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.     

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 .     

Entropy of Bogoliubov automorphisms of the canonical anticommutation relations

We compute the entropyh _A ( _U ) in the sense of Connes, Narnhofer and Thirring of Bogoliubov automorphisms _U of the CAR-algebra with respect to invariant quasifree states _A with 0A1 having pure point spectrum.Supported in part by a grant from the National Science Foundation     

On the magnetic susceptibility of Pd1−x Ag x in the range 0.5≦x≦1

The weak variation of the magnetic bulk susceptibility of Pd_1–x Ag _x with temperature T and silver mole fractionx within 0.5x1 has been investigated in the range 5KT400K. Experimental evidence can be given for an intersection point of the susceptibility isotherms (T=const,x) atx=0.55. The observed dependence of on T andx is interpreted by means of a semiphenomenological alloy susceptibility function (T,x).     

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.     

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.     

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.     

Far-infrared spectroscopy of the supreconductor YBa2Cu4O8

The frequencies of allB _1u (z) phonon modes predicted by a group-theoretical analysis were measured and found to agree well with recent lattice dynamical calculations for this compound. We report also the determination of two superconducting gap values in YBa₂Cu₄O₈ through phonon self-energy effects in the normal and superconducting conducting state. The gap-to-T _c ratios obtained from an analysis of these effects are 2 ₁/kT _c 2.5 and 5.82 ₂/kT _c 9.2. This coincides with previous results of both phononic and electronic Raman scattering where values of 2.1 and 6.3 were found. We further find anomalous softenings of two phonon modes 40 Kabove T _c , which correlate with an observed deviation from the linear temperature dependence of the average plasma frequency _p (T).     

Ozone production in oxygen by means of F2-laser irradiation at λ=157.6 nm

Ozone is generated in pure oxygen (p5 kPa), synthetic air (p7 kPa) and oxygen-argon mixtures (p3 kPa) by irradiation of these gases with the VUV light of a repetitively pulsed (f _L15 Hz) F₂-laser at =157.6 nm with maximum about 4 mJ/pulse. An absorption photometer measurement operating at 253.7 nm (Hg line) determines the ozone concentration as a function of oxygen and/or additive gas pressure, the repetition frequency of the laser and the wall temperature of the reaction chamber. The temporal development of the ozone concentration as a function of these parameters is calculated by means of rate equations for the species O(³ P), O₂(X ³ _g ^– ), O₃(¹ A ₁), O(¹ D), O₂(a ¹_g), O₂(b ¹ _g ⁺ ) and vibrationally excited O ₃ ^* (¹ A ₁) and the photon distribution. The maximum concentration of O₃ in the sealed-off chamber reaches 1.6% in pure O₂, 4.1% in air and 1.2% in a 1:5 O₂-Ar mixture at 3 kPa. The annihilation of O₃ by the wall and temperature dependent volume processes (300 KT395 K) is studied and the experimental and theoretical results are compared.     

Bounds in the Yukawa2 quantum field theory: Upper bound on the pressure,Hamiltonian bound and linear lower bound

We prove bounds of the formZ e ^a|| and (SZ)e ^a|| in theY ₂ Euclidean field theory and from this obtain Glimm's Hamiltonian bound and Schrader's linear lower bound.This work partially supported by USNSF grants GP-40768X and GP-39048.On leave from Max-Planck-Institut für Physik und Astrophysik, München, Federal Republic of Germany.A. Sloan Foundation Fellow.     

The spectrum of a Schrödinger operator inL p ℝ v isp-independent

LetH _p =–1/2+V denote a Schrödinger operator, acting inL _p ^v , 1p. We show that (H _p )=(H ₂) for allp[1, ], for rather general potentialsV.     

Critical currents of type ii superconductors in non-transversal magnetic fields

The force on flux lines near narrow defects elongated in the direction of the transport current is calculated. This force, together with the maximum interaction forcek _m on the central flux line element, gives the volume pinning forceF _p on the flux line lattice. The dependence ofk _m (and of the critical current densityj _c ) on the angle between the magnetic field and the transport current is calculated for different defect dimensions (with respect to the coherence length of the superconductor) and compared with the experimental results. We obtainj _c sin^–n , where 1n3 in dependence on the defect dimensions and on the angle interval. The possibility of testing theF _p k _m ² dependence of the statistical theory of pinning is proposed.     

Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2

LetH _l be the Hamiltonian in aP()₂ theory with sharp space cutoff in the interval (–l/2,l/2). LetE _l =inf(H _l ), (l)=–E _l /l, and let _l be the vacuum forH _l . discuss properties of (l) and _l . In particular, asl, there are finite constants <0 and such that (l), ((l)–)l, and hence (l)=+/l+o(l ^–1). Moreover exp(–c ₁ l) _{l 1}exp(–c ₂ l) forc ₁,c ₂ positive constants, where _{l 1} is theL ¹(Q, d₀) norm of ₁ with respect to the Fock vacuum measure. We also present a new proof of recent estimates of Glimm and Jaffe on local perturbations ofH _l in the infinite volume limit.Research sponsored by AFOSR under Contract No. F44620-71-C-0108.On leave from Istituto di Fisica Teorica, Universitá di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli.A. Sloan Foundation Fellow.     

Gentle perturbations

By introducing a specific type of perturbation,A, in the Hamiltonian, we define a class of gently perturbed states, ,A, of a canonical ensemble, . The perturbations are chosen so as to preserve a relationship of the form ,A constant ×. Applications in ergodic theory and phase transitions are described.     

The surfboard Schrödinger equations

We study the large time behavior of solutions of time dependent Schrödinger equationsiu/t=–(1/2)u+t V(x/t)u with bounded potentialV(x). We show that (1) if>–1, all solutions are asymptotically free ast, (2) if–1 a solution becomes asymptotically free if and only if it has the momentum support outside of suppV for large time, (3) if –1 <0 all solutions are still asymptotically modified free ast and that (4) if 0 <2, for each local minimumx ₀ ofV(x), there exist solutions which are asymptotically Gaussians centered atx=tx ₀ and spreading slowly ast.     

An unambiguous procedure for discovering relaxation influence on Mössbauer spectra

A mathematical procedure which gives an opportunity to distinguish between relaxation and distribution mechanisms of the Mössbauer line broadening is proposed. It is based on the method of Mössbauer line sharpening developed recently [1] and allows one to answer unambiguously the question whether or not relaxation manifests itself in Mössbauer measurements by examining the wings of the spectrum. The procedure is applied to the spectra of high spin ferric metmyoglobin and (Fe_0.65Ni_0.35)_1–x Mn _x alloys. Analysis of the metmyoglobin spectra manifests the presence of the relaxation influence in the temperature range 10 KT100 K. Analysis of the alloy spectra shows that for the temperatures 4 KT300 K and Mn concentrations 0x0.245 no relaxation is observed and the line broadening is mainly caused by the distributions of magnetic hyperfine fields. A possible explanation of this result is given.     

Realizability of a model in infinite statistics

Following Greenberg and others, we study a space with a collection of operatorsa(k) satisfying the q-mutator relationsa(l)a (k)a(l)= _k,l (corresponding forq=±1 to classical Bose and Fermi statistics). We show that then!×n! matrixA _n (q) representing the scalar products ofn-particle states is positive definite for alln ifq lies between –1 and +1, so that the commutator relations have a Hilbert space representation in this case (this has also been proved by Fivel and by Bozejko and Speicher). We also give an explicit factorization ofA _n (q) as a product of matrices of the form(1–q ^jT)^±1 with 1jn andT a permutation matrix. In particular,A _n (q) is singular if and only ifq ^M=1 for some integerM of the formk ²–k, 2kn.     

Energy dependence of the fast fragment of the target nucleus in high energy hadron-nucleus interaction

This paper presents an extensive study on the dependence of the mean number of the fast fragment of the target nucleus n _g on the incident beam energy in proton-nucleus interaction in emulsion in the range 6·2E ₀400 GeV/c. It has been observed that n _g decreases in the range 6·2E ₀200 GeV/c, then increases and attains an approximately steady value up to 400 GeV/c. It is very difficult to explain this behaviour with the help of the existing nuclear production models.The author would like to thank Prof A. J. Herz (CERN), Prof. K. D. Tolostov (Dubna, U.S.S.R.), Prof. P. L. Jain (State University of New York, U.S.A.), Prof. G. Giacomelly (Italy) for kindly supplying the exposed emulsion plates.     

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.     

Casimir operators for infinite-dimensional representations ofosp(1,2) andosp(1, 4) lie superalgebras

All independent Casimir operatorsK _2j , 1 j n, are considered for the Schurean -dimensional representations ofosp(1, 2n),n= 1,2, that were constructed recently. For these representations (which are expressed in terms of tensor products of linear differential operators andN byN matrices belonging to a finite set and depending on a real parameter) a method is presented by which the differential-operator part of operators K_2j is effectively eliminated and expressions for K_2j via matrices in are obtained. In the same way we treat the Casimir operators _2j of the even subalgebra sp(2n, ) osp(1, 2n). The eigenvalues of K_2j and _2j are evaluated as functions of the parameter for the representations of osp(1, 2) withN= 2 and ofosp(1, 4) withN = 2, 4.