The use of the repulsive potential in the quantum theory of solids

A new method is proposed for calculating the energy in certain special points of the Brillouin zone. The wave functions of valence and conduction electrons are given in the form of the linear combination of plane waves and the orthogonality condition of these functions to the wave functions of lower states is replaced by the repulsive potential. The practical application of this very simple method is illustrated on the energy spectrum of silicon in the centre of the Brillouin zone. It is proved that the results are comparable with some other methods, e. g. the orthogonalized plane-wave method.

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. . . , , .

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The basic thesis of this paper, together with concrete calculation of the energy spectrum of diamond, was delivered at the Czechoslovak-Polish conference in Sopoty in November 1956.

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In conclusion the autor would like to thank K. Trnková for carrying out the numerical calculations.     

Das Anhaften von Exzitonen an Störstellen des Kristallgitters

Zusammenfassung Es wird der Proze des Anhaftens von Exzitonen an Vakanzen und F-Zentren in den Ionenkristallen studiert. Die Bewegung der Exzitonen im Felde der Vakanz und des F-Zentrums wird in adiabatischer Annäherung untersucht. Mit Hilfe der klassischen Methoden werden die Wirkungsquerschnitte des Anhaftens des Exzitons an den Vakanzen und F-Zentren bestimmt und diskutiert.

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F- . F- . F- .

     

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.     

К ТЕОРИИ РЕЗОНАНСНОЙ МИГРАЦИИ ЭНЕРГИИ ВОЗ БУЖДЕНИЯ В ТВЕРДЫХ ТЕЛАХ

- - . - .     

Новый тип рентгеновс кого спектрографа

. 1', . . .     

Струи паров материал ов электродов нри кратковременном электрическом разря де с Большой силой тока

. . , .

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The vapour jets of electrode material of a short-time high-intensity electric discharge

The velocity of vapours from electrodes and the values of the electric gradient of the channel were measured. An explanation is given of the dependence of the discharge rate of the vapours on the electrode material and the thermal origin of the jets is confirmed. The validity of the results is shown for the case of a different experimental arrangement, or the formation of other types of discharges on electrodes.

     

ЭЛЕКТРИЧЕСКАЯ ЭКВИВ АЛЕНТНАЯ СХЕМА ЗАТУХАЮЩИХ КОЛЕБАНИ Й СДВИГА ПЬЕЗОЭЛЕКТРИЧЕСКИХ СТЕРЖНЕЙ

n - , - .     

Sur la remanence de la magnétisation par déplacement des parois de Bloch et la cinétique de sa desaimantation

Sans résumé

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,

     

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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. , . , .

     

The interaction of pions with deuterons

Summary There has been remarkable experimental and theoretical progress in the field ofd interactions in the last few years. Within the uncertainties of the theory the experimental data in thed breakup and thed elastic scattering reaction can be fairly well reproduced. Theoretical problems remain in the absorption channel, but there is a hope that with a few additional measurements of tensor polarization and spin transfer observables in this reaction a partial wave amplitude analysis may localize the theoretical difficulties. In addition it is very important to provide data on the deuteron tensor polarizations and the spin transfer parameters for thed elastic scattering reaction in order to obtain a reliable set of phase shifts, which may reveal resonance structures in this reaction channel.Invited talk to the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

Derivations commuting with abelian gauge actions on lattice systems

Let be an action of a compact abelian groupG on aC*-algebraA, and assume that the fixed-point subalgebraA is an AF-algebra. We show that if is a closed *-derivation onA commuting with , and the restriction of toA generates a one-parameter group of *-automorphisms, then itself is a generator. In particular, the result applies if is an infinite product action ofG on a UHF algebra. Furthermore, if in this situation ₁ and ₂ are two derivations both satisfying the hypotheses on , and ₁ and ₂ have the same restriction toA , then there exists a one-parameter subgroup of the action with generator ₀ such thatD(₁)D(₂)D(₀) is a joint core for the three derivations, and ₂=₁+₀ on this core.     

Bunching phenomena during electron injection into the betatron II. Theory of starting conditions

A theory of the azimuthal bunching of electrons injected into the betatron is presented and compared with the experiments described in [1]. The bunching is treated as a small perturbation of the stationary beam.The stationary injected beam is replaced by the corresponding equilibrium beam of the same perveance so that the angular velocity spread of the injected electrons is proportional to the square root of the injection perveance.Self-consistent wave solutions for the perturbation of the stationary solution are then found. Equations giving the amplification of small density or energy disturbances along the beam are derived. These disturbances are assumed to be introduced by density or velocity modulation of the injected beam. The condition for the spontaneous occurrence of bunching is deduced by assuming that the disturbances do not vanish even when there is no modulation of the injected beam. The resulting expressions for the threshold perveance and the rise-time of the disturbance are in reasonably good agreement with the experiments. Such agreement may be considered as further verification of the statement made in [1] that the amplification of the disturbances is caused by the negative mass instability mechanism.

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, .

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

     

Electronic processes andZ centres in NaCl and KC1 crystals

The paper gives the experimental results of the team-work study of coloured pure and Ca doped NaCl and KC1 crystals. The mechanism of the formation ofR centres by coagulation ofF centres and of the formation ofZ centres fromF centres, cation vacancies and Ca ions is discussed. An alternative model forZ ₃ centres is proposed. The possible connections between physical and chemical behaviour are indicated.

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Z- NaCl 1

NaCl KCl . R- F- Z- F-, Ca. Z ₃-. .

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This work was presented by the courtesy of Prof. R. Maurer at the Symposium on Color Centers, Corvallis, Oregon (1959).

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The authors wish to express their gratitude to K. Suk, K. Listoová and M. Javrková for carefully carrying out the measurements and I. Kunzlová and L. Nováková for preparing the crystals.     

Kinetic limits of the HPP cellular automaton

We study the Boltzmann-Grad limit in various versions of the two-dimensional HPP cellular automaton. In the completely deterministic case we prove convergence to an evolution that is not of kinetic type, a well-known phenomenon after Uchyiama's paper on the Broadwell gas, whereas the limiting equation becomes of kinetic type in the model with random collisions. The main part of the paper concerns the case where the collisions are deterministic and the randomness comes from inserting, between any two successive HPP updatings, ^- stirring updatings, <1 being any fixed positive number and a parameter which tends to 0. The initial measure is a product measure with average occupation numbers of the order of (low-density limit) and varying on distances of the order of ^–1. The limit as 0 of the system evolved for times of the order of ^-1- corresponds to the Boltzmann-Grad limit. We prove propagation of chaos and that the renormalized average occupation numbers (i.e., divided by) converge to the solution of the Broadwell equation. Convergence is proven at all times for which the solution of the Broadwell equation is bounded.     

Homogeneous and hypersurface-homogeneous shear-free perfect fluids in general relativity

Shear-free, general-relativistic perfect fluids are investigated in the case where they are either homogeneous or hypersurface-homogeneous (and, in particular, spatially homogeneous). It is assumed that the energy density and the presurep of the fluid are related by a barotropic equation of statep = p(), where +p 0. Under such circumstances, it follows that either the fluid's volume expansion rate or the fluid's vorticity (i.e., rotation) must vanish. In the homogeneous case, this leads to only two possibilities: either = = 0 (the Einstein static solution), or 0, = 0 (the Gödel solution). In the hypersurface-homogeneous case, the situation is more complicated: either = 0, 0 (as exemplified,inter alia, by the Friedmann-Robertson-Walker models), or 0, = 0 (which pertains, for example, in general stationary cylindrically symmetric fluids with rigid rotation, or = = 0 (as occurs for static spherically symmetric solutions). Each possibility is further subdivided in an invariant way, and related to the studies of other authors, thereby unifying and extending these earlier works.     

Stationary states of an electron in the field of a hole in an ionic crystal

An approximate solution is given of the Schrödinger equation for S-states of an electron in the field of a hole, when the potential energy of the electron has the form — e²/r [1+exp (–qr].

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s- , –e²/r [1+exp (–qr].

     

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.     

The quantum theory of multipole radiation in a dielectric

The potentials of an electromagnetic field of multipoles in a dielectric, which is realized by a dielectric sphere having a perfectly conducting surface, are derived. The diagonal values of the energy for thez component of the angular momentum and the square of the angular momentum of the field are determined and also the ratio between thez component of the angular momentum and the energy and the ratio between the square of the angular momentum and the square of the energy. It is shown that the total angular momentum can be divided in the usual way into orbital and spin parts but that these parts cannot be interpreted as the orbital and spin angular momentum because their eigenvalues cannot be the eigenvalues of any operator of infinitesimal rotation. In the commutation rules of a multipole field the vector character of the field is to a certain extent suppressed and the spin of the photon in a state with a certain value of the energy, parityz component of the angular momentum and the square of the angular momentum is not defined.

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, . ,z— , , z— . , , , , , - . , ,z— .

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In conclusion the author thanks Dr. . Muziká for directing the work, F. Samek for valuable remarks and discussion and J. Kvasnica for help in preparing the paper for publication and for adding a number of remarks.     

Adiabatic calculation of the three-nucleon force

A preliminary estimate of the three-nucleon force within the adiabatic framework has already been done. In this work we try to improve the first calculation by using relativistic kinematics for the pion and including theP 11 absorption channel, as well as theP 33 and the less importantS 13,S 11,P 13,P 31 channels, in theN interaction.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia. May 27–June 1, 1985.     

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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