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.     

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.     

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.     

Phase diagrams of the semi-infiniteZ(q) models by real space renormalization-group method

We investigate the three-dimensional semi-infiniteZ(q) models using an infinitesimal Migdal-Kadanoff method. A rich variety of phase diagrams is obtained. The massless spin-wave phase which appears in the infinite two-dimensionalZ(q) models on the Clock line between the disordered and ferromagnetic phase forqq _c is also present in the semi-infinite system on the surface when the bulk is disordered. We also observe that if the bulk is in the phase to which the symmetry is engendered by a subgroupZ(p), such thatp, the surface of the system is in the same phase or in a less symmetrical phase to which the symmetry is engendered by a subgroupZ(m) ofZ(p) such thatp=m (mp) with an integer number satisfying 1p. The case =p corresponds to the least symmetrical phase. Since the infiniteZ(q) models exhibit a rich variety of phase transitions and multicritical points, the semi-infinite models present new ordinary, extraordinary, surface and special phase transitions which do not occur in the semi-infinite Ising-like systems. As theZ(q) model transforms into theX–Y model whenq, we have deduced the phase diagram of the semi-infiniteX–Y model. It is qualitatively similar to the phase diagram of the semi-infinite Ising model.     

Total dynamic structure factor of icosahedral and As-quenched and relaxed glassy Pd58.8Si20.6U20.6 measured at 296 K

The total dynamic structure factorsS(Q, ) of icosahedral, glassy Pd_58.8Si_20.6U_20.6, and the crystallized sample have been determined at room temperature using inelastic scattering of cold neutrons (IN6 of ILL). In contrast to the static structure factorS(Q), where the long range bond orientational order (BOO) leads to pronounced diffraction peaks with finite half width, the dynamic structure factor shows little or no influence of the long range BOO on the atomic dynamics of icosahedral PdSiU in the range of frequencies (0.525 meV) and momentum transfers Q(5Q30 nm^–1 for inelastic scattering) investigated here. The wavelength-dependence of the atomic dynamics of icosahedral PdSiU is very similar to that of the metallic glass and is different from that of the crystallized sample. As for glassy PdSiU no well defined vibrational collective excitations are found as peaks in the inelastic part ofS(Q, ) of the icosahedral sample,-quite in contrast to theoretical expectations and to the dispersions of pronounced excitations determined under identical experimental conditions fromS(Q, ) of the crystallized sample. On structural relaxation of the metallic glass Pd_58.8Si_20.6U_20.6 the largest amount of low energy modes is annealed out at lowest energy.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

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 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.     

The ground state energy of Sdhrödinger operators

We studye()=inf spec(-+V) and examine whene()<0 for all 0. We prove thatc ²e()–d ² for suitableV and all small ||.Research partially funded under NSF grant number DMS-9101716.     

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.     

Semimodularity and the logic of quantum mechanics

If (, ,P, ) is an event-state-operation structure, then the events form an orthomodular ortholattice (, , ) and the operations, mappings from the set of states into , form a Baer *-semigroup (S, , *, ). Additional axioms are adopted which yield the existence of a homomorphism from (S, , *, ) into the Baer *-semigroup (S(), , *, ) of residuated mappings of (, , ) such thatx S maps states while _x S () maps supports of states. If (, , ) is atomic and there exists a correspondence between atoms and pure states, then the existence of provides the result: (, , ) is semimodular if and only if every operationx S is a pure operation (maps pure states into pure states).Supported in part by the United States Atomic Energy Commission and in part by the Fonds National Suisse.     

Strong coupling in the quantum field theory with nonlocal nonpolynomial interaction

In the relativistic quantum field theory the representation for theS-matrix elements is obtained for any coupling constantsg in the case of a one component scalar field (x) with nonlocal nonpolynomial interaction _I ()=gU() when the causal function is bounded in the Euclidean region 0D _c (x _E ² D _c (0)< and the function |U(u)|1 for realu. It is proved that the two point Green function is bounded in the physical region of momenta variablep ².     

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.     

Sharp bounds on the number of scattering poles for perturbations of the Laplacian

Sharp bounds on the numberN(r) of the scattering poles in the disc |z|r for a large class of compactly supported perturbations (not necessarily selfadjoint) of the Laplacian in ⁿ ,n3, odd, are obtained. In particular, in the elliptic case the estimateN(r)Cr ⁿ+C is proved.Partially supported by Bulgarian Scientific Fondation under grant no. MM8/91     

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.     

Low temperature thermal properties and intrinsic defects in vitreous silica

Measurements of the low temperature specific heatC _p (0.04KT2.4K) and thermal conductivityk (0.5KT20K) of high purity vitreous silica (Suprasil W) in the as-received and electron-irradiated states are reported. In the temperature range where the localized excitations inherent in glasses dominateC _p (T0.5K) no change is observed upon electron irradiation of up to 10¹⁹e^– (total dose). An anomalyC around 1.8K is observed inC _p which is reduced by 40% upon irradiation. However, ask is not affected by electron irradiation, localized excitations as origin forC can be ruled out. The density of paramagnetic centers in the most heavily irradiated sample is 510¹⁷cm^–3 as obtained from the ESR signal. It has been suggested that these centers have diamagnetic precursors in the unirradiated glass. Our measurements indicate that those defects are not associated with the localized excitations.     

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.     

Oxygen content of superconducting Ba2YCu3O6.5+x

Single-phase non-stoichiometric Ba₂YCu₃O_6.5+x with –0.248x0.300 can be obtained by annealing prereacted samples at 0.01–1 bar oxygen partial pressure. Samples withx=–0.248 are semiconducting, samples at 0.239x0.300 are metallic withT _c increasing from 92.2 to 94.0 K for annealing in 0.02–1 bar O₂.     

Estimating the strength of chaos from the power spectrum

It is rigorously proved that for nonlinear dynamical systems whose time dependence is described by one dimensional, everywhere expanding maps, the width of broadband noise in the power spectrum is bounded by the generalized entropiesK ₂ andK ₃, which measure the strength of chaos in this system asK ₂2K ₃.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

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.     

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