High resolution X ray spectroscopy in light antiprotonic atoms

At the LEAR facility, CERN, antiprotonic Lα transitions in light elements have been investigated with a focussing crystal spectrometer. The high resolution of the experiment allowed for the first time to resolve in H the 2³P₀ state from the close lying states 2³P₂, 2¹P₁, and 2³P₁. In D the corresponding transitions were found to be more than an order of magnitude broader. To a large extent the results for H support the meson exchange model. This revised version was published online in August 2006 with corrections to the Cover Date.     

The nature of the {\bar p} metastability in helium

A new interpretation of the nature of the metastable states of antiprotons in helium is proposed. The first step is the formation of an ion ( ), which shall be called “ioncule”. After its decay a neutral “atomcule” ( ) is formed which was observed in the experiments on metastable antiprotonic helium. This model explains the experiments in a natural way, in particular the quenching by atomic and molecular admixtures and the pressure dependence of quenching in pure helium. At high helium densities the ioncule creates a vacuum bubble in helium. It is shown that the annihilation of slowed-down can be suppressed at helium pressures of ∼ 10 000 bar. This revised version was published online in August 2006 with corrections to the Cover Date.     

Theoretical analysis of collisional shift and broadening of antiprotonic helium spectral lines

Effect of medium density on shift and broadening of ( ) spectral lines is considered in the framework of binary-collision approximation with an effective ( )–He potential including the long-range attraction and short-range repulsion. Quantum calculations of the scattering phase shifts at reasonable values of the potential parameters allow to explain the main features of the observed density effect on the shape of ( ) spectral lines in low-temperature helium. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Preferred Invariant Symplectic Connections on Compact Coadjoint Orbits

Let be the Haag--Kastler net generated by the (2) chiral current algebra at level 1. We classify the SL(2, )-covariant subsystems by showing that they are all fixed points nets ^H for some subgroup H of the gauge automorphisms group SO(3) of . Then, using the fact that the net ₁ generated by the (1) chiral current can be regarded as a subsystem of , we classify the subsystems of ₁. In this case, there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge invariant subsystem .     

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.     

Calculation of quadrupole interactions in the high pressure phase of \beta {\text{ - }} gallium metal

Electric field gradient q and quadrupole interaction frequency calculated at 256.7 K in the high pressure phase (orthorhombic) of Ga metal are reported. The results are: q=+0.251 atomic units (au), =5.479 MHz. These are compared with results from experiment and previous calculation available for the monoclinic phase of Ga metal at normal pressure. The results from the previous calculation at 248 K are: q=-0.250 au and =5.318 MHz. The result from experiment extrapolated to 256.7 K is: =4.871 MHz. The sign reversal of the calculated q is attributed mainly to the change of point symmetry of the lattice from the orthorhombic to monoclinic. That the interaction frequency in high pressure phase is higher than experiment may be partly due to the increase of pressure and partly to the structural phase change.     

The Fe2+ quadrupole splitting at octahedral sites in chain silicates: Correlations with the site‐distortion parameters

Correlations between the quadrupole splitting of Fe²⁺ ions and the distortion of their octahedral coordination in chain silicates is presented. The distortions are quantified by the variance of the angles and by the mean quadratic elongation. It is found that initially increases very steeply with increasing distortion parameters, and subsequently shows a moderate lowering. The observed correlations are discussed in terms of the crystalfield model.     

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.     

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.     

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.     

Integrals of Vertex Operators and uantum Shuffles

Given a braided vector space , we show that iterated integrals of operator-valued functions satisfying a certain exchange relation give rise to representations of the quantum shuffle algebra built on . Using the quantum shuffle construction of the 'upper triangular part' of a quantum shuffle, this provides a simple proof of the result of Bouwknegt, MacCarthy and Pilch saying that integrals of vertex operators acting on certain Fock modules give rise to representations of .     

High-precision laser spectroscopy of antiprotonic helium atomcules and effects of collisions at high-density conditions

We have performed laser spectroscpy of metastable antiprotonic helium atoms (or “atomcules”) ( He⁺) and have observed a density dependence of the resonance vacuum wavelengths for the known transitions (n,l)=(39,35)→(38,34) and (37,34)→(36,33). They showed linear red-shifts of 0.61±0.01 GHz and 0.22±0.02 GHz per 1 g℞, respectively. With the shift parameters above, the transition vacuum wavelengths were extrapolated to zero-density limits, yielding λ₀ = 597.2570± 0.0003 nm and λ₀ = 470.7220±0.0006 nm, respectively. These values were compared with the result of recent theoretical calculations on the energy of the Coulombic three-body system, including relativistic corrections and the Lamb shift. The agreements between our experimental values and the calculations have become as good as 2×10^-6. This sets a severe constraint on the antiproton charge ( ) and mass ( ) with |Q _p - |/e < 5 × 10^-7 and |M _p - |/M _p < 5 × 10^-7, under a more precisely known constraint on the charge-to-mass ratio. Thus we have opened a new possibility of measuring fundamental constants of the antiproton. This revised version was published online in August 2006 with corrections to the Cover Date.     

Exactly Solvable su(N) Mixed Spin Ladders

It is shown that solvable mixed spin ladder models can be constructed from su(N) permutators. Heisenberg rung interactions appear as chemical potential terms in the Bethe Ansatz solution. Explicit examples given are a mixed spin- spin-1 ladder, a mixed spin- spin- ladder and a spin-1 ladder with biquadratic interactions.     

New comprehensive calculation of muon initial sticking to 4He in dtμ fusion

The initial αμ sticking probability, , is revisited by a new sophisticated calculation which does not assume the three approximations taken usually in the literature calculations. It is found that magnitude of increases very slightly by the removal of the approximations. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Mössbauer studies of baotite and bafertisite

The Mössbauer effect was used to study silicate minerals of baotite and bafertisite at 298 K and 95 K. Each spectrum of baotite at 298 K and 95 K consists of two doublets, and they are contributed from Fe²⁺ and Fe³⁺ in the octahedral Tisites, respectively. Each spectrum of bafertisite at 298 K and 95 K is composed of two doublets, and they are mainly caused by Fe²⁺ in the octahedral Fe(I) and Fe(II)sites, respectively. The average effective ionic radii of the Ti sites in baotite and the Fe(I) and Fe(II)sites in bafertisite were estimated based on the correlation of the isomer shifts with the average effective ionic radii in silicates, and they are 0.56 , 0.73 and 0.73 , respectively.     

How to Describe the Space-Time Structure with Nets of C*-Algebras

The major subject of algebraic quantum fieldtheory is the study of nets of local C*-algebras, i.e.,maps ( ) assigning to each open,relatively compact region of space-time (M, g) aC*-algebra ( ), whose self-adjoint elements describe localobservables measurable in the region . A question discussed recently in a number ofpapers is how much information about the geometricstructure of the underlying space-time (M, g) is encoded in the algebraicstructure of the net ( ). Followingthese ideas, it is demonstrated in this paper howspace-time-related concepts like causality and observerscan be described in a purely algebraic way, i.e., using only thelocal algebras ( ).These results are then used to show how the space-time(M, g) can be reconstructed from the set _loc := { ( )| M open, compact} of local algebras.     

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.