Adiabatic hyperspherical approach to the Coulomb three-body problem: Theory and numerical method

The adiabatic hyperspherical (AH) approach to the three-body Coulomb bound-state problems is considered. The variational method of computation of the AH harmonics potential curves and coupling matrix elements is developed. The method takes into account the asymptotic behaviour of the AH harmonics at large and small values of the hyperradius . The developed method allows to perform calculations with high accuracy and stability for any hyperradius (0,) with only a few AH harmonics. The efficiency of the method and its convergence is illustrated by calculations of energy levels of the mesic moleculesdd anddt.     

Influence of Solvent Polarity and Viscosity on Nonradiative Processes in Oligothiophenes with Intramolecular Charge Transfer

By the methods of luminescence, picosecond spectroscopy, and quantumchemical calculations the mechanisms of electron excitation energy deactivation in some oligothiophenes with intramolecular charge transfer depending on the solvent polarity and viscosity have been investigated. While for 2Npiperidino5(2,2dicyanovinyl)thiophene (PDCVT) the main channel of nonradiative deactivation is the transition to a lower intermediate state with a twisted double bond controlled by the medium viscosity, in the case of (E){2[25piperidino2thienyl]6(trifluoridemethyl)4H4pyranylidene}propanedinitryl (PTFDN) fluorescence quenching is initiated by the solvent polarity. For two other oligothiophenes, 2Npiperidino5cyanothiophene (PCT) and 2Npiperidino5cyanoterthiophene (PCTT), differing in the length of the thiophene chain, we have revealed, along with the effective quenching of fluorescence in shortchain PCT (independent of the solvent polarity and viscosity), an increase in the radiation capacity in PCTT with increasing polarity of the solvent. The possible mechanisms of nonradiative deactivation in the investigated oligothiophenes are discussed.     

A new class of long-tailed pausing time densities for the CTRW

We present some asymptotic results for the family of pausing time densities having the asymptotic (t) property(t) [t ln¹⁺(t/T)]^–1. In particular, we show that for this class of pausing time densities the mean-squared displacement r ²(t) is asymptotically proportional to ln(t/T), and the asymptotic distribution of the displacement has a negative exponential form.     

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

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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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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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Relativistic scattering theory for long-range potentials of the nonelectrostatic type

We define a modified free-time evolution for the Dirac equation with long-range potentials (1/|x|), where is the Dirac matrix, and prove a strong asymptotic completeness of the corresponding wave operators. Our methods also work for the magnetic fields ·A(x).     

Radius,perimeter, and density profile for percolation clusters and lattice animals

Monte Carlo simulation and series expansion shows the radius of gyration of large clusters withs sites each to vary ass with0.56 in two and0.47 in three dimensions at the percolation threshold, and with(d=2)0.65 and(d=3)0.53 for random lattice animals (zero concentration). Clusters up tos=100 were used. The perimeter of random animals approaches 2.8s for larges on the simple cubic lattice. Monte Carlo simulation of the Eden process (growing animals) up tos=5,000 indicates a systematic variation of about ±0.05 for the effective exponent=(s) and thus suggests that the true asymptotic exponents may be compatible with the predictions of hyper-scaling.     

Radiation of relativistic electrons in a magnetic undulator

Expressions are obtained for the spectral-angular characteristics of the radiation in two limiting cases: 1 and 1 ( is the angle of deflection of the electron in the field, and is the energy of the electron in units of mc²). It is shown that in the latter case the maximum of the radiation occurs at higher harmonics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 88–91, October, 1973.In conclusion the authors thank Professor A. A. Sokolov for useful discussions.     

THe mechanism of the amplification of moving striations in a d-c discharge

To determine the mechanism of the amplification of moving striations one starts out from the processes which [3] showed to be decisive for the production of stratification of the plasma of a positive column. An analysis of the influence of other processes shows that the main processes leading to the decay of space charges and thus to a smoothing out of the inhomogeneities and thereby to the attenuation of the periodic structure, cannot by overcome by ionization phenomena caused by changes in the concentration of electrons but only partially compensated.It was found that the process which can lead to the predomination of the processes of amplification over the attenuation is the process of the spatial shift of the temperature deflections of the electrons with respect to the additional electric field, which is expressed in a simplified way by Eq. (12).By solving the extremely simplified basic equations it is proved that under favourable conditions this displacement can lead to both a time and a spatial amplification of the striations. Such a possibility is also verified quantitatively by substituting numerical values into the formulae obtained.

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Equilibrium state of toroidal electron beam

The paper deals with the collective behaviour of electrons which rotate in a magnetic field used in a betatron. It is shown experimentally that there exists strong interaction between the electrons, which leads to the rapid formation of the equilibrium state with characteristic distribution of the charge density in the cross-section of the toroidal beam. The corresponding relaxation time is of the order of 1 sec. A statistical theory of the equilibrium beam is elaborated. Its main result is that the effective radius of the beam is a function of two parameters, one of which is proportional to the thermal energy of the electrons and the other to the perveance of the beam. The charge contained in a toroidal beam of given effective cross-section is equal to the product of the charge the beam would contain at zero temperature and a coefficient, which is a function of the temperature of the beam. Its value is unity at zero temperature and rapidly decreases with increasing temperature. The cause of cooling of the beam is shown.

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, . , , . 1S. . , , — I/(E₀/q)^3/2 (I — , ₀ — q ). , , , , , . . .

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Now Institute of Vacuum Electronics, Czechosl. Acad. Sci., Prague.

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In conclusion the author thanks J. Luká and L. Hyttych for invaluable help in the experiments, A. Rajský for constructing the electronic apparatus and J. Sokol for preparing the miniature probe.     

Влияние краевых поле й на бетатронные колебания в ускорите ле с разрезным магнитом II

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The influence of fringing on betatron oscillations in an accelerator with a sectioned magnet II

The influence of stray fields at the edges of pole pieces on the deformation of equilibrium trajectory and betatron oscillations is studied. A new definition of the effective length of segments for the approximative solution is given.

     

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

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ФИЗИЧЕСКИЕ ОСНОВЫ ИЗ МЕРЕНИЯ НАПРАВЛЕНИЯ ВОЗДУШНОГО ПОТОКА МЕ ТОДОМ НАКАЛЕННОЙ ПРО ВОЛОКИ ПРИ ВЫСОКНХ ПОДЗВУКО ВЫХ СКОРОСТЯХ

d - l - t _d R _max - J , ( ) - - , . . - ( ) - - R R _max —R. ,      

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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Сцинтилляционный сп ектрометр с сложение м импулъсов от двух кри сталлов

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Влияние переменного магнитного поля на остаточное состоя ние магнитно — Мягких материалов

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The influence of an alternating magnetic field on the remanent state of magnetically soft materials

A study is made of the influence of an alternating magnetic field of varying maximum amplitude on the remanent state, or rather, apparent remanent state of toroidal and open samples of metallic and non-metallic magnetically soft ferromagnetics. An interpretation of the corresponding dependences is given on the basis of Kondorski's conception of the composition of a polycrystalline jerromagnetic material.

     

ЭЛЕКТРОПРОВОД НОСТЬ И ТЕРМОЗЛЕКТРОДВИЖУ ЩАЯ СИЛА СЕРОГО ОЛОВА

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РЕНТГЕНОВСКОЕ ИЗЛУЧ ЕНИЕ, ВОЗБУЖДАЕМОЕ ПР ОТОНАМИ в Zn,Cu, Ni,Co и Fe

, , - 400–700 Zn, Cu, Ni, Co Fe. NaCl. - -. -. - , - .     

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.