Implementation of comparative probability by normal states. Infinite dimensional case

Let be an infinite dimensional Hilbert space and () the set of all (orthogonal) projections on . A comparative probability on () is a linear preorder on () such thatOP1,1O and such that ifP┴R,Q┴R, thenPQP+RQ+R for allP, Q, R in (). We give a sufficient and necessary condition for to be implemented in a canonical way by a normal state onB(), the bounded linear operators on .     

Proton spin-lattice relaxation times in ytterbium hydrides

The measurements of the proton (NMR) spinlattice relaxation times have been made in a series of ytterbium hydrides, YbH _x . Results are reported forx=1.80, 1.95, 2.00 and 2.62 and temperatures 4.2T297K. In the orthorhombic phase (1.80x2.00), the spin-lattice relaxation times are dominated by the hyperfine interaction of protons with conduction electrons and the spin diffusion mechanism. In the cubic phase (x=2.62), the relaxation times are five orders of magnitude shorter than in the orthorhombic one. This is interpreted in terms of the proton coupling with the Yb³⁺ ion spin fluctuations.     

Measurement of the refractive index and optical absorption spectra of epitaxial bismuth substituted yttrium iron garnet films at uv to near-ir wavelengths

Refractive-index and optical-absorption spectra of Bi-substituted yttrium iron garnet films, epitaxially grown by liquid-phase epitaxy, have been measured in the spectral regime 0.26 m1.9 m by thin-film interference for 0.52 m and by ellipsometry for0.52 m. The Y_3–x–y Bi _x Pb _y Fe_5–z Pt _z O₁₂ films contain bismuth in the range Ox 1.42, lead in the range 0.01 y0.08 and platinum in the range 0.005<=z0.03. There is satisfactory coincidence between the results from ellipsometry and thin-film interference in the overlapping wavelength region. The materials investigated are the same as reported earlier from this laboratory in ter mof their magnetic and magnetooptic properties.     

The magnetic structures of NdCu2 determined by single crystal neutron diffraction

We investigated the magnetic structure of NdCu₂ by means of neutron diffraction as a function of temperature between 1.5 K and 8 K in zero external field. The diffraction data were obtained on two single crystals with different orientations using the triple-axis-spectrometer TAS6 at the DR-3 reactor at Risø. Two magnetic phases were observed between 1.5K andT _N =6.5K. From 1.5 K to 4.1 K the magnetic reflections can be described by the commensurate wave vector =(3/5 0 0) and its higher harmonics 3 and 5. Below 2.5K the structure is completely squared-up. For 4.1 KT6.5 K the magnetic structure is incommensurate with the chemical lattice and can be described by the wave vector=(3/5 0 0) and its higher harmonies 3 and 5M. Below 2.5 K the structure is completely squared-up. For 4.1 K T 6.5 K the magnetic structure is incommensurate with the chemical lattice and can be described by the wave vector ^*=(0.62 0.044 0). In both phases the Nd-moments are oriented along the easyb-direction.     

Intrinsic carrier concentration in Hg1−xCdxTe

The effective mass of heavy holes has been determined on the basis of simultaneous analysis of the Hall coefficient and conductivity data obtained in the temperature region 100–300 K on well characterized p-type Hg_1–x Cd_xTe (x0·2) samples. Its value is 0·7m₀. The calculation of intrinsic carrier concentration for 0·19 x0·3 and 50 Kg T 300 K has been carried out using the above value of the effective mass of holes, Hansen's expression for the band gap and momentum matrix element from magneto-optical measurements.     

Valence change of europium in the Eu(Ir1−x Pd x )2Si2 silicides

Eu(Ir_1–x Pd _x )₂Si₂ solid solutions which exist only for 0x0.125 and 0.75x1 crystallize in the tetragonal ThCr₂Si₂-type structure. X-ray diffraction data, magnetic susceptibility and¹⁵¹Eu Mössbauer measurements suggest that these compounds can be characterized as homogeneous mixed valence systems. At room temperature and for 0x0.125, the europium valence decreases asx increases. For 0.75x1, a sharp continuous valence transition from Eu²⁺ to Eu³⁺ occurs near 48 K, 54 K and 78 K forx=0.75, 0.81 and 0.94 respectively. These valence changes are discussed in relation with the Eu–(Ir, Pd) interatomic distance.     

Strong far-infrared laser action in carbonyl fluoride and vinyl fluoride

Intense far-infrared laser action is reported for carbonyl fluoride and vinyl fluoride. Eleven new lines with wavelengths between 339 m538 m were obtained by optically pumping carbonyl fluoride with numerous lines of the 10.4 m band of a cw CO₂ laser. Twenty-three lines with wavelengths in the range 172 m783 m were detected when pumping the recently discovered efficient FIR laser molecule vinyl fluoride. In addition, three very weak new lines were found using 1.1-difluoroethylen.     

57Fe Mössbauer studies in a new cluster spin glass system RuxFeGa (0.5≦x≦1.5)

⁵⁷Fe Mössbauer and bulk magnetization studies have been carried out in a new magnetic system Ru_xFeGa for 0.5x1.5. The system is seen to freeze into a cluster spin glass phase at 70 K. The freezing temperature and the hyperfine field at Fe at the lowest measured temperature, 190 kOe, is essentially same for all values of x investigated.     

Green's functions for body-centred cubic lattices

The presented paper contains the tables of Green's functions for bcc lattices for outband frequencies 1·0/ _m 1·6. The central-force model is used, the interaction with 8 nearest and 6 next-nearest neighbours is considered and the number of different Green's functions is fairly decreased by symmetry. Numerical difficulties arising by computing Green's functions are discussed. The derivation of symmetry relations for a dynamical matrix is generalized for the matrix of Green's functions.     

Magnetic properties of Nd3+ in Nd−Ba−Cu−O-compounds

Neutron diffraction, neutron spectroscopy and magnetization measurements have been employed to study the structural, electronic, and magnetic behavior of eleven compounds with the general formula Nd_1+y Ca _v Ba_2–y–v Cu₃O _x (0y0.5; 0v0.25; 6x7). The structure turned out to react to oxygen reduction similar as other 123-compounds, yielding discontinuities close to the metal-insulator-transition and the well-known relations of bond lengths as a function ofT _c. The crystalline electric field (CEF) interaction, splitting the 10-fold degenerate ground-state J-multiplet of the Nd³⁺-ions into five doublet states, was investigated by neutron spectroscopy. The derived CEF parameters have been used to determine changes in the electronic surroundings of the Nd³⁺ ions. In addition, with the help of the CEF parameters the thermodynamic magnetic properties of these compounds were calculated which turn out to be in good agreement with the experimental data.     

β-Relaxation and low-temperature specific heat in (KBr)1−x(KCN)x

The specific heat in (KBr)_1–x(KCN)_x has been measured for concentrations 0.00x0.93 and for temperatures 2 KT50 K. In addition, the dipolar relaxation phenomena were studied using dielectric spectroscopy. The relaxation behaviour was parametrized assuming a Gaussian distribution of energy barriers and the mean activation energies, the distribution widths, and the attempt frequencies have been determined as a function of the CN^– concentration. With these parameters the linear and the excess specific heat contributions were calculated and compared to the calorimetric results.     

A contribution to the semi-focusing method with a flat polycrystalline sample

Condition are derived for the approximate focusing of diffraction lines in the chosen, relatively wide angular region, using the semi-focusing method with a flat sample, if a bent crystal monochromator is employed. The form of the absorption factor for a flat polycrystalline sample is derived for the case of uniform oscillation of the sample in the angular region ± around the axis of the camera.

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Deposition of silver films by plasma-enhanced chemical vapour deposition

Plasma-enhanced chemical vapour deposition of silver films has been performed using perfluoro-1-methylpropenylsilver as a precursor. Under most conditions of rf power, substrate temperature and gas composition shiny films with resistivities of 2 cm and impurities of 1 % are obtained.     

Spectroscopic factors of9Be,10B and13C from (d,t) reactions

The differential cross sections of tritons from the (d, t) reaction on⁹Be,¹⁰B and¹³C targets have been measured in the angular range of 5° _LAB110° with relatively small errors, 5%. The experimental data were analysed in terms of the standard DWBA using both zero-range and exact finite-range approaches.     

Intersection properties of simple random walks: A renormalization group approach

We study estimates for the intersection probability,g(m), of two simple random walks on lattices of dimensiond=4, 4– as a problem in Euclidean field theory. We rigorously establish a renormalization group flow equation forg(m) and bounds on the -function which show that, ind=4,g(m) tends to zero logarithmically as the killing rate (mass)m tends to zero, and that the fixed point,g*, ind=4– is bounded by const' g*const. Our methods also yield estimates on the intersection probability of three random walks ind=3, 3–. For =0, these results were first obtained by Lawler [1].     

The small momentum transfer k L o C→K S 0 C regeneration at high energies

Results of the first elastic K _S ^o regeneration experiment on carbon, using magnetic spark chamber spectrometer, are presented in the beam momentum interval 10p50 GeV/c. The d ifferentia cross section d/dt is reconstructed in the range 0·0025–t0·02 (GeV/c)² and its slopeB is found to be momentum independent with an average valueB=(65±11) (GeV/c)^–2. The results are in agreement with the calculations using the coherent production model.     

Singular measures without restrictive intervals

For the transformationT:[0,1][0,1] defined byT(x)=x(1–x) with 04, a is shown to exist for whichT has no restrictive intervals, hence is sensitive to initial conditions, but for which no finite absolutely continuous invariant measure exists forT.Supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University     

X-ray coherence and ultra small angle resolution at grazing incidence and exit angles

We measure the nonspecular x-ray scattering at grazing incidence and exit angles from a GaAs surface, modulated by an one-dimensional lateral grating of effectively variable periodicity 1 md60 m. Due to the projection onto the sample surface, the lateral coherence length is enlarged by a factor of more than 100. The line broadening of the diffraction maxima is used to deduce the number of periods that add up coherently for a given periodd and given angle of incidence. We demonstrate that the scattering geometry used allows for large coherently illuminated lengths on the sample and ultra small angle resolution of one- or two-dimensional objects. Thus structures of m size and larger will be accessible by coherent x-ray scattering.     

Convergent perturbation expansions for Euclidean quantum field theory

Mayer perturbation theory is designed to provide computable convergent expansions which permit calculation of Greens functions in Euclidean quantum field theory to arbitrary accuracy, including nonper-turbative contributions from large field fluctuations. Here we describe the expansions at the example of 3-dimensional ⁴-theory (in continuous space). They are not essentially more complicated than standard perturbation theory. Then ^th order term is expressed in terms ofO(n)-dimensional integrals, and is of order ^k if 4k–3n4k.Dedicated to the memory of Kurt Symanzik     

The electrical resistivity of the reentrant spin glass alloys (Fe0.65Ni0.35)1−x Mn x in the temperature range 4 to 280 K

The specific electrical resistivityp(T) was measured for the reentrant spin glass system (Fe_0.65Ni_0.35)_1–x Mn _x (0x0.102) in the temperature range 4 KT280 K. We used our own phenomenological ansatz to explain the results obtained in order to provide the fitted parameters with physical meaning. The cause of the observed minimum in the measured curves can be given by a model of local magnetism.