The Uehling correction to the energy levels in a pionic atom

We consider a correction to energy levels in a pionic atom induced by the Uehling potential, i.e., by a free electron vacuum-polarization loop. The calculation is performed for circular states (l=n-1). The result is obtained in a closed analytic form as a function of $Z\alpha$ and the pion-to-electron mass ratio. Certain asymptotics of the result are also presented

Hematite at Meridiani Planum, Mars, Investigated by Simultaneous Fitting of MER Mossbauer Spectra

The Mars Exploration Rover Opportunity encountered sedimentary outcrop rocks at its landing site. Spherules with diameters in the millimeter range were found to weather from the outcrop rocks. With Opportunity s miniaturised M ssbauer spectrometer MIMOS II, hematite was detected in spherules and in the outcrop matrix [1,2]. Figure 1 shows the target Berry Bowl, where brushed outcrop and an accumulation of spherules could be investigated on sols 46 and 48 of Opportunity s mission. Hematite undergoes a transition from a weakly ferromagnetic above to an antiferromagnetic state below the Morin temperature (T(sub M) approx.265 K for chemically pure, crystalline hematite). The magnetic hyperfine splitting (B(sub hf)) shows a general decrease with increasing temperature and a drop of approx.0.8 T at T(sub M). The quadrupole splitting ((Delta)EQ) changes its sign at T(sub M), with negative values above and positive values below the transition. Crystallinity and particle size influence the magnitude and temperature dependence of the magnetic splitting and the quadrupole splitting [3]

Properties of Martian Hematite at Meridiani Planum by Simultaneous Fitting of Mars Mossbauer Spectra

Mossbauer spectrometers [1] on the two Mars Exploration Rovers (MERs) have been making measurements of surface rocks and soils since January 2004, recording spectra in 10-K-wide temperature bins ranging from 180 K to 290 K. Initial analyses focused on modeling individual spectra directly as acquired or, to increase statistical quality, as sums of single-rock or soil spectra over temperature or as sums over similar rock or soil type [2, 3]. Recently, we have begun to apply simultaneous fitting procedures [4] to Mars Mossbauer data [5-7]. During simultaneous fitting (simfitting), many spectra are modeled similarly and fit together to a single convergence criterion. A satisfactory simfit with parameter values consistent among all spectra is more likely than many single-spectrum fits of the same data because fitting parameters are shared among multiple spectra in the simfit. Consequently, the number of variable parameters, as well as the correlations among them, is greatly reduced. Here we focus on applications of simfitting to interpret the hematite signature in Moessbauer spectra acquired at Meridiani Planum, results of which were reported in [7]. The Spectra. We simfit two sets of spectra with large hematite content [7]: 1) 60 rock outcrop spectra from Eagle Crater; and 2) 46 spectra of spherule-rich lag deposits (Table 1). Spectra of 10 different targets acquired at several distinct temperatures are included in each simfit set. In the table, each Sol (martian day) represents a different target, NS is the number of spectra for a given sol, and NT is the number of spectra for a given temperature. The spectra are indexed to facilitate definition of parameter relations and constraints. An example spectrum is shown in Figure 1, together with a typical fitting model. Results. We have shown that simultaneous fitting is effective in analyzing a large set of related MER Mossbauer spectra. By using appropriate constraints, we derive target-specific quantities and the temperature dependence of certain parameters. By examining different fitting models, we demonstrate an improved fit for martian hematite modeled with two sextets rather than as a single sextet, and show that outcrop and spherule hematite are distinct. For outcrop, the weaker sextet indicates a Morin transition typical of well-crystallized and chemically pure hematite, while most of the outcrop hematite remains in a weakly ferromagnetic state at all temperatures. For spherule spectra, both sextets are consistent with weakly ferromagnetic hematite with no Morin transition. For both hematites, there is evidence for a range of particle sizes

Light-Front Bethe-Salpeter Equation

A three-dimensional reduction of the two-particle Bethe-Salpeter equation is proposed. The proposed reduction is in the framework of light-front dynamics. It yields auxiliary quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded according to the number of particles exchanged at a given light-front time. An example suggests that the convergence of the expansion is rapid. This result is particular for light-front dynamics. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional ones. The technical procedure is developed for a two-boson case; the idea for an extension to fermions is given. The technical procedure appears quite practicable, possibly allowing one to go beyond the ladder approximation for the solution of the Bethe-Salpeter equation. The relation between the three-dimensional light-front reduction of the field-theoretic Bethe-Salpeter equation and a corresponding quantum-mechanical description is discussed.Comment: 42 pages, 5 figure

Molecular motion in concentrated solutions of spherical polystyrene microgels studied with the pulsed field gradient n.m.r.

Results of a pulsed field gradient n.m.r. study of the motion of swollen spherical microgels in solution are presented. We have measured the echo attenuation (or the incoherent dynamic structure function) of the protons in the microgels in the dynamic range from qR≪1 up to qR ≈ 1.8 (where q=scattering vector and R = particle radius), and in the timescale from a few milliseconds up to 100 ms. Rotational diffusion of the microgel spheres could not be detected with certainty. However, restricted diffusion of the spheres within a cage was observed, in particular for the large microgel with R =125 nm, where the short-time diffusion could be monitored. For apparent volume fractions (φ > 0.6, the diffusion is restricted within a space scale of root mean square displacement, 〈z2〉 1 2 120 nm. With increasing volume fraction of the microgels in solution, (φ > 0.6, the diffusion becomes increasingly restricted. This crossover corresponds to the dynamic glass transition observed by Bartsch et al. for a similar system using quasielastic light scattering. © 1994

NMR-investigation of restricted self-diffusion of oil in rape seeds

The self-diffusion of oil and water in rape seeds (Brassica napus L.) was measured with the NMR pulsed field gradient technique. The self-diffusion of oil was found to be completely restricted for diffusion times Δ > 30 ms. The experiments could be explained in terms of the model of diffusion within spherical droplets and a Gaussian mass distribution of the droplet radii. The mean droplet radius was found to be about 0.7 μm; this value decreased somewhat with increasing moisture content of the seeds. The experiments could also be explained with a Gaussian number distribution of droplet radii and a fraction of immobile protons in the NMR signal of 5 ... 10%, possibly arising from lipid protons. Though the transverse nuclear magnetic relaxation decay of the oil protons is not a single exponential we observe one uniform diffusive mobility for the oil molecules. The water self-diffusion coefficient at maximum moisture content of about 40% was determined to be 4.2 · 10-10 m2 s-1 which is typical for swollen polymer-solvent systems at such a concentration. © 1990 Springer-Verlag

Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms

We reconsider the well-studied Selfish Routing game with affine latency functions. The Price of Anarchy for this class of games takes maximum value 4/3; this maximum is attained already for a simple network of two parallel links, known as Pigou's network. We improve upon the value 4/3 by means of Coordination Mechanisms. We increase the latency functions of the edges in the network, i.e., if $\ell_e(x)$ is the latency function of an edge $e$, we replace it by $\hat{\ell}_e(x)$ with $\ell_e(x) \le \hat{\ell}_e(x)$ for all $x$. Then an adversary fixes a demand rate as input. The engineered Price of Anarchy of the mechanism is defined as the worst-case ratio of the Nash social cost in the modified network over the optimal social cost in the original network. Formally, if \CM(r) denotes the cost of the worst Nash flow in the modified network for rate $r$ and \Copt(r) denotes the cost of the optimal flow in the original network for the same rate then [\ePoA = \max_{r \ge 0} \frac{\CM(r)}{\Copt(r)}.] We first exhibit a simple coordination mechanism that achieves for any network of parallel links an engineered Price of Anarchy strictly less than 4/3. For the case of two parallel links our basic mechanism gives 5/4 = 1.25. Then, for the case of two parallel links, we describe an optimal mechanism; its engineered Price of Anarchy lies between 1.191 and 1.192.Comment: 17 pages, 2 figures, preliminary version appeared at ESA 201

Exploring CP Violation with BcB_c Decays

We point out that the pure ``tree'' decays $B_c^\pm\to D^\pm_s D$ are particularly well suited to extract the CKM angle $\gamma$ through amplitude relations. In contrast to conceptually similar strategies using $B^\pm\to K^\pm D$ or $B_d\to K^{\ast0} D$ decays, the advantage of the $B_c$ approach is that the corresponding triangles have three sides of comparable length and do not involve small amplitudes. Decays of the type $B_c^\pm\to D^\pm D$ -- the $U$-spin counterparts of $B_c^\pm\to D^\pm_s D$ -- can be added to the analysis, as well as channels, where the $D^\pm_s$- and $D^\pm$-mesons are replaced by higher resonances.Comment: 9 pages, LaTeX, 3 figures, reference adde

Temporal dynamics of tunneling. Hydrodynamic approach

We use the hydrodynamic representation of the Gross -Pitaevskii/Nonlinear Schroedinger equation in order to analyze the dynamics of macroscopic tunneling process. We observe a tendency to a wave breaking and shock formation during the early stages of the tunneling process. A blip in the density distribution appears in the outskirts of the barrier and under proper conditions it may transform into a bright soliton. Our approach, based on the theory of shock formation in solutions of Burgers equation, allows us to find the parameters of the ejected blip (or soliton if formed) including the velocity of its propagation. The blip in the density is formed regardless of the value and sign of the nonlinearity parameter. However a soliton may be formed only if this parameter is negative (attraction) and large enough. A criterion is proposed. An ejection of a soliton is also observed numerically. We demonstrate, theoretically and numerically, controlled formation of soliton through tunneling. The mass of the ejected soliton is controlled by the initial state.Comment: 11 pages, 6 figures, expanded and more detailed verions of the previous submissio

Electron Spin Dynamics and Hyperfine Interactions in Fe/Al_0.1Ga_0.9As/GaAs Spin Injection Heterostructures

We have studied hyperfine interactions between spin-polarized electrons and lattice nuclei in Al_0.1Ga_0.9As/GaAs quantum well (QW) heterostructures. The spin-polarized electrons are electrically injected into the semiconductor heterostructure from a metallic ferromagnet across a Schottky tunnel barrier. The spin-polarized electron current dynamically polarizes the nuclei in the QW, and the polarized nuclei in turn alter the electron spin dynamics. The steady-state electron spin is detected via the circular polarization of the emitted electroluminescence. The nuclear polarization and electron spin dynamics are accurately modeled using the formalism of optical orientation in GaAs. The nuclear spin polarization in the QW is found to depend strongly on the electron spin polarization in the QW, but only weakly on the electron density in the QW. We are able to observe nuclear magnetic resonance (NMR) at low applied magnetic fields on the order of a few hundred Oe by electrically modulating the spin injected into the QW. The electrically driven NMR demonstrates explicitly the existence of a Knight field felt by the nuclei due to the electron spin.Comment: 19 Figures - submitted to PR