Über die Einteilchensingularitäten in Relativistischen Quantenfeldtheorien

By subtraction of products of three-point functions the four-point functions in relativistic quantum field theory are decomposed into two parts, in one of which there does not occur any mass-shell-singularity in the variables (; 1, 4). All these singularities are given explicitly by the kernels of the products of the three-point functions. — Necessary and sufficient conditions for the non-triviality of unitaryS-matrices or some of their elements are proved in terms of statements on the occurence of mass-shell-singularities in the vacuum expectation values of field operators. The strongest result we have gained is: If is equal to zero for someN>3, then all transition amplitudesT _2n vanish for everyn.     

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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Влияние давления на а бсорбцию галогенидо в серебра. Часть II

AgBr, Agcl AgI — 160°C. AgBr AgCl . AgI .     

ДЕФОКУСИРОВКА ДИФФР АКТОМЕТРА ШУЛЬЦА

, .     

ЛЮМИНЕСЦЕНЦИЯ КРИСТ АЛЛОВ AgCl

AgCl –180°. . , ( : =4640 Å, =5080 Å). , , . . - . –183°, =1,6. 10^–8%±10%.

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Luminescence of AgCl crystals

The luminescence of normal and deformed single crystals of AgCl of different thickness was measured at a temperature of –180°C. With deformed samples the decrease in intensity of the luminescence was measured. On the luminescence band of the above crystals we observed a fine structure for which the series rule could be used (edge of series =4640 Å, =5080 Å).The observed luminescence was explained by means of the exciton mechanism proposed by Matyá, i.e. annihilation of a localized exciton either on a cation vacancy or on a cation vacancy on a dislocation jog. The luminescence yield at –183°C, =1.6×10^–3%±10%, was measured by a photographic method.

     

Gelfand Pairs with Coherent States

The notion of solvable Gelfand pairs (K,N) (K is a compact Lie group acting on N, a solvable connected and simply connected Lie group) is due to Benson, Jenkins and Ratcliff. Thanks to the localization lemma, they came back to the case where K is a connected subgroup of U(n) acting on N = Hn, the 2n + 1-dimensional Heisenberg group. They gave a geometrical condition for such a pair: (K,Hn) is a Gelfand pair if and only if the intersection of each coadjoint orbit of G = K Hn with (Lie K) contains at most one integral K-orbit. Using coherent states, we define here a generating function of multiplicity m for each in K^. m is holomorphic on D(0,1), m (r) = n = 0 an rn, an and limr 1 m (r) = mtp (, W) (W is the generic representation of Hn naturally extended to K). (K,Hn) is thus a Gelfand pair if and only if limr 1 m 1. We prove here that if m is a non homogeneous function, then there is at least two K-orbits in the intersection of the generic coadjoint orbit associated to with (Lie K).     

Equivalence of Deviau's, Hestenes', and Parra's Formulations of Dirac Theory

Daviau showed the equivalence of matrix Dirac theory, formulated within a spinor bundle , to a Clifford algebraic formulation within space Clifford algebra Pauli algebra (matrices) biquaternions. We will show, that Daviau's map : is an isomorphism. It is shown that Hestenes' and Parra's formulations are equivalent to Daviau's Clifford algebra formulation, which uses outer automorphisms. The connection between different formulations is quite remarkable, since it connects the left and right action on the Pauli algebra itself viewed as a bi-module with the left (resp. right) action of the enveloping algebra . The isomorphism established in this article and given by Daviau's map does clearly show that right and left actions are of similar type. This should be compared with attempts of Hestenes, Daviau, and others to interprete the right action as the iso-spin freedom.     

The propagation of excitation energy in perturbed crystals

The process of the propagation of excitation energy in perturbed dielectric crystals with a weak bond between the atoms having zero permanent dipole moment is studied. It is shown that on certain assumptions this process of propagation can be regarded as the motion of a Frenkel exciton in the electrostatic field of the defect. Frenkel's exciton can be characterized in this case as a neutral polarizable particle having induced dipole moment equal to the change in the induced dipole moment of the crystal during the excitation of one of its atoms.

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, . , . .

     

К СПЕКТРУ ПОГЛОЩЕНИЯ АМОРФНОГО СЕЛЕНА В ИНФРАКРАСНОЙ ОБЛАС ТИ

0,6 25 . , , . , 13,4 20,4 , , , . . , . .

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A contribution to the absorption spectrum of amorphous selenium in the infra-red region

The absorption spectrum of amorphous selenium was measured in the region of 0·6 to 25 on samples of high purity and homogeneity. The absorption bands of amorphous and liquid sulphur were also measured in the same wave-length region. The measurements showed that the absorption bands 13·4 and 20·4 , appearing in the spectrum of amorphous selenium, are its intrinsic absorption bands and are not caused by impurities, as some authors think. The similarity between the infra-red spectra of selenium and sulphur is shown.

     

Mössbauer effect and discovery of new hexagonal ferrites prepared at 980^\circ C

In the present article, undoped and Codoped Mtype Srhexaferrites have been prepared at low temperatures down to 980 C for the first time by the usual ceramic procedure and sintering technique. On these materials, a CoK Xray diffraction analysis and the room temperature ⁵⁷Fe Mössbauer spectroscopy (MES) were carefully performed. The results obtained are described and interpreted. The mechanism of Co substitution partially in place of iron and the site of its occupancy were proposed and established.     

Hydrogenated and irradiatedA15 Nb3Sn layers — Preparation,Rutherford scattering analysis,resistivity and superconductivity

Niobium films on sapphire were reacted in tin-vapour to Nb₃Sn with resistance ratiosR(297 K)/R(18.3 K) up to 6 and resistively measured superconducting transition temperaturesT _c up to 17.93 K. The composition Nb_3+z Sn_1–z H _x of electrolytically hydrogenated samples was determined depth dependent by Rutherford backscattering of 30 MeV³²S and simultaneous detection of recoiled protons. Considerable concentration gradients in the thin layers (0.27 m) were detected. The increase of resistivity with hydrogen content and the change in the temperature dependence of is analyzed. A correlation betweenT _c and ₀= is found: An increase of T _c =0.2 K at ₀25cm andx0.03 is followed by a drastic decrease toT _c <1.1 K at ₀80cm andx1. TheT _c vs. ₀ andT _c vs. (T) characteristic correlations are different from universal irradiation or preparation induced correlations. The discrepancies can be interpreted by a stiffening of phonon modes and a band-shifting caused by the hydrogen.     

тЕМпЕРАтУРНАь жАВИс ИМОсть МОДУлЕИ УНгА сплАВОВ АлУМИНИь с цИ НкОМ И ЕЕ ВлИьНИЕ НА кОгЕРЕНтНУУ ДИАгР АММУ сОстОьНИь

. . . — - . . . , . , .

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Temperature dependence of the young's modulus of the Al-Zn alloys and its influence upon the metastable coherent phase diagram

The paper describes the measurements of the temperature dependence of Young's modulus for several Al-Zn alloys. The moduli were measured by the method of a composite oscillator at resonance frequencies of about 100 kHz. When decreasing the temperature from the state of homogeneous solid solution, the undercooling phenomena cause a hysteresis effect. Young's modulus decreases approximately linearly with increasing atomic fraction of zinc at 390C. The determined temperature and concentration dependence was used for thermodynamic calculation of the form of metastable coherent solubility gaps by which the separation of the solid solution into coherent zones can be described.

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B. K. Kardaev, S. P. Nikanorov,A. F. Ioffe Physico-Technical Institute, Acad. Sci. U.S.S.R., Politechnieskaja 26, Leningrad K- 21, U.S.S.R.

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J. Laek,Institute of Solid State Physics, Czechosl. Acad. Sci., Cukrovarnická 10, Praha 6, Czechoslovakia.     

Some exact models for nonspherical collapse.I

Evolution of incoherent matter distributions with cylindrical, pseudoplanar, and toroidal symmetries is considered. The system is described in terms of the scale factora (R, T) and the anisotropy factor (R, T) of the (x², x³ surfaces. A number of exact solutions is obtained under the assumptions=(a), =(R), and=(T) and their physical properties are breifly discussed. In particular, the solution with=(T) is noncollapsing and describes a matter distribution with unchanging density.     

The interaction of foils activated by thermal neutrons

The interaction of foils lying in a plane during their activation by thermal neutrons has been calculated. Numerical values of functions are listed, which can be used in calculations, especially for graphite. The interaction was measured in the graphite column of the VVR-S reactor.

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, , . , , . VVR-S.

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We thank J. Frytacký, T. Kania and V. ervenka for their help in the numerical calculations and measurements.     

Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

Основные соотношени я длн построения механических селект оров нейтронов

, . , , . . , , .     

Minimal supersymmetric standard model with the gauge mediated supersymmetry breaking and the neutrinoless double-beta decay

Neutrinoless double-beta decay within Minimal Supersymmetric Standard Model with gauge mediated supersymmetry breaking is considered. Limits on R-parity breaking constant coming from non-observability of 0 in ⁷⁶Ge are found. The dependence of on different parameters at the messenger scale M are shown, with special attention paid to nuclear part of calculations. We have found that strongly depends on the effective supersymmetry breaking scale only and deduced limits imposed on this non-standard parameter by the germanium experiment.     

The influence of successive asymmetrical magnetization reversal on the magnetic state of open samples

A study is made of the influence of successive asymmetrical magnetization reversal on the magnetic state of open samples, where the macroscopic demagnetization field has a significant effect during magnetization reversal and leads to a sort of rotation of the asymmetrical loops performed one after another. This effect is similar to reptation, which was studied experimentally by Nguyen van Dang [1–4] and theoretically explained by Néel [5, 6]. The quantitative expression of the rotation of asymmetrical loops in open samples as a function of the number of loops and amplitude of the disymmetry is similar to that with the reptation effect.

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In conclusion the authors thank Dr. L. Valenta, C. Sc., and Z. Málek, C. Sc., for valuable discussions.     

Additivity of the entropy and definition of the temperature for quantum systems

A closed quantum systemL is considered which is described by a microcanonical ensemble.L consists of two rather weakly interacting subsystemsL ₁,L ₂. In a rigorous way, the additivity of the entropy is proved by deriving an expression for the entropy density ofL in terms of the entropy densities ofL ₁ andL ₂. Rigorous implies that the thermodynamic limit is taken. In the second part, it is shown how a microcanonical state of the composite system — provided this limit exists — gives rise to a canonical state , when restricted toL ₁, providedL ₁ is very small as compared toL ₂; is defined as a limit of Gibbs states. This yields a definition of the equilibrium temperature ^–1.On leave of absence from the Institut für Theoretische Physik, Universität Göttingen.     

The influence of oscillations on ionization in a discharge path

The paper solves the problem of gas ionization in a discharge path in a very dilute gas, where the free path of the electrons is much larger than the dimensions of the path and the transit time of the electrons between the electrodes is of the order of the period of the applied h-f voltage. It was found that for a certain ratio of the transit time of the electrons between the electrodes in the discharge path to the period of the h-f oscillation, resonance occurs when the wattless current component is zero. The electron density rises in the path and thus also the gas ionization.

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In conclusion, the author would like to thank F. Benda for preparing the equipment, M. Kivánek for preparing the equipment and some of the measurements, and A. Hrdá for the measurements and for working out the case with equally large a-c and d-c voltages within the framework of her thesis.