Some critical exponent inequalities for percolation

For a large class of independent (site or bond, short- or long-range) percolation models, we show the following: (1) If the percolation densityP (p) is discontinuous atp _c , then the critical exponent (defined by the divergence of expected cluster size, nP _n (p) (P _c –P)^– asp p _c ) must satisfy 2. (2) or (defined analogously to, but asp p _c ) and [P _n (p _c ) (n ^–1–1/) asn ] must satisfy, 2(1 – 1/). These inequalities for improve the previously known bound 1(Aizenman and Newman), since 2 (Aizenman and Barsky). Additionally, result 1may be useful, in standardd-dimensional percolation, for proving rigorously (ind>2) that, as expected,P _x has no discontinuity atp _c .     

Stochastic Schrödinger operators and Jacobi matrices on the strip

We discuss stochastic Schrödinger operators and Jacobi matrices with wave functions, taking values in ^l so there are 2l Lyaponov exponents ₁..._l0 _l+1..._2l =–₁. Our results include the fact that if ₁=0 on a set positive measure, thenV is deterministic and one that says that {E|exactly 2j 's are zero} is the essential support of the a.c. spectrum of multiplicity 2j.Research partially supported by USNSF under grant DMS-8416049     

High-spin isomer in 93Mo

The high-spin states of ⁹³Mo have been studied by a ⁸²Se( ¹⁶O, 5n) ⁹³Mo reaction at a beam energy of 100 MeV using techniques of in-beam -ray spectroscopy. Measurements of -t, --t coincidences, -ray angular distributions and -ray linear polarizations were performed. The high-spin isomer was found as a (39/2^-) state at about 9.7 MeV. The near-yrast states in ⁹³Mo were interpreted using the weak-coupling picture of a d_5/2 neutron to a neutron magic core nucleus ⁹²Mo.     

On the 3+ level in Os186 populated in Re186 Β-decay

The coincidences of the 400–1100 keV gammas with the conversion electrons of the 137 keV transition were measured with the intermediate image spectrometer modified for - coincidences. The e_L 137- 770 keV coincidences were observed. Consequently, in addition to the known 768 keV transition, there is another one with closed energy. For this transition the relative intensity ratioI ⁶³² /I ⁷⁷³ =8±2 was determined. The corrected decay scheme of Re¹⁸⁶ is presented.     

A “hydrodynamic” theory of surface reaction rates

The Brownian motion of adsorbed particles is described in terms of the first four velocity moments of the distribution function (number density, momentum density, energy density and energy current density). The resulting hydrodynamic equations turn out to be sufficient for a simple derivation and extension of Kramers' results for chemical reaction rates in terms of the friction constant of an underlying Fokker-Planck equation. An interpolation formula is obtained for() containing Kramers' results for small and large as limiting cases. For temperaturesT small compared to the well depthV ₀ one finds a large regionT/V ₀/v ₀V ₀/T in which Eyring's absolute rate theory is approximately valid.On leave of absence from Physikdepartment der TUM, München-Garching     

Gamma-ray spectroscopy in 110Sn and 111Sn

Excited states in ¹¹⁰Sn and ¹¹¹Sn nuclei have been investigated using in-beam -ray spectroscopic methods. An ¹⁶O beam with an energy of 60-80MeV was used to bombard a ⁹⁸Mo target. On the basis of the relative excitation functions, -ray angular distributions, - and -time distributions, -ray multiplicity and total energy data, the level schemes of ¹¹⁰Sn and ¹¹¹Sn have been studied and extended up to E_exc 11.5MeV, I = 24, and E_exc 11.1MeV and I = (51/2), respectively. An extension of the intruder, g.s. and negative-parity bands, as well as 5 new band-like structures are proposed in ¹¹⁰Sn. The nature of newly introduced collective band 8 as well as 10⁺ states fed in the decay of the collective band is discussed. In the ¹¹¹Sn nucleus an intruder band based on the 23/2^- state has been reinvestigated and the extension of the g.s. band and second negative-parity band is given. Evidence for neutron-core coupling in ¹¹¹Sn is found. The structure and systematics of excited states in light Sn isotopes is discussed.     

The exact phase diagram of the quantumXY spin glass model in a transverse field

The infinite rangeXY spin glass model in a transverse field is investigated by means of the Trotter-Suzuki approach. The exact phase diagram is obtained showing that a spin glass transition takes place for non-zero values of the transverse field up to a critical value _c =1.440.01. The present numerically exact calculations are in good agreement with our previous approximate results and they clear remaining discrepancies from previous work.     

Asymptotic Expansion of the Pressure in the Inverse Interaction Range

We consider an Ising system in d2 dimensions with a ferromagnetic Kac potential whose scaling parameter is denoted by . We derive an asymptotic series for the thermodynamic pressure P _, in powers of . The 0th-order term of the expansion is the mean-field pressure of the Lebowitz and Penrose theory.     

Analytical electron microscopy study of diffusion-bonded multiphase system

This study presents diffusion experiments of NiAl coupled with pure Ni (Ni/NiAl). The couple produces the Ni₃Al-based intermetallic phase ( phase) as an intermediate layer at the interface during diffusion annealing. Analytical electron microscopy is used to examine microstructural features, crystallographic orientation and compositional variations across the interface. Interdiffusivities are measured from the compositional variations. It is shown that the growing behavior of the phase changes between higher and lower annealing temperatures. The growth kinetics of the phase is also discussed.     

Nonlinear two-photon interaction in a strong magnetic field

Sections of nonlinear photon-photon scattering processes and merger of photons in the nucleus (Ze) (Ze) in a strong magnetic field are computed by using a developed two-dimensional formalism. Closed expressions are obtained for the sections with a graphical illustration of the results and they are compared with the case of no external fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 16–19, June, 1988.     

Temperature-dependent bandstructure of ferromagnetic metals with localized moments

We consider a theoretical model for ferromagnetic metals like Gd, which takes into account the exchange interaction and the hybridization between two electronic subsystems. The first is built up by quasi-localized electrons, which take care for the existence of permanent magnetic moments, and is described by an atomic limit multiband Hubbard-Hamiltonian. The second subsystem consists of relatively broad conduction bands with more or less free electrons. We investigate the influence of electron correlations on the conduction band states in dependence of temperatureT and bandfillingn. A sensitive reaction of the band states on the magnetic ordering of the moment system leads to strong band deformations. The main goal is the determination of a quasiparticle bandstructure, which we derive in analogy to the experiment (PES, IPE) directly from the spectral density. The new aspect is a splitting of the bare dispersion _m (k) into several quasiparticle dispersion curves with stronglyT-andn-dependent spectral weights. Even forT>T _c an exchange-caused splitting is found. — In this paper we use as input for the free band energies _m (k) a nondegenerate simple cubic-tight binding expression, and in addition seven dispersionlessf-levels, in order to stress mainly the influence of many body effects. It is discussed how the model can be coupled to a LDA bandstructure calculation, in order to get quantitative results for theT-dependent electronic structure of the ferromagnetic 4f-metal Gd, the presentation of which is intended in a forthcoming paper.     

On the mechanism of conduction and photoconduction in PbTe films

Conductivity, photoconductivity, thermoelectric, Hall and photothermoelectric measurements have been carried out on vacuum evaporated, air exposed PbTe films of different thickness in the temperature range 300 K-130 K to probe into the mechanism of conduction and photoconduction in these films. The dark electronic transport properties have been explained considering accumulation layers on the free surface and substrate-film interface and also the diffusion of oxygen inside PbTe microcrystals. It appears that both bulk and potential barrier scattering predominate in the high temperature region (300 K-250 K) and only barrier scattering can explain the low temperature carrier mobility at lower temperatures (250 K-130 K). Photoconductivity can be described with trapping of minority carriers within the PbTe microcrystals in the low temperature region and in the high temperature region with diffusion of minority carriers to the surface. The same oxygen trap situated at a depth of 0·06 eV from the conduction band is found to be responsible for both conduction and photoconduction in the low temperature region.Notation N _t Total trap concentration - N _r Total recombination centre concentration - n _t Electron concentration at the trapping centres - n _r Electron concentration at the recombination centres - _n Capture coefficient of electrons by recombination centres - _p Capture coefficient of holes by recombination centres - Capture coefficient of electrons/holes by trapping centres - E _t, E ₁ ^* Trap energies - E _c Conduction band edge - E _v Valence band edge - f Number of electron-hole pairs generated per unit volume per unit time - N _c Effective density of states at the conduction band edge - Potential barrier height - _p Life time of non-equilibrium holes - _s Surface barrier height in dark - _sl Surface barrier height under illumination - n _b Free electron concentration - P _b Free hole concentration - _s Surface mobility of holes - _b Bulk mobility of holes The authors are grateful to Prof. H. N. Bose for helpful discussions.     

Positronium atom in an ionic crystal

The Sommerfeld-Welker model of a hydrogen atom in a spherical, impenetrable force cavity is used to calculate the basic properties of positronium in an ionic crystal. The basic properties of positronium (the lifetime against 2- and 3-annihilation, the count rate of 3 coincidences, and the magnetic-quenching parameter) are found as functions of the radius of the spherical force cavity.Translated from Izvestiya VUZ. Fizika, No. 7, pp. 71–75, July, 1970.     

Is the Cabibbo Angle a Function of the Weinberg Mixing Parameter?

The (u, c) quarks and (d, s) quarks arerequired to have mass matrices of a certainform. To achieve these mass matrices appropriate Lagrangians are assumed. Theu quark is coupled to the standard Higgs scalar _L. Thec quark has a ₅ couplingwith _L and _R, where _R is the Higgs scalar corresponding to theleft-rightmodel. The u quark has no ₅ coupling. Both u,c quarks have a Yukawa couplingwith a Higgs multiplet. Exactly similar Lagrangians are chosen for thed, s qurks.Using these mass matrices, the Cabibbo angle is found to be 13° 11. The ratiom _c/m _s is shown to be approximately 3.1 with the help of the Weinberg mixingparameter. The mixing angles ₂ and ₁ determine the Cabibbo angle. The ratiotan ₂/ tan ₁ is shown to be a function of the Weinberg mixing parameter.     

Electromagnetic radiation of relativistic electrons in thick crystals

Angular distributions of soft gamma quanta and spectra of electron radiation intensity are compared in diamond crystals of various thickness for axial orientation. Narrow directionality of the soft gamma quanta and a weak dependence of angular width of the distribution on crystal thickness are noted. For axial orientation the angular width of the soft gamma quantum distribution comprises ± 2_L for diamond, silicon, and tungsten crystals. Radiation losses into the collimator _c = 1/ for axial orientation increases with thickness and reach their maximum value at t 0.1 radiation length. It is shown experimentally that maximum values of radiation loss into the cone ^–1 can be achieved in crystals of the light-elements.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 32–38, September, 1986.     

Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits

We present and discuss the derivation of a nonlinear nonlocal integrodifferential equation for the macroscopic time evolution of the conserved order parameter (r, t) of a binary alloy undergoing phase segregation. Our model is ad-dimensional lattice gas evolving via Kawasaki exchange with respect to the Gibbs measure for a Hamiltonian which includes both short-range (local) and long-range (nonlocal) interactions. The nonlocal part is given by a pair potential ^dJ(|x–y|), >0 x and y in ^d, in the limit 0. The macroscopic evolution is observed on the spatial scale ^–1 and time scale ^–2, i.e., the density (r, t) is the empirical average of the occupation numbers over a small macroscopic volume element centered atr=x. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (Part II) we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.     

The van der Waals limit for classical systems

For a -dimensional system of particles with the two-body potentialq(r)+ ^v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.     

Elimination of variables in simple laser equations

The usual way of obtaining rate equations (RE) and a single equation for the field amplitude (EFA) from the semiclassical laser equations (Lorenz-Haken model) is reexamined by undertaking a systematic elimination procedure developed in synergetics. The RE and EFA are justified in the case 1 (, ) and case 2 (, ), respectively. We show that, because the eliminated variable happens to contain a considerable contribution from an unstable mode, the usual elimination technique in the case 3 (, ) leads to an inconsistency. As important by-products we obtain the RE and EFA for arbitrary cavity relaxation constant (). Some remarks are given on the direct elimination technique in the non-diagonal representation in the study of instabilities.     

Resonant magnetopolaron effects in parabolic quantum wells in a tilted magnetic field

We study the resonant magnetopolaron effects in parabolic quantum wells in a tilted magnetic field. The renormalization of the first excited level, which is resonant with the ground state level plus one longitudinal-optical phonon is calculated at the resonance using an improved resonance approximation to be E= where is the polaron coupling constant. The exponent and the factor are calculated in dependence on the tilt angle of the magnetic field and the confinement energy.