Semi-classical asymptotics in solid state physics

This article studies the Schrödinger equation for an electron in a lattice of ions with an external magnetic field. In a suitable physical scaling the ionic potential becomes rapidly oscillating, and one can build asymptotic solutions for the limit of zero magnetic field by multiple scale methods from homogenization. For the time-dependent Schrödinger equation this construction yields wave packets which follow the trajectories of the semiclassical model. For the time-independent equation one gets asymptotic eigenfunctions (or quasimodes) for the energy levels predicted by Onsager's relation.     

Quantum‐Chemical Investigation of Hydrogen Bonds in Porphin

Using the DFT Becke–Lee–Yang–Parr exchangecorrelation threeparametric functional (B3LYP), we have calculated the geometry, the electron density distribution, and the vibration frequencies for pyrrole, porphin, and their 13 analogs with a regularly varying structure. It is shown that the determining role in the change in the frequencies of stretching and outofplane deformation vibrations of porphin compared to pyrrole is played by intramolecular hydrogen bonds at the porphyrin macroring center. We have separately considered and compared with the data for porphin complexes of pyrrole with different intermolecular hydrogen bonds: with an aromatic ring (NH··· cluster formed by the pyrrole selfaggregation in the liquid state) and an unshared electron pair (NH···OH₂ and NH···NC₄H₄ clusters). The degree of participation of the NH group in the hydrogen bonds increases in the series NH··· cluster, porphin, NH···OH₂ and NH···NC₄H₄ clusters.     

Positron annihilation in ionic media and an optical model of the positron

It is proposed that positron motion in quasiatomic positron + anion systems formed in anionic media can be described by a potential of the form V_eff(r) = Z_eff/r²-/r, where Z_eff is the effective charge of the nucleus, and n is the effective charge of the anion. It is shown that the positron wave function of the ground state of the quasiatomic positron + anion system in the field of such a potential is _X(r) = l/4·A_nx·r^X·e^–ar. Thus the validity of selecting a test variation positron wave function (r) = l/4·A·r·e^–ar is demonstrated for the potential V_eff = at r = 0 and V_eff = –/r for r > 0 (Gol'danskii-Prokop'ev optical positron model, Fiz. Tverd. Tela,8, 515 (1966)), belonging to the class of functions _X(r). Having the wave function _X(r) and Slater wave functions _ns,p(r) of the electrons, annihilation photon angular distribution (APAD) curves are calculated, together with halfwidths of the APAD curves and positron lifetimes _ns,p.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 52–56, May, 1990.     

Cross-section asymmetry for the reactions γd →pn, γd → π0 d by linearly polarized photons in the energy rangeE γ = 0·4 – 0·8 GeV

The beam asymmetryB has been measured for the reactiond pn in the energy rangeE = 0·4 ÷ 0·8 GeV and angles _p ^cm = 45 ÷ 95° and ford ⁰d at energiesE =0·5, 0·6, 0·7 GeV and angle ^cm = 130°. The results obtained are compared to existing theoretical predictions which take into account the possible contribution of dibaryon resonances.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

The prediction of the behaviour of Λ-hyperon electromagnetic form factors

The behaviour of the -hyperon electric and magnetic form factors is predicted within the modified three resonance ((783), (1020), (1680)) vector-meson dominance (VMD) model with correct analytic properties and the asymptotic behaviour predestinated by the quark model for baryons. The resonance couplings to are evaluated from the known couplings to nucleons by utilizing theSU(3) symmetry and normalization conditions for Dirac and Pauli form factors. The masses and widths of the considered vector mesons are fixed at the world averaged values. The optimal position of the effective inelastic threshold, common for Dirac and Pauli form factors, is determined from the fit of the only existing Orsay DM2 point on the cross section att=5·693 GeV². The mean square charge and magnetic radii of the -hyperon are found to be r _E ² =0·018 F² and r _M ² =–0·027 F², respectively.The authors are very much indebted to Prof. R. Baldini-Ferroli for calling their attention to the problem of -hyperon e.m. ff 's in connection with the FENICE experiment.     

Electrical properties of p-type ZnGeP2 irradiated by H+ ions

The properties of p-type ZnGeP₂ [p₀=(5–10)·10¹⁰ cm^–3, ₀=(2–5)·10^–7 (·cm)^–1], irradiated with H⁺ ions [E=5 MeV, T_irr=300 K, D=(1·10¹²–1.7·10¹⁶) cm^–2] are studied. An increase in the resistivity (to gr_max - 5·10¹¹ ·cm) and subsequent reduction in for large currents of H⁺ ions ( - 9·10⁸ ·cm for D - 1.7·10¹⁶ cm^–2), is observed in irradiated crystals. The resistivity of irradiated p-type ZnGeP₂ is found to be very sensitive to hydrostatic pressure [(4–5)·10^–5 bar^–1]. The annealing of radiation defects in the temperature interval (20–600) °C is examined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 91–93, October, 1991.     

The effect of low-temperature electron irradiation on the transition temperature of YBa2Cu3O7−δ superconductors

Measurements of the complex susceptibility =–i of electron-irradiated YBa₂Cu₃O_7– show a strong influence of the electron irradiation dose, ·t on the transition temperatureT _c . For irradiation doses of ·t=2.2·10¹⁹ e^–/cm² we find a damage rate of T _c /(·t)=–1.6·10^–19 K/(e^–/cm²). It is assumed that the decrease ofT _c is mainly a bulk effect due to the production of atomic defects like vacancies and interstitials in the Cu–O–Cu chains and in the basal planes of the unit cells.     

Study of the influence of iron and lanthanum oxides on the band structure of Pb(Zr,Ti) O3

The measurements of diffuse reflectance spectra in the range of 400; 2500 nm and of photoacoustic spectra in the range of 350; 800 nm were used for the study of the influence of iron (III) oxide and lathanum oxide additions on the band structure of polycrystalline lead zirconate — lead titanate solid solutions. The molar ratio of zirconium and titanium in the studied solid solutions was 60 40, and the concentrations of the dopants werex FeO_1.5, andy LaO_1.5, werex 0; 0·05 mol, andy 0; 0·10 mol, respectively. The diffuse reflectance spectra were expressed in terms of the Kubelka-Munk function values versus incident electromagnetic radiation energy. These dependences were decomposed into partial absorption bands using a computer. Transitions of charged carriers between energy levels or bands which differ mutually by the energy of 0·9, 1·2–1·3, 1·6, 1·65–1·7, 2·4–2·5, 2·75–2·8, 2·9–3·2, 3·4–3·8 eV, were identified. Their intensities depend on the concentration of Fe and/or on La in the Pb(Zr_0.60 Ti_0.40) solid solutions.The authors are very grateful to Mrs. Iva Havlasová, Vra Andrsová, Ing. Jan Netuka, and Mrs. Liana Karlíková from the first authors' institute, for their technical assistance.     

Quantum supports and modal logic

LetA be a quasi-manual with finite operations. Associate to each E = {e ₁ ,..., e_n} A the set _E of modal formulas: (e ₁ ··· e_n), e_i (e ₁ ··· e_i–1 e_i+1 ··· e_n), i=1,..., n. Set _A = {_E|E A}. We show that supports ofA are in one-to-one correspondence with certain Kripke models of _A where the supports are given by {x |A x is true}.On leave from the Department of Mathematics, Pontificia Universidade Catolica, Rio de Janeiro, Brazil.     

Determination of the strain potential constant by means of the p-InSb photoconductivity spectra under uniaxial compression

The influence of uniaxial pressure (0 < P < 2600 kg/cm2) on the intrinsic photoconductivity (PC) spectrum of p-InSb at 93 and 15°K is investigated. At 77°K the carrier concentration and mobility in the specimens were, respectively, (1.4–3.2)·10¹⁴ cm^–3 and 7000 cm²/V. sec. It is established that the maximum in the PC(E_m) spectra under compression is shifted towards higher energies. In the low-compression range E_m/P=5·10^–6eV·cm²/kg, while E_m/P=1·10^–6eV·cm²/kg for P > 1000 kg/cm². It is shown that the shift of the maximum of the intrinsic PC spectra with pressure is due to the growC;th in the forbidden bandwidth (E_g), and the change in parameters characterizing carrier diffusion in the specimen bulk (the diffusion coefficient, lifetime, surface recombination velocity) plays no part. The change in E_m/P with pressure is explained by the influence of valence band splitting. The deformation potential constants of the valence band |b|=(1.7±0.3) eV and |d|=(4.4±0.8)eV are calculated on the basis of a comparison between experimentally obtained data and theoretical results.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 159–162, February, 1976.     

МЕТОД ОБРАБОТКИ ДВУХ МЕРНЫХ СПЕКТРОВ СОВП АДЕНИЙ И ЕГО ПРИМЕНЕНИЕ К АНА ЛИЗУ γ-γ-СОВПАДЕНИЙ НА Ge(Li)-ДЕТЕКТОРАХ ПРИ РА СПАДЕ155Tb

The method of data processing of two-dimensional coincidence spectra is described and its application for the --coincidence spectra analysis in¹⁵⁵Tb is shown. The existence of levels with energies 86·5; 105·3; 118·0; 235·2; 266·6; 268·6; 286·8; 326·0; 367·7; 427· 4; 451·3; 488·8 keV in¹⁵⁵Gd nucleus is proved on the basis of --coincidences measured in¹⁵⁵Tb decay with Ge(Li)-detectors. Two new transitions with energies of 192 and 163 keV were found.     

Electrodynamics of moving particles

A consistent relativistic theory of the classical Maxwell field interacting with classical, charged, point-like particles is proposed. The theory is derived from a classical soliton-like model of an extended particle. An approximation procedure for such a model is developed, which leads to an already renormalized formula for the total four-momentum of the system composed of fields and particles. Conservation of this quantity leads to a theory which is universal (i.e. does not depend upon a specific model we start with) and which may be regarded as a simple and necessary completion of special relativity. The renormalization method proposed here may be considered as a realization of Einstein's idea of deriving equations of motion from field equations. It is shown that the Dirac's 3-dots equation does not describe a fundamental law of physics, but only a specific family of solutions of our theory, corresponding to a specific choice of the field initial data.     

On the mechanism of the induced anisotropy of magnesium ferrites in the range of higher temperatures

A simple mechanism explaining not only the magnitude but also the type of induced anisotropy on the magnesium ferrite Mg_0·78 Fe_2·22 O_4·026 in the temperature range from 400 to 500°K has been designed. The experimentally estimated values of the microscopic bond energyl _p 7×10^–16 erg of the configuration contributing to theF-type anisotropy and the activation energy _exp = 1·1 eV are in good correspondence with the valuesl _d1·6×10^–16erg and _cal = 1·1₅ eV which have been calculated theoretically.Dedicated to Professor Dr. Jaromír Bro on his sixtieth birthday.The author would like to express his thanks to Dr. S. Krupika for valuable discussions and his interest in this paper.     

Electrical properties of GaAs layers irradiated by H4 ions

The quantities(D) and(T) are studied in n- and p-GaAs, irradiated at T = 300°K by H⁺ ions (5 MeV). It is shown that the resistance of lightly doped GaAs specimens increases from original values of ₀ to 10⁹ ·cm upon irradiation by H⁺ ions (5 MeV) to integral fluxes up to D^* – 10¹⁵ H⁺/cm². For D > D^* the layer resistance decreases from 10⁹ ·cm to 1 ·cm at 300°K. It was found that all the GaAs specimens intensely irradiated by H⁺ ions had p-type conductivity near 300°K. Isochronic annealing of radiation defects was studied in the temperature interval 20–700°C.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 39–43, January, 1982.     

On neutron charge structure

The aim of the present work is to investigate the charge structure of neutron by calculating its root mean square charge radius r _n ^{2 1/2} and the corresponding charge form factor,G _n(q), within the general framework of quark-parton model. The neutron (the nucleon in general) is considered to be disc-like in conformity with the idea of Lorentz invariance. Using the proton charge radius, r _p ² =0·707 fm² as input, our calculations not only reproduce the observed negative sign correctly but also give reasonable value for the magnitude of r _n ² when compared with the experimental limits. –0·16r _n ² –0·11 (fm²). Predictiona are also made for the proton and the neutron charge form factors and the results compared with the data.One of us (D. P.) would like to express his gratitude to Professor A. N. Mitra for his interest and advice in the work, and to Dr. S. M. Mustafa for the warm hospitality at the University of Mosul.     

Hyperfine anomalies and nuclear γ-factors of56Co,57Co and60Co isotopes studied by NMR/ON

The results of NMR/ON measurements on^56,57,60Co isotopes in iron are presented in the paper. To avoid the uncertainties caused by local demagnetizing field inhomogeneities the measurements on two cobalt isotopes in one sample have been carried out. The values of nuclear-factors ratios ⁵⁷/ ⁶⁰=1·805(20), ⁶⁰/ ⁵⁶ = 0·761(20), ⁵⁶/ ⁵⁷ = 0·726(20) and hyperfme anomalies^{56 60} = –0·036(10),^{60 57} = 0·017(10) and^{57 56} = 0·018(10) have been calculated from the experimental results.Dedicated to the 30th anniversary of the Joint Institute for Nuclear Research.     

ИжМЕРЕНИЕ пОльРИжАцИИ пРОтОНОВ с ЁНЕРгИЕИ 6,7 MeV пРИ РАссЕьНИИ НА УглЕРОДЕ

A carbon polarimeter for proton polarization measurements at energies higher than 4 MeV has been designed. Considerable transmission has been attained by using a thick polarimeter target and larger scattering solid angles. The effective polarization value at the region ofE _p from 4·6 to 6·0 MeV varies only slightly with energy and attains an average value ofP _eff–0·8. Solid state detectors were used for proton recording. The instrument calibration curve was determined by means of a triple experiment.The angular distribution of polarized protons scattered elastically has been measured at an energy of 6·7 MeV and in an angle range of _lab form 30 to 120. This distribution has two minima ofP(40_lab)=–056±0·03 andP(100_lab)=–088±0·06 and one maximum ofP(70_lab)=+1·03±0·04.     

Collisionless kinetic equations for massive particles with spins 1/2 and 0 in gravitational and electromagnetic fields

We define a covariant and gauge-invariant generalization of the Wigner functions of particles with spins 1/2 and 0. The collisionless kinetic equations are obtained for these particles in external gravitational and electromagnetic fields in the quasiclassical approximation; also obtained are the momentum representations of the energy-momentum tensor, current, and spin tensor, taking into account the effects of the spin's interaction with the gravitational field an electromagnetic field. The following notation is used: e and m are the charge and mass of the particles; is Planck's constant; (x) are the covariant-fixed Dirac matrices; ^,=(1/4)[, ]: a(^b)=(1/2) (a b +ab ); [A, B]=A·B – B·A; A,B=A·B+B·A; g(x)=det(g (x));R = –...; the speed of light c=1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 47–53, September, 1990.The author wishes the thank Yu. G. Ignat'ev and members of the seminar in General Relativistic Statistics and Cosmology of the Kazan' Pedagogical Institute for useful discussions.     

Spectral response of CdS with Ag,Cu, and in impurities

High-resistance (dark 10⁸ · cm) photosensitive CdS samples (light 10²–10³ · cm at saturation) were obtained from low-resistance ( 0.1 · cm) nonphotosensitive CdS single crystals by thermal diffusion of Cu, Ag, and In in vacuum at 2 · 10^–5 torr. The spectral response of impurity and pure high-resistance photosensitive single-crystal CdS samples was studied in the wavelength range from 0.35 to 3. The short-wave and long-wave limits of the spectral curves, the wavelength range of maximum photoconductivity and the forbidden band width, the depth of impurity levels, the upper edge of the impurity band, and the depth of maximum-density activation centers have been determined from the spectral curves. The results are discussed and compared with published data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 117–121, June, 1972.     

Internal conversion investigations for the 127·37 keV E3 transition in134Cs

Relative conversion line intensities of the 127·37 keV E3 isomeric transition in¹³⁴Cs have been measured for ten atomic subshells, using the (/2) 13 beta-ray spectrometer. The multipolarity E3 + (0·07±0·04)% M4 was determined. Internal conversion coefficients were calculated in different physical approximations. Precise calculations were performed for two atomic models (non-relativistic Hartree-Fock-Slater and relativistic Hartree-Fock-Slater). Experimental data were found in agreement with tabulations of Hager and Seltzer and mentioned calculations. An upper limit for the -branching ratio (138·6 keV M4)/(127·37 keV E3) was found to be 0·2%. The measurement of the half-life of the isomeric state has been carried out with a NaJ(Tl) crystal. The result obtained isT _1/2 = (2·95 ± 0·02) h.The authors would like to thank Prof. U.Schmidt-Rohr for the interest in this work.