИCTAЛЛИЧECКИE ПЛACTИHКИ AgCl

The paper deals with the influence of light,=403 m, on the absorption of single-crystal plates of AgCl, grown by the capillary method. It was found that crystals with blue luminescence show no maximum in the region measured. For crystals with green luminescence a broad absorption maximum was found at – 590 m, which is partly bleached during further irradiation by light from the region of the absorption maximum. Measurements were preformed at room temperature.

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On existence of a bound state in an L-shaped waveguide

We investigate the Laplace operator in an L-shaped strip of a widthd with Dirichlet boundary conditions. It is shown that it has a unique eigenvalue corresponding to a square-integrable eigenfunction, namely = 0·93 (/d)². This result has implications for the theory of waveguides as well as for electron motion in some microscopic semiconductor devices.Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.On leave of absence from Nuclear Physics Institute, Czechoslovak Academy of Sciences,250 68 e near Prague, Czechoslovakia.On leave of absence fromDepartment of Mathematics, Faculty of Nuclear and Technical Engineering, Czech Technical University, Trojanova 13, 120 00 Prague, Czechoslovakia.     

ЗАТУХАНИЕ КОЛЕБАНИЙ ЧАСТИЦ В ОБЩЕМ ПОЛЕ С ПЕРИОДИЧЕСКОЙ СТРУКТУРОЙ I

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The damping of particle oscillations in a general field with periodic structure I

A liner theory is derived, discussing the dynamics of particles in the region of an equilibrium orbit in a general electromagnetic field, which forms a periodic system. The total particle damping is determined from the Hamiltonian found and from dissipative forces brought out by a classical reaction radiation. Relations for the damping of the synchrotron oscillations are derived from the study of the appropriate phase space.

     

ЭЛЕКТРИЧЕСКАЯ ЭКВИВ АЛЕНТНАЯ СХЕМА ЗАТУХАЮЩИХ КОЛЕБАНИ Й ИЗГИБА У ПБЕЗОЭЛЕКТРИЧЕСКИ Х СТЕРЖНЕЙ

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The formation of dislocations by a spark discharge

The arrangement of dislocations formed in a single crystal of the alloy Fe-4·2% Si by a spark discharge in air is studied. The dislocations are made visible by etching on the surfaces perpendicular and parallel to the axis of the crater. The results of the observations are explained on the basis of microphysical conceptions of plastic deformation.

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, Fe— 4,2% Si . , . .

     

Notes on the classical and the nonrelativistic limits in quantum mechanics

A method is presented which can be used to discuss both the classical and also the nonrelativistic limit of quantum mechanics. A one-to-one correspondence may be established between the asymptotic convergence of the resolvent and that of the timedependent solution. In so far as the question of dynamics is concerned we investigate the relation between families of nonrelativistic Hamiltonians and the corresponding Dirac-Hamiltonians when c± or when c±0. The nonrelativistic free theory formally shows the same pattern when ±0 (the classical limit) or when ±. The investigation finally shows how the asymptotic convergence of the relativistic theory can take place under some fairly general conditions of the radiation field.     

Fatigue of Sb-Cs photocathodes

This experimental work deals with the influence of fatigue on the properties of the antimony cesium (Cs₃Sb) photocathode sensitized with oxygen. Photocells of special construction were prepared for the measurement and they were fatigued by illuminating them with white light from a tungsten lamp. The effect of fatigue on the spectral response curve, on the optical properties, values of activating energies, type of conductivity, current-voltage curves and integral sensitivity were investigated. In connection with the fatigue a shift of the long wavelength threshold towards shorter wavelengths, a decrease of response in the whole spectral range, changes in absorption and a drop in the value of the refractive index were observed. The maximum values of the activation energies, determined from measurements of the temperature dependence of the dark conductivity did not change. The conductivity of the photocathode was found to be of thep-type. The fatigue had certain effects on the current-voltage curves, the starting point of the anode current and the saturation point showing a certain shift towards lower positive anode voltages with fatigue. The relation between the fatigue and temperature rise of the photocathode due to the absorption of radiation was investigated. Finally some problems related to the mechanism of photoemission from the photocathodes are discussed.

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Sb-Cs

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Time production and spatial distribution of macroscopic space charges in D-C discharge plasma

It is shown for a one-dimensional approximation that, around a disturbance in the ion concentrationn ₊(x, t) in the axial direction of a cylindrical plasma, a corresponding electron distributionn _–(x, t) is established with such a large velocity that under the usual conditions of a discharge plasma this electron distribution follows the relatively slow changes in ion concentration practically without delay. Relation (24) then holds for the electron concentration, the parametersl ₁,l _D being given by Eqs. (15) and (16). As long as the disturbance of the ions isn ₊(x) 0, a space chargeq ₀(n ₊-n_–) is produced and maintained in the plasma even if the disturbance of the equilibrium state of the plasma in the initial stage was electrically neutral (i.e.n ₊(x, t=0)==n _–(x,t=0)). The dimensions of these space charges can be many orders larger than the Debye characteristic lengthl _D ; this is shown on an example of a spatially periodic curven ₊(x). The unique (quasi-stationary) expression of the electron concentrationn _– by means of the deflection of the ion concentrationn ₊(x, t) permits a considerable simplification of the solution of the problems connected with axially disturbing the homogeneous state of a plasma, sincen _–(x, t) can be eliminated from the equations of continuity of the plasma by substituting from (24), and the problem becomes that of determining the curve of the ion concentrationn ₊ from the equations modified in this way.

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, ₊(, t) - _–(, t) , . (24), l ₁ l _D (15) (16). ₊() 0, q ₀(n₊ — n_–), , (..n ₊(x,0)=_–(, 0)). () _{– +}(, t) , , . . _–(, t) n ₊ .

     

РАДИАЦИОННЫЙ ЗАХВАТ ТЕПЛОВЫХ НЕЙТРОНОВ ЯДРОМ II

, -, Na, Co, Zn, Ag J 20÷1000 keV. Co, Zn, Te J .

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Radiative capture of thermal neutrons on nucleus II

The energies and intensities of gamma rays from the capture of a neutron on Na, Co, Zn, Ag, Te and I nucleus in the 20–1000 keV energy region were measured with a single-crystal, single-channel scintillation spectrometer. New energies of radiative transition were measured when measuring Co, Zn, Te and I nuclei.

     

Far-field techniques for the characterization of single-mode fibres

The characterization of single-mode fibres is important not only for determining the system parameters for a particular fibre, but also for the specification of fibres for manufacturing purposes. We present a detailed analysis of two new methods of characterizing single-mode fibres. The strip integrated far-field method involves measuring the light power passed by a thin slit scanned across the far-field pattern and the area integrated far-field method involves measuring the light power passed by a knife edge scanned across the far-field pattern. It is shown that, for either method, the measured data is related to the transverse offset transmission coefficient by the Fourier-cosine transform and hence that the far-field r.m.s. spot-size can be directly calculated. Noise analysis shows that the area integrated far-field method is superior to the strip integrated far-field method and similar to the far-field mask method when a broadband light source is used to measure the far-field r.m.s. spot-size. It is also shown that the area integrated far-field method has smaller systematic errors than the far-field mask method.     

ОПРЕДЕЛЕНИЕ ПОСТОЯН НЫХ ДВУХПАРАМЕТРОВЫ Х РЕШЕТОК МЕТОДОМ ОТНО ШЕНИЙ

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к ВОпРОсУ О БЕтАтРОННых кОлЕБАНИьх В УскОРИтЕлЕ с ОБОБЩЕННыМ пОлЕМ

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A remark on betatron oscillations in an accelerator with a generalized field

The paper discusses the stability region for a canonical system of equations of motion describing the behaviour of a particle in an accelerator with a generalized field, defined on the general rotation surface [1], [2], The stability region is determined in the plane of two invariants.

     

On the energy balance in the optics of metals

On the basis of the boundary conditions of the electromagnetic theory an explicit calculation of the absorption in a thin metallic film was carried out with the result that transport and interference components were found to exist. By applying the method to a simple metal-dielectric boundary the physical interpretation was given of the energy balance, which had hitherto been regarded as unclear. It was also explained why the reversibility principle fails when applied to a metal-dielectric boundary.

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The basic equations of the dynamics of the continuous distribution of dislocations III. special problems

The basic equations of the dynamics of the continuous distribution of dislocations analogical to Maxwell equations are derived in a series of papers [I, II, III]. The analogy of the elastic and electromagnetic fields is analyzed. In part [III] some special problems are discussed, such as the density of the forces acting on the dislocations, the energy dissipation during the movement of dislocations, which is expressed by an equation analogical to Ohm's law. The equations derived in the previous parts in four-dimensional symbolics are considered in the three-dimensional differential and integral form. It is found that in special cases the relations become the known ones of elastodynamics, hydrodynamics and the static theory of the continuous distribution of dislocations. It is found that Kröner's method of integrating the equations of the dislocation field by means of so-called incompatibility tensors is analogical to the integration of the Maxwell equations by means of Hertz vectors. The analogy between the elastic dislocation field and the electromagnetic field is discussed in detail.

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III.

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The internal friction of longitudinal oscillations in ferromagnetic materials

The paper deals with the theory of the new magnetomechanical phenomenon in an alternating field [6, 7]. The first part concerns the internal friction of longitudinal oscillations of a ferromagnetic material in the shape of a wire in a constant magnetic field. It is assumed that the medium in which the sample oscillates is conducting and has a certain permeability. Equations defining the magnetic field in the oscillating material are derived from the basic thermodynamic relations. The term describing the non-conservative force component in a complex formulation is used to determine the internal friction. A general relation between the internal friction and the magnetic field is derived, as well as other expressions, which are a simplification of it. The second part of the paper deals with internal friction in an alternating field. It is shown that the solution can be transformed to the sum of the internal frictions of the different harmonic oscillations, which are obtained as a partial solution of the problem on the assumption that the elastic oscillations in interaction with the field oscillations are separated into their harmonic components. The calculation then becomes that of the internal friction considered in the first part of the paper. In this case the internal friction significantly depends on the field amplitude. The functional dependence of the internal friction peak on the frequency of the mechanical oscillations is also calculated. The agreement of the theory with experiment is satisfactory.

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Der Einfluss der positiven Ionen auf die Exoelektronenemission

Zusammenfassung Es werden die Ergebnisse der Messung des Einflusses der auf den Emitter bei der Messung der Exoelektronenemission mittels Geiger-Müller-ZÄhlers auffallenden positiven Ionen beschrieben und die möglichen Mechanismen der Beeinflussung der Emission diskutiert.

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Der Einfluss von Beimengungen auf die Fasersubstruktur von Zink-Einkristallen

Zusammenfassung An Einkristallen von Zn mit Beimengungen von Cd oder Cu wurde experimentell die Abhä agigkeit der Größe des Durchmessers der Fasersubstruktur vom Gehalt der Beimengungen untersucht, die aus der Theorie von Rutter und Chalmers [1] hervorgeht. Es wird die Möglichkeit gezeigt, die Größe des Verteilungskoeffizientenk aus den erzielten Ergebnissen abzuschätzen.

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The nucleon-nucleon triple scattering parameters for recoil particles

Relativistic formulae are obtained, expressing the polarization of the initially unpolarized particle in the scattering of an unpolarized nucleon on a polarized one, in terms of the polarization transfer tensor and in terms of the scattering matrix elements.On leave of absence from theFaculty of Technical and Nuclear Physics, Czech Technical University, Prague, Czechoslovakia.On leave of absence from theNuclear Research Institute of the Czechoslovak Academy of Sciences, e, Czechoslovakia.In conclusion the authors express their profound gratitude to S. M. Bilenky, L. I. Lapidus, R. M. Ryndin and Ya. A. Smorodinsky for useful discussions and to E. Dudova and J. Fingerova for help in the work.