Hard gamma radiation in the decay of Lu176m

Gamma lines 1·05 MeV(4 × 10^–6 quanta/decay) and 1·14 MeV (9 × 10^–6 quanta/decay), giving evidence of the existence of a new level in Hf¹⁷⁶ with an energy of 1·14 MeV, were found in the decay of Lu^176m with a half-life of 3·7 hours, using the scintillation method. The component of the beta spectrum, exciting this level, has a maximum energy of 0·17 MeV and logft=8·3. The spin of this level proved to be equal to one. The level was interpreted as a single-particle neutron level withn ₀: 5/2^– (512),n ₁: 7/2^– (514);I=1⁺.

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- Lu^176m

Lu^176m 3,7 - 1,05 MeV (4.10^–6 /) 1,14 MeV (9.10^–6 / /), Hf¹⁷⁶ 1,14 MeV. -, , 0,17 MeV logft = =8,3. . cn ₀: 5/2^– (512),n ₁: 7/2^– (514);I = 1⁺h

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The authors thank L. K. Peker from the Leningrad State University for a helpful discussion of their results.     

Instanton Expansion of Noncommutative Gauge Theory in Two Dimensions

We show that noncommutative gauge theory in two dimensions is an exactly solvable model. A cohomological formulation of gauge theory defined on the noncommutative torus is used to show that its quantum partition function can be written as a sum over contributions from classical solutions. We derive an explicit formula for the partition function of Yang-Mills theory defined on a projective module for an arbitrary noncommutativity parameter which is manifestly invariant under gauge Morita equivalence. The energy observables are shown to be smooth functions of . The construction of noncommutative instanton contributions to the path integral is described in some detail. In general, there are infinitely many gauge inequivalent contributions of fixed topological charge, along with a finite number of quantum fluctuations about each instanton. The associated moduli spaces are combinations of symmetric products of an ordinary two-torus whose orbifold singularities are not resolved by noncommutativity. In particular, the weak coupling limit of the gauge theory is independent of and computes the symplectic volume of the moduli space of constant curvature connections on the noncommutative torus.     

One-dimensional harmonic lattice caricature of hydrodynamics

We derive the hydrodynamic (Euler) approximation for the harmonic time evolution of infinite classical oscillator system on one-dimensional lattice ¹ It is known that equilibrium (i.e., time-invariant attractive) states for this model are translationally invariant Gaussian ones, with the mean 0, which satisfy some linear relations involving the interaction quadratic form. The natural parameter characterizing equilibrium states is the spectral density matrix function (SDMF)F(), [– , ). Time evolution of a space profile of local equilibrium parameters is described by a space-time SDMFF(t;x, ) t, xR ¹. The hydrodynamic equation forF(t; x, ) which we derive in this paper means that the normal mode profiles indexed by are moving according to linear laws and are mutually independent. The procedure of deriving the hydrodynamic equation is the following: We fix an initial SDMF profileF(x, ) and a familyP ,>0 of mean 0 states which satisfy the two conditions imposed on the covariance of spins at various lattice points: (a) the covariance at points close to the value ^–1 x in the stateP is approximately described by the SDMFF(x, ); (b) The covariance (on large distances) decreases with distance quickly enough and uniformly in. Given nonzerotR ¹, we consider the states P _–1 ,>0, describing the system at the time moments ^–1 t during its harmonic time evolution. We check that the covariance at lattice points close to ^–1 x in the state P _–1 is approximately described by a SDMFF(t;x, ) and establish the connection betweenF(t; x, ) andF(x,).     

Further consequences of Einstein locality

The results of a previous paper for the properties of the correlation functionP() at small angles following from Einstein locality are extended to the general case whereP(0)–1. Experimental investigations are suggested to check the validity of some theorems on the behavior of the correlation functionP() which are deduced directly from Einstein locality.     

Nuclear physics with ion traps at ISOLDE: present and future

Nuclear physics experiments with ion traps started at the on-line separator ISOLDE/CERN, Geneva, with the installation of the tandem Penning trap mass spectrometer ISOLTRAP. With this device the massM of a stored ion is determined by measuring its cyclotron frequency _c=(q/M)B in a magnetic fieldB. Mass measurements with a resolving powerR=_c/_c(FWHM)1×10⁶ and accuracies of M/M10^–7 were performed on more than sixty unstable isotopes of the elements Rb, Sr, Cs, Ba, Fr, and Ra.     

Kinetics of random sequential parking on a line

We study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line. For the simplest fixed-length parking distribution the model reduces to the known car-parking problem and we present an alternate solution to this problem. We also consider the general homogeneous case when the parking distribution varies asx ^–1 atx 1 with the lengthx of the filling interval. We develop a scaling theory describing such mixture-deposition processes and show that the scaled hole-size distribution(), with =xt ^z a scaling variable, decays with the scaled mass as ^–exp(—const·¹⁺) as . We determine scaling exponentsz and, and find that at large times the coverage(t) has a power-law form 1 – (t)t ^–v with nonuniversal exponent =(2–)/(1+) depending on the homogeneity index .     

The Landau Problem on the θ-Deformed Two-Torus

We study the Landau problem on the -deformed two-torus and use well-known projective modules to obtain perturbed energy spectra. For a strong magnetic field B, the problem can be restricted to one particular Landau level. First we represent generators of the algebra of the noncommutative torus T ² as finite-dimensional matrices. A second approach leads to a reducible representation with a -dependent center. For a simple periodic potential, the rational part of the Hofstadter butterfly spectrum is obtained.     

The inverse backscattering problem in three dimensions

This article is a study of the mapping from a potentialq(x) onR ³ to the backscattering amplitude associated with the Hamiltonian –+q(x). The backscattering amplitude is the restriction of the scattering amplitudea(, , k), (, , k)S ²×S ²×₊, toa(,–, k). We show that in suitable (complex) Banach spaces the map fromq(x) toa(x/|x|, –x/|x|, |x|) is usually a local diffeomorphism. Hence in contrast to the overdetermined problem of recoveringq from the full scattering amplitude the inverse backscattering problem is well posed.     

Matrix field theory for disordered local pairing superconductors with two glass order parameters and spin-flip pairbreaking processes

We derive the exact matrix field theory for a replicated grassmannian representation of a local pairing superconducting disorder ensemble including three superconducting order parameters and the spin-flip pairbreaking mechanism. Disorder is assumed to be gaussian distributed. We find by exactly solving the saddle-point equation the criterion for a vanishing gap ^–1 + ^–1 , where denotes the averaged superconducting order parameter, ^–1 the spin-flip scattering rate, and ^–1 the scattering rate corresponding to correlations of Re(–). Taken at =0, our field theory, which is exact in all orders of ^–1 , contains new terms in addition to those of theO( ^–1 ) model derived by Efetov et al. Our formulation transfers correctly to all orders the invariances of the action into symmetries of the matrix field theory. The saddle point approximation is outlined and it is shown how singular corrections to the saddle point density of states arise atE _F in a gapless superconductor. Finally singular corrections in the two particle propagator, the density correlation function and the conductivity are calculated for =0 in one loop order. It turns out that these corrections can be entirely expressed by those of the single particle density of states.     

Modal interference of X-intersecting waveguide switches at large branching angles

The X-intersecting waveguide switch with large branching angles (=2–12°) is analysed using coupled mode theory. The results strongly highlight the importance of modal interference and are in good agreement with measured data.     

A Far IR Study of NbN in the Normal and Superconductive State

A thin film of NbN (thickness t = 300 Å), has been deposited on an MgO and a Si wafer. Both samples have been studied by transmission from 10 or 20 to 120 cm^–1, and have exhibited one maximum of transmission at a given frequency like the classical superconductors as Pb, Sn or Hg in the superconductive state. From the Far IR experimental data, the characteristic temperature _c, and the gap frequency (_gap () = 2 (), () being the energy gap) are immediately obtained (for instance for the NbN / MgO sample, _c = 15.5 K; _g (5 K) = 39.7 cm^–1), and it is seen that as expected from the BCS theory for a weak coupling. To fit the data we had to adjust only two additionnal parameters: collision and plasma frequency, _c () and _p (including all carriers). At = 5 K, thebest fit for the NbN / MgO sample is obtained with _c = 371 cm^–1 and _p = 12,600cm^–1.     

Dynamic recovery,strain hardening and flow stress in hot working of 316 steel

The strain hardening rate was determined as a function of flow stress in torsion tests over the range 900–1200 °C, 0·1–5·0s^–1 in both as-cast and worked 316 stainless steel. Changes in slope of the- curves and extrapolation to the=0 axis permitted determination of the saturation stress _s ^* , and the critical strain for recrystallization which could be compared with the peak in the flow curve. Analysis of the dependence on temperature and strain rate showed that the data could be fitted either to the Kocks-Mecking equations or to the sinh and Arrhenius functions. The flow stresses and the empirical constants in the above equations are compared with those of 304 and 317 steels which contain less and more Mo, respectively.Presented at the 4th International Symposium on Plasticity of Metals and Alloys, Srní, Czechoslovakia, September 7–11, 1987.     

Effect of rotation of the universe on the relative position angle of radiosources

The effect of the space-time curvature on the relative position angle between the vector of radio waves and the direction of maximum elongation of an extended radiosource is studied during propagation of radiation from the source to the observer. A detailed analysis is carried out for the Gödel type cosmological model. It is found that the rotation of the Universe cannot induce a Birch-type anisotropy with proportional to cos , where is the angle between the direction of the ray and the rotational axis. An anisotropy with proportional to sin² should be expected. In the case of a Gödel-type model, we have calculated the change in the eccentricity of the ellipse of the source image relative to the eccentricity of the real object.M. Gorky State University, Perm' Branch of Theoretical Problems, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 3–8, June, 1992.     

Non-commutative spheres

LetA be the irrational rotation algebra, i.e. theC ^*-algebra generated by two unitariesU, V satisfyingVU=e ²ⁱ UV, with irrational, and consider the fixed point subalgebraB under the flip automorphismUU ^–1,VV ^–1. We prove thatB is an AF-algebra.Dedicated to Professor Huzihiro Araki on the occasion of his 60'th birthday     

Zeta functions and transfer operators for piecewise monotone transformations

Given a piecewise monotone transformationT of the interval and a piecewise continuous complex weight functiong of bounded variation, we prove that the Ruelle zeta function (z) of (T, g) extends meromorphically to {z<^-1} (where =lim g^°T^n-1...g^°Tg ^1/n ) and thatz is a pole of if and only ifz ^–1 is an eigenvalue of the corresponding transfer operator L. We do not assume that L leaves a reference measure invariant.Research partially supported by the Fonds National Suisse     

A non-commutative version of the Arnold cat map

We provide a treatment of the ergodic properties of a noncommutative algebraic analogue of the dynamical system known as the Arnold cat map of the two-dimensional torus. Here, the algebra of functions on the torus is replaced by its noncommutative analogue, formulated by Connes and Rieffel, which arises in the quantum Hall effect. Our main results are that (a) the system is mixing and, as in the classical case, the unitary operator, representing its dynamical map, has countable Lebesgue spectrum; (b) for rational values of the noncommutativity parameter, , the model is a K-system, in the algebraic sense of Emch, Narnhofer, and Thirring, though not in the entropic sense of Narnhofer and Thirring; (c) for irrational values of , except possibly for a set of zero Lebesgue measures, it is neither an algebraic nor an entropic K-system.Supported in part by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. P7101-PHY.     

Dynamic scaling for spin glasses near the de Almeida-Thouless line

We calculate the dynamic local susceptibility () of an Ising spin glass near the de Almeida-Thouless (AT) line within the soft spin dynamics for the Sherrington-Kirkpatrick model. We find a crossover from analytic behaviour of () at =0 above the AT line to a power law behaviour ()(–i) ^v on the AT line and discuss the analytic properties of the crossover function. The frequencyscale is proportional to ^1/v , where measures the distance from the AT line. We determine the spectrum of relaxation times which diverge as ^1–1/v . The average relaxation time diverges as ^–1/v wherev1/2. In addition we determine the absolute frequency scale and prove the consistency of the ansatz of Sompolinsky and Zippelius ()–(0)(–i) ^v at and below the AT line.     

Analyticity of the d-Dimensional Bond Percolation Probability Around p=1

Let (p) be the percolation probability of a d-dimensional bond percolation process on Z ^d . We prove that 1–(p) can be written as an absolutely convergent series in powers of (1–p)/p, provided that |(1–p)/p| is sufficiently small. This implies that (p) is an analytic function of the complex variable p, around p=1.