High precision X-ray spectroscopy in hydrogen-like fermionic and bosonic atomic systems

Some time after its formation an exotic atom may be considered a hydrogen-like system consisting of a nucleus and an exotic particle in a bound state. In this situation it is an ideal tool to study cascade properties, while for the innermost orbits it can be used to probe the interaction with the nucleus. From an extended series of experiments using high resolution X-ray spectroscopy for both aspects typical examples are reported and preliminary results are given: 1. To determine the complex scattering length in H the hyperfine transitions have been measured. 2. To determine the pion mass the 5 4 transitions in N have been studied. In all cases a major contribution to the uncertainty originates from the calibration. Therefore a new method is proposed that will establish a universal set of high precision calibration lines for pionic, muonic and electronic systems. This revised version was published online in July 2006 with corrections to the Cover Date.     

Energy dependence of the charge exchange reaction from muonic hydrogen to oxygen

The charge exchange reaction of negative muons from the atom to oxygen has been measured in gaseous mixtures of H₂ + O₂. The measurements were performed at three different relative oxygen concentrations ranging from 0.2% to 0.8% and total pressures 3.5–15 bar. A mean transfer rate of , describing the transfer from the ground state of thermalized atoms to oxygen, was determined. In order to investigate the energy dependence of the transfer rate, Monte Carlo simulations of the thermalization and the muon transfer were carried out. The comparison of measured and simulated time spectra yielded an epithermal transfer rate =3.9 10¹¹ s^-1 in the energy interval 0.12–0.22 eV. The analysis with the model of Two components shows that all measured time spectra can be reproduced with the same set of parameters.     

On Continuous and Differential Hochschild Cohomology

We show that there are canonical isomorphisms between Hochschild cohomology spaces , where is the algebra of smooth functions on a manifold M and the space of skew multivector fields over M. This implies that continuous and differential deformation theories of coincide.     

Bicross-Product Structure of Affine Quantum Groups

We show that the affine quantum group is isomorphic to a bicross-product central extension of the quantum loop group by a quantum cocycle in R-matrix form.     

Relaxation effects in the Mössbauer spectra of iron complexes with fatty acids

Six new oxo trinuclear iron(III) complexes of the type [Fe₃O(R–COO)₆(H₂O)₃] X, where X= or Cl^– and R=C₅, C₇, C₈, C₉ were synthesized and investigated by Infra Red, Mössbauer Spectroscopy and magnetic measurements. The data pointed to a high spin state (S=5/2) for iron and for antiferromagnetic interactions. The asymmetrical shape of the Mössbauer doublet and its temperature dependence was treated using the Blume relaxation model. The relaxation process is influenced by both X and R components.     

NMRON studies of MnBr2 \cdot 4H2O in applied magnetic fields

NMRON studies for the ⁵⁴Mn transitions in antiferromagnetic MnBr₂ 4H₂O, in the millikelvin regime, are presented and discussed. New values are given for (i) the sum of the effective molecular exchange and magnetic anisotropy fields acting on the Mn²⁺ ions, =2.23(2) T, and (ii) the magnetic dipole hyperfine splitting, A=-201.99(1) MHz, electric quadrupole hyperfine splitting P=0.049(8) MHz and pseudoquadrupole splitting =1.63(2) MHz for the ⁵⁴Mn nuclei.     

Nuclear moments of neutron deficient iridium isotopes from laser spectroscopy

Laser spectroscopy measurements have been performed on neutron deficient iridium isotopes. The hyperfine structure and isotope shift of the optical Ir I transition 5d⁷6s^{2 4}F_9/2 → 5d⁷6s6p ⁶F_11/2 at 351.5 nm have been studied for the ^182–189Ir, and ^191,193Ir isotopes. The nuclear magnetic and quadrupole moments were obtained from the HFS measurements and the changes of the mean square charge radii from the IS measurements. A large mean square charge radius change between ¹⁸⁷Ir and ¹⁸⁶Ir and between and has been observed. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the Product of Real Spectral Triples

The product of two real spectral triples and , the first of which is necessarily even, was defined by A.Connes as given by and, in the even-even case, by . Generically it is assumed that the real structure obeys the relations , , , where the -sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes' >-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this -sign table. In this Letter, we propose an alternative definition of the product real structure such that the -sign table is also satisfied by the product.     

The COMPLIS experiment on neutron deficient Au, Pt and Ir isotopes

The COMPLIS (COllaboration for spectroscopic Measurements using a Pulsed Laser Ion Source) experiment is carried out at the ISOLDE Booster facility at CERN. The aim is to measure the hyperfine structure and the isotope shift of a series of radioactive laser desorbed atoms by multiple step laser ionization. This technique is especially suitable for refractory elements not directly available as beams from the isotope separator. By collecting a primary radioactive beam, it is possible to delay the laser desorption as long as necessary to obtain the particular daughter of interest. Laser spectroscopy measurements have been carried out on very neutron deficient gold, platinum and iridium isotopes. Magnetic moments μ_I, spectroscopic quadrupole moments and changes of the nuclear mean square charge radius along each isotopes series have been extracted. From some results, a detailed comparison with the predictions of the models is presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Low Temperature Hydrogen Antihydrogen Interactions

In view of current interest in the trapping of antihydrogen ( ) atoms at low temperatures [1–3], we have carried out a full four-body variational calculation to determine s-wave elastic phase shifts for hydrogen antihydrogen scattering, using the Kohn Variational Principle. Terms outside the Born–Oppenheimer approximation have been taken into account using the formalism of Kołos and Wolniewicz [4]. As far as we are aware, this is the first time that these terms have been included in an H scattering calculation. This is a continuation of earlier work on H– interactions [5–7]. Preliminary results differ substantially from those calculated using the Born–Oppenheimer approximation [8–10]. A method is outlined for reducing this discrepancy and taking the rearrangement channel into account. This revised version was published online in August 2006 with corrections to the Cover Date.     

Laser spectroscopy of the antiprotonic helium atom–molecule {\bar pHe}^+

The metastable antiprotonic helium atom–molecule (in short, atomcule), , which was discovered in 1991 as being the cause of the anomalous longevity of antiprotons with an overall lifetime of about 3 μs, now provides an exotic playground for laser spectroscopy, helped by the existence of numerous long lived states with 1–2 μs lifetimes. This three body system is characterized by a large angular momentum l ∼ 38 of coupled with the electron in the 1s ground orbital, and looks like an exotic hydrogen isotope with many different “nuclear states” as well as an exotic molecule with two centers (He²⁺ and ). So far, a number of laser resonance transitions have been identified. The present talk will cover the following topics: (1) high precision spectroscopy in comparison with three body theories involving the relativistic effect and QED, and (2) hyperfine structure of ;laser-microwave triple resonance. This revised version was published online in August 2006 with corrections to the Cover Date.     

Long-Time Asymptotics of Solutions to the Cauchy Problem for the Defocusing Nonlinear Schrödinger Equation with Finite-Density Initial Data. II. Dark Solitons on Continua

For Lax-pair isospectral deformations whose associated spectrum, for given initial data, consists of the disjoint union of a finitely denumerable discrete spectrum (solitons) and a continuous spectrum (continuum), the matrix Riemann–Hilbert problem approach is used to derive the leading-order asymptotics as of solutions to the Cauchy problem for the defocusing nonlinear Schrödinger equation ( NLSE), , with finite-density initial data

Multipoint Series of Gromov–Witten Invariants of CP1

We derive explicit formulas for the multipoint series of in degree 0 from the Toda hierarchy, using the recursions of the Toda hierarchy. The Toda equation then yields inductive formulas for the higher degree multipoint series of . We also obtain explicit formulas for the Hodge integrals , in the cases i=0 and 1.     

Lamb shift calculations for high-Z lithium like ions

We present ab initio calculations of the complete gauge invariant set of the self energy and vacuum polarization screening diagrams for the 2p transition in Li like ions. Various contributions to the transition energy are collected. The accuracy of theoretical predictions is discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Glueball Spectroscopy in Regge Phenomenology

We show that linear Regge trajectories for mesons and glueballs, and the cubic mass spectrum associated with them, determine a relation between the masses of the meson and the scalar glueball, , which implies MeV. We also discuss relations between the masses of the scalar, tensor and 3^-- glueballs, , which imply MeV.     

Observables and Statistical Maps

This article begins with a review of the framework of fuzzy probability theory. The basic structure is given by the -effect algebra of effects (fuzzy events) and the set of probability measures on a measurable space . An observable is defined, where is the value space of X. It is noted that there exists a one-to-one correspondence between states on and elements of and between observables and -morphisms from to . Various combinations of observables are discussed. These include compositions, products, direct products, and mixtures. Fuzzy stochastic processes are introduced and an application to quantum dynamics is considered. Quantum effects are characterized from among a more general class of effects. An alternative definition of a statistical map is given and it is shown that any statistical map has a unique extension to a statistical operator. Finally, various combinations of statistical maps are discussed and their relationships to the corresponding combinations of observables are derived.     

Temperature and density dependence of μ-catalysis cycling rate in dense D/T and H/D/T gas mixtures

Muon catalyzed dt fusion in dense D/T and H/D/T gas mixtures of hydrogen isotopes is studied by the MCF collaboration at JINR. The measurements were carried out with a high pressure target at the JINR phasotron in the temperature range 300-800 K at mixture densities . Tentative experimental results obtained by several analysis methods are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Zero Energy Modes of Massless Fermions in S3R Spacetime

The Dirac-type equation on topology is worked out and the complete set of solutions in the particular physical case of the zero-energy modes of the massless field quanta is derived. Unlike the Minkowskian case, the 1/2fermionic vacua on the manifold is made of nontrivial static modes of defined chirality.     

NMR dynamics in disordered magnets

The excitation dynamics of site diluted magnets can be described at low energies (long length scales) by magnons, and above a crossover frequency, ω_c, (short length scales) by fractons. The density of fracton states is given by , where is the fracton dimensionality. Dilution gives rise to a characteristic length ξ∝(p−p _c)^ν, wherep _c is the critical concentration for (magnetic) percolation. The crossover frequency ω_c is proportional to ξ^-1[1+(θ/2)], where θ is the rate at which the diffusion constant decays with distance for diffusion on an equivalent network. A fractal dimensionD describes the density of magnetic sites on the infinite network, and . For percolating networks, for all dimensions ≥2. Neutron scattering structure factor measurements by Uemura and Birgeneau compare well with calculations using fracton concepts. Magnons are extended at low energies, while the fracton states are geometrically localized, with a wave function envelope proportional to exp . Here, is the fracton length scale at frequency ω. The exponentd _ϕ lies between 1 andd _min, the chemical length index (of the order of 1.6 in three dimensions). The localization of the magnetic excitations causes a spread in the NMR relaxation rates. A given nuclear moment will experience only a limited set of fracton excitations, resulting in an overall non-exponential decay of the NMR relaxation signal. When strong cross-relaxation is present, the relaxation will be exponential, but the temperature dependence will be strongly altered from the concentrated result.