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.     

Antihydrogen at sub-Kelvin temperatures

We discuss the behavior of magnetically trapped antihydrogen ( ) at temperatures relevant for gravity and spectroscopy experiments (well below 1 K) and the possibilities of attaining these temperatures. Two possible options are considered. In the discussion of the first one, i.e. as admixture in cold H gas, we develop the quantum-mechanical theory of -H (and also -H) elastic and rearrangement collisions at ultra-low (sub-Kelvin) energies, when s-wave scattering in the incoming channel dominates. The rate constant of rearrangement leading to decay turns out to be large, which makes the possibilities for collisional cooling in H gas and -H coexistence rather limited. As we show, the most promising is the other option, i.e. atoms in the collisionless regime. For this regime the possibility of one-dimensional adiabatic cooling of is demonstrated by using the example of the Ioffe trap. This phenomenon, interesting from the fundamental point of view, offers the opportunity to cool below 1 mK.     

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.     

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.     

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.     

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.     

A remark on extensions of quasi-free derivations on the CAR-algebra

Let δ be a quasi-free derivation of the CAR algebra, and let be a closed *-derivation which is an extension of δ. We use Price's techniques from [6] to show that if the polynomials in the linear field operators a(f)→a ^* (f) in D( ) is a core for , then is quasi-free.     

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.     

Image states on beryllium surfaces with low indices

Using the self-consistent pseudopotential method, we have calculated the binding energy of the image states for the (0001) , and surfaces of beryllium. It is shown for the (0001) face that there exists a pronounced resonance image state with n=1 and energy −0.95 eV at the point of the surface Brillouin zone. In the surface, which has a wide band gap in the vicinity of the vacuum level, the calculated image state with n=1 at the point has energy −1.2 eV and is a surface state of gap type. For the face in the vicinity of the point band gaps are absent. However, the symmetry of the bulk states near the vacuum level enables the existence of a resonance image state with n=1 and energy −0.6 eV. Fiz. Tverd. Tela (St. Petersburg) 41, 935–940 (June 1999)     

Behaviour and spectroscopy of (anti) hydrogen atoms in strong magnetic fields

Since it has been demonstrated that antiprotons can be captured in sizeable amounts in ion traps, the intriguing question has been raised whether or not these antiprotons can be used for producingantihydrogen atoms. One route proposed is the merging of trapped antiprotons with a cold trapped plasma of positrons. In this case the formation of antihydrogen proceeds most likely through three-body recombination (p⁻e⁺e⁺→ e⁺) into high Rydberg states of , followed by a rapid cascade of transitions to low-lying states. To assess the influence of the trapping magnetic field (on the order of a few tesla) upon the formation process of we review the present knowledge of the behaviour and properties of hydrogen (and antihydrogen) atoms in strong magnetic fields — a subject which has been very topical in recent years because of its relation to the problem of “quantum” chaos.     

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.     

Solution of two mutually-reducible problems in electrostatics

There are two well-known problems in electrostatics whose solutions reduce to each other. One of them is that of a grounded conductor containing a cavity with given boundary . A charge distribution is specified on another surface S inside the cavity, or within the volume enclosed by S. It is required to find the charge density induced on . The other problem is that of finding “equivalent” sets of charges (producing identical external fields). Here again there are surfaces and S and the same original distributed charge as in the first problem, but the system is now in empty space and the problem is to find the charge distribution on that produces the same external field as the given distribution on S. Mutual reducibility means that it is sufficient to consider one of the two problems, say, the second. The problem examined in this paper is that of confocal ellipsoids S and and charge distributions described in terms polynomial functions of Cartesian coordinates. The method of multipole moments which leads directly to the solution (i.e., without the need to evaluate the field) is described. Analytical solutions are given for simple surface and volume charge distributions. Special and limiting cases are examined, including degenerate surfaces S and in the form of confocal elliptic cylinders. Zh. Tekh. Fiz. 67, 1–6 (April 1997)     

Universal R-Matrix for Esoteric Quantum Groups

The universal R-matrix for a class of esoteric (nonstandard) quantum groups q(gl(2N+1)) is constructed as a twisting of the universal R-matrix S of the Drinfeld–Nimbo quantum algebras. The main part of the twisting cocycle is chosen to be the canonical element of an appropriate pair of separated Hopf subalgebras (quantized Borel's (N) q (gl(2N+1))), providing the factorization property of . As a result, the esoteric quantum group generators can be expressed in terms of Drinfeld and Jimbo.     

The Standard Model in strong fields: electroweak radiative corrections for highly charged ions

Electroweak radiative corrections to the matrix element are calculated for highly charged hydrogen like ions. The operator represents the parity nonconserving relativistic effective atomic Hamiltonian at the tree level. The deviation of these calculations from the calculations valid for the neutral atoms demonstrates the effect of the strong field. This revised version was published online in August 2006 with corrections to the Cover Date.     

Theoretical cross sections for keV antiprotons

Partial and total close-coupled semiclassical (impact parameter) cross sections and total classical Monte-Carlo cross sections for interactions in and , p+H collisions are computed in the intermediate keV range for antiprotons, , up to 100 keV lab. Total cross sections for antihydrogen, , formation are found to be large, 10−20×10⁻¹⁶ cm² in a wider energy range than was anticipated earlier, up to some 20 keV lab. New estimates of cross sections for ionisation of atomic hydrogen by antiproton impact are reported for the low-energy range 1–30 keV lab where they are 10−20×10⁻¹⁷ cm², being much larger than the corresponding cross sections for ionisation of hydrogen by proton impact. Data for excitation of H by impact is also presented.     

\mathfrak{g}-Relative Star Products

We consider Kontsevich star products on the duals of Lie algebras. Such a star product is relative if, for any Lie algebra, its restriction to invariant polynomial functions is the usual pointwise product. Let be a fixed Lie algebra. We shall say that a Kontsevich star product is -relative if, on ^*, its restriction to invariant polynomial functions is the usual pointwise product. We prove that, if is a semi-simple Lie algebra, the only strict Kontsevich -relative star products are the relative (for every Lie algebras) Kontsevich star products.     

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.     

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.     

Bounds on neutrino mixing with exotic singlet neutrinos

We examine the effects of mixing induced non-diagonal light-heavy neutrino weak neutral currents on the amplitude for the process (with a=e, μ or τ). By imposing constraint that the amplitude should not exceed the perturbative unitarity limit at high energy , we obtain bounds on light-heavy neutrino mixing parameter sin² where is the mixing angle. In the case of one heavy neutrino (mass mξ) or mass degenerate heavy neutrinos, for Λ=1 TeV, no bound is obtained for mξ<0.50 TeV. However, sin² ≤3.8 × 10⁻⁶ for mξ=5 TeV and sin ≤6.0 × 10⁻⁸ for mξ=10 TeV. For Λ=∞, no constraint is obtained for mξ<0.99 TeV and sin² ≤3.8 × 10⁻² (for mξ=5 TeV) and sin² ≤9.6 × 10⁻³ (for mξ=10 TeV).