Decay of Re186

The decay of Re 186 was investigated with a double focusing spectrometer and scintillation spectrometer. Four transitions were observed with energies of 122·7±0·1 keV, 137·2 keV, 632·2±1·5 keV and 768·2±1·5 keV and the relative-ray intensities 18, 246, 0·9 and 1 respectively. TheK-conversion coefficients determined for low-energy transitions are in good agreement with the theoretical values ( _K ^122·7 =0·53±0·05, _K ^137·2 =0·44±0·02). The relative intensities of theK, L, M andN conversion lines were also determined for these transitions:KL _I +IIL _III M=1·20±0·201·32±0·20 1±0·150·57±0·08 for 122·7 keV transition,KL _I +IIL _III MN=1·57±0·081· 72±0080·70±0·030·20±0·01 for 137·2 keV transition. In the beta spectrum two groups were observed with the end points of 1076±3 keV and 939±3 keV and relative intensities 74±4% and 21±4% respectively. For the branching ofK-capture it was found that 1·5% populates the 122·7 keV level and 3·5% the ground state. The decay scheme from the present results is proposed.The authors would like to thank M. Buriánek and V. Kopiva for help in the measurements.     

Magnetic relaxation spectrum of ferrites Mn x Fe3−x O4+γ

The initial permeability disaccommodation in ferritesMn _x Fe₃–xO₄₊ , 0·5x1, was studied in a temperature range around –200°C to +180°C. Four separate bands were found in the relaxation spectrum of these ferrites.

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Mn _x Fe_3–x O₄₊

Mn _x Fe_3–x O₄₊ , 0,5x1, –200°C +180°C. .

     

Internal Lifschitz singularities of disordered finite-difference Schrödinger operators

The integrated density of states has C-like singularities, ln|k(E)–k(E _c )|=–|E–E _c |^–v/2 _c (E), with _c >0, a milder function at the edges of the spectral gaps which appear when the distribution function of the potentiald has a sufficiently large gap. The behaviour of _c nearE _c is determined by the local continuity properties ofd near the relevant edge: _c (E)=O(1) ifd has an atom and =O(ln|E–E _c |) if is (absolutely) continuous and power bounded.     

Thermal conductivity and specific heat of amorphous Zr0.67Ni0.33 after structural relaxation

Low-temperature measurements of the thermal conductivity (0.3KT5K) and of the specific heatC (0.07KT3.5K) of splat-cooled amorphous superconducting Zr_0.67Ni_0.33(T _c 2.7K) after different annealing stages are reported. increases progressively (up to 55%) after annealing. An analysis of with the help of normal-state measurements belowT _c in an overcritical field shows that the phonon-electron scattering remains unaltered after annealing. Hence the increase in must be entirely attributed to structure-induced (intrinsic) scattering, i.e. by two-level tunneling states (TLS) at low temperatures (T1K). The specific heat shows a small decrease aboveT _c (by 8%) which is attributed to a small diminution of the electronic density of states at the Fermi level and to a small increase in the Debye temperature. ForTT _c where TLS dominate, the specific heatC decreases less upon annealing than expected from the increase of in the standard tunneling model. This points to a change in the TLS relaxation time spectrum upon annealing, as observed previously for Zr _x Cu_1–x glasses.     

The asymmetric contact process on a finite set

The contact process onZ has one phase transition; let _c be the critical value at which the transition occurs. Let _N be the extinction time of the contact process on {0,...,N}. Durrett and Liu (1988), Durrett and Schonmann (1988), and Durrett, Schonmann, and Tanaka (1989) have respectively proved that the subcritical, supercritical, and critical phases can be characterized using a large finite system (instead ofZ) in the following way. There are constants ₁() and ₂() such that if < _c , lim _{N N} /logN = 1/₁(); if > _c , lim _N log _N /N = ₂(); if = _c , lim _{N N} /N= and lim _{N N} /N ⁴=0 in probability. In this paper we consider the asymmetric contact process onZ when it has two distinct critical values _c1< _c2. The arguments of Durrett and Liu and of Durrett and Schonmann hold for < _c1 and > _c2. We show that for [ _c1< _c2), lim _{N N} /N=-1/, (where _i is an edge speed) and for = _c2, lim _N log _N /logN=2 in probability.     

Quantum shot noise: Expansions in powers of the pulse density

Quantum shot noise consists of individual pulses which contribute time-dependent (operator) potentials toward a total potentialV(t). The averaged quantity T exp _t0 ^t dtV(t) in general can no longer be calculated explicitly, in contrast to the classical case, and expansions are of interest. Noncommutative cumulant expansions are not directly applicable if the correlation functions ofV(t) have singularities, as happens in applications. It is shown here that these expansions, when applied to quantum shot noise, can be partially summed to give expansions in powers of the pulse density. Three types of such expansions are established explicitly, and for two of them the derivation is direct. For one of them the first-order approximation is closely connected to the so-called unified theory of spectral-line broadening.     

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.     

Three-Mode Entangled State Representation of Continuum Variables and Optical Four-Wave Mixing

We establish a new three-mode entangled state representation , of continuum variables, which make up a complete set. Using optical four-wave mixing and a beam splitter transform we can prepare , . Based on , a new number-difference--operational-phase uncertainty relation is established and the corresponding squeezing dynamics is discussed.     

The central limit theorem for the spectrum of the random one-dimensional Schrödinger operator

Let H_L = –d²/dt²+q(t,) be an one-dimensional random Schrödinger operator in ²(–L, L) with the classical boundary conditions. The random potential q(t,) has a form q(t, )=F(x_t), where x_t is a Brownian motion on the Euclidean v-dimensional torus, FS^v R¹ is a smooth function with the nondegenerated critical points, min_s ^v F = 0. Let are the eigenvalues of H_L) be a spectral distribution function in the volume [– L,L] and N() = lim_L(1/2L)N_L() be a corresponding limit distribution function.Theorem 1. If L then the normalized difference N _L ^* ()=[N_L() -2L·N()]2L tends (in the sense of Levi-Prokhorov) to the limit Gaussian process N^*(); N^*()0, 0, and N^*() has nondegenerated finitedimensional distributions on the spectrum (i.e., > 0). Theorem 2. The limit process N^*() is a continuous process with the locally independent increments.     

Slowing down of retrieval in the hopfield model

The variation of the convergence time, as a function of the storage capacity is studied numerically for systems ranging in size fromN=1000 toN=16,000 neurons. is found to increase likeexp[–A(_c–)] as one nears the critical storage capacity _c =0.142=0.002.     

Self-diffusion in simple models: Systems with long-range jumps

We review some exact results for the motion of a tagged particle in simple models. Then, we study the density dependence of the self-diffusion coefficientD _N() in lattice systems with simple symmetric exclusion in which the particles can jump, with equal rates, to a set ofN neighboring sites. We obtain positive upper and lower bounds onF _N()=N{(1–)–[D_N()/D_N(0)]}/[(1–)]x for [0, 1]. Computer simulations for the square, triangular, and one-dimensional lattices suggest thatF _N becomes effectively independent ofN forN20.     

A matrix method for estimating the Liapunov exponent of one-dimensional systems

Let : [0, 1][0, 1] be a piecewise monotonie expanding map. Then admits an absolutely continuous invariant measure. A result of Kosyakin and Sandler shows that can be approximated by a sequence of absolutely continuous measures _n invariant under piecewise linear Markov maps _itn. Each _itn is constructed on the inverse images of the turning points of . The easily computable measures _n are used to estimate the Liapunov exponent of . The idea of using Markov maps for estimating the Liapunov exponent is applied to both expanding and nonexpanding maps.     

Magnetic moments of proton drip-line nuclei13O and9C

The magnetic moments of the proton drip-line nuclei¹³O(I = 3/2^–,T _1/2 = 8.6 ms) and 9C(I = 3/2^–,T _1/2 = 126 ms) have been determined for the first time through the combined techniques of polarized radioactive nuclear beams and-NMR detection. The observed magnetic moments are ¦(¹³O)¦ = 1.3891 ±0.0003 _N and ¦(⁹C)¦ = 1.3914 ±0.0005 _N. Spin expectation values are deduced to be 0.76 and 1.44 for¹³O and⁹C, respectively. While the of¹³O is consistent with the systematics from isospinT= 1/2 mirror pairs, the of⁹C is unusually large, even far larger than the single particle value, = 1.     

Static and stationary axially symmetric gravitational fields of bounded sources II. solutions obtainable from Weyl's class

This paper shows that a new class of axially symmetric static electrovacuum/magnetovacuum solutions is obtainable from Weyl's class of static vacuum solutions. The new class contains an infinite set of asymptotically flat solutions (in closed form) each of which involves an arbitrary set (d, _i) of parameters. These parameters have to be interpreted as functions of massm, chargee, and higher electric/magnetic multipole moments _i of the particle. The cased = 0, _i =0 leads to the Darmois solution and the cased = 0, _i 0 leads to the results of [1]. The case d=0, e=_i=0 leads to the Schwarzschild solution, the cased 0, _i =0,e 0 leads to the Reissner-Nordström solution. To get more general examples is a lengthy but straightforward exercise.     

A four-thirds law for phase randomization of stochastically perturbed oscillators and related phenomena

LetI be a set of invariants and be a set of angle variables for a system of differential equations with anO() vector field. When time dependent stochastic perturbations, also ofO(), are added to the system, we have shown that under suitable conditionsI becomes a stochastic adiabatic invariant satisfying a diffusion equation on time scales of order 1/², in the limit as »0. Here we show that the angle variables converge weakly to a Gaussian Markov process on an O(^-4/3) time scale, and thus the phase becomes randomized at these times. Application to nearly integrable Hamiltonian systems is considered.Supported by NSF grant DMR-8704348     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

Microstructure of fiber-like SiC/Si3N4 composite particulate

The microstructure of fiber-like SiC/Si₃N₄ composite particulate was investigated using high-resolution transmission electron microscopy techniques. The SiC/Si₃N₄ composite particulate consisted of a-SiC core and a -Si₃N₄ outer shell. Two kinds of composite particulate were distinguished when the observed orientation of the SiC core was <110>. In one type of the SiC/Si₃N₄ composite particulate, a crystal relationship of (111)-SiC | (102) -Si₃N₄ and (111)-SiC (114) -Si₃N₄ was identified; in the other type of the SiC/Si₃N₄ composite particulate, a crystal relationship of (111)-SiC (001) -Si₃N₄, and (111)-SiC (101) -Si₃N₄ was observed.     

The Crystallography of Interphase Boundaries Between Silicon Carbide and Silicon Nitride in Silicon Nitride—Silicon Carbide Particulate Composites

Interphase boundaries between 3C SiC grains and two different -Si₃N₄ morphologies in Si₃N₄–SiC composites have been studied by transmission electron microscopy. In general, boundaries between small -Si₃N₄ intragranular precipitates and surrounding SiC grains were relatively free of intergranular films, whereas boundaries between large -Si₃N₄ grains and adjacent SiC grains were invariably covered with thin intergranular films. Orientation relationships approximating to [110] 3C SiC [0001] -Si₃N₄ and (001) 3C SiC (10 0) -Si₃N₄ were found to dominate between 3C SiC grains and the intragranular -Si₃N₄ precipitates, but there was no evidence of any favoured orientation relationship between the large -Si₃N₄ grains and adjacent SiC grains. The rationale for special orientation relationships arising when there is no intergranular film present at 3C SiC–-Si₃N₄ interfaces is explored geometrically using the near-coincidence site lattice model, with the significant result that the dominant orientation relationships between 3C SiC grains and the intragranular -Si₃N₄ precipitates have low misfits relative to all other possible orientation relationships between 3C SiC and -Si₃N₄.     

Statistical mechanics of the isothermal lane-emden equation

For classical point particles in a box with potential energy H^(N)=N ^–1(1/2) _ij=1 ^N V(x _i,x _j) we investigate the canonical ensemble for largeN. We prove that asN the correlation functions are determined by the global minima of a certain free energy functional. Locally the distribution of particles is given by a superposition of Poisson fields. We study the particular case =[–L, L] andV(x, y)=}- cos(x–y),L}>0, }>0.References     

On X-ray measurements of residual stresses in materials with lattice strain gradient

The non-linear distribution of lattice strain ³¹⁰vs sin² observed on the surface of a polished steel specimen can be interpreted by tri-axial stress state with surface components of stress tensor ₁₁(0)= ₂₂(0) and gradientsg ₁₁= ₁₁/T, g ₃₃= ₃₃/T. The distribution of experimental values is duscussed from the viewpoint of various ways of calculating ₁₁.The authors would like to thank Dr. J. Musil, D. Sc. of the Institute of Physics of Czechoslovak Academy of Sciences for kindly providing the samples which made possible this study.