Probing nucleon structure on the lattice

The QCDSF/UKQCD Collaboration has an ongoing program to calculate nucleon matrix elements with two flavours of dynamical O(a) improved Wilson fermions. Here we present recent results on the electromagnetic form factors, the quark momentum fraction 〈x〉 and the first three moments of the nucleon's spin-averaged and spin-dependent generalised parton distributions, including preliminary results with pion masses as low as 320MeV.     

Halide ion determination from luminescence of the diprotonated form of porphyrin

We have studied quenching of the fluorescence of the diprotonated form of 3,7,13,17-tetramethyl-2,8,12,18-tetrabutylporphyrin by iodide ions in solutions. We have established that there is both static quenching of fluorescence when nonfluorescent complexes are formed with the iodide ions, as a result of an internal heavy atom effect, and also dynamic diffusion-controlled quenching. Based on analysis of the dependences of the fluorescence intensity and fluorescence lifetime on the iodide ion concentration in solution, we suggest using the diprotonated form of this porphyrin as the base compound for designing a fluorescent molecular receptor for halide ions. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 6, pp. 750–755, November–December, 2007.     

Helicity amplitudes and crossing relations for one-photon exchange antiproton proton reactions

Antiproton proton annihilation reactions allow unique access to the moduli and phases of nucleon electromagnetic form factors in the time-like region. We present the helicity amplitudes for the unequal-mass single-photon reaction pˉ → l ⁺ l ^- in the s channel including the lepton mass. The relative signs of these amplitudes are determined using simple invariance properties. Helicity amplitudes for one-photon exchange annihilation reaction pˉ → Bˉ are also given, where B is any spin-one-half particle with structure. Crossing relations between the ep → ep scattering and the pˉ → l ⁺ l ^- annihilation channels are discussed and the crossing matrix for the helicity amplitudes is given. This matrix may be used to verify known expressions for the space-like helicity amplitudes due to one-photon exchange.     

Neutron-proton mass difference in isospin-asymmetric nuclear matter

Isospin-breaking effects in the baryonic sector are studied in the framework of a medium-modified Skyrme model. The neutron-proton mass difference in infinite, asymmetric nuclear matter is discussed. In order to describe the influence of the nuclear environment on the skyrmions, we include energy-dependent charged and neutral pion optical potentials in the s - and p -wave channels. The present approach predicts that the neutron-proton mass difference is mainly dictated by its strong part and that it strongly decreases in neutron matter.     

High-codimensional static bifurcations of strongly nonlinear oscillator

The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied. We consider the averaged equations of a system subject to Duffing--van der Pol and quintic strong nonlinearity by introducing the undetermined fundamental frequency into the computation in the complex normal form. To discuss the static bifurcation, the bifurcation problem is described as a 3-codimensional unfolding with $Z_{2}$ symmetry on the basis of singularity theory. The transition set and bifurcation diagrams for the singularity are presented, while the stability of the zero solution is studied by using the eigenvalues in various parameter regions.     

Assigning vibrational polyads using relative equilibria: application to ozone

We demonstrate how relative equilibria of a vibrating molecule, which are families of principal periodic orbits otherwise known as nonlinear normal modes, can be used to describe the global polyad structure of vibrational energy levels. The classical action integral n(E) computed along these orbits at different energies E corresponds to the polyad quantum number n so that the energy En of different relative equilibria describes the splitting of n-polyads. Further information on the internal polyad structure can be driven from the stability analysis of relative equilibria. We use the ozone molecule as a concrete example where n-polyads or "hyperpolyads" should be distinguished from the well-known polyads of the 1:1 stretching mode resonance; the stretching polyads are structural elements of hyperpolyads. We give dynamical interpretation of the relation between relative equilibria and n-polyads based on the normal form reduction in the limit of small vibrations near the equilibrium.     

Sensitivity of the pQCD deuteron structure to the nucleon form factors

We discuss the applicability of pQCD to the elastic scattering of electrons on protons and deuterons. We analyze the Q²-dependence of the reduced deuteron form factor, taking into account the recent data on the electric proton form factor and we find that the value of the QCD-scale parameter Λ differs essentially from the value Λ = 0.1 GeV, previously found using the dipole parametrization of the electromagnetic nucleon form factors G_E and G_M. Moreover, the predicted scaling behavior of the reduced deuteron form factor cannot be recovered in the Dirac and Pauli representations for the nucleon electromagnetic form factors. Received: 14 October 2002 / Accepted: 12 November 2002 / Published online: 11 March 2003 RID="a" ID="a"Permanent address: National Science Center KFTI, 310108 Kharkov, Ukraine. RID="b" ID="b"e-mail: etomasi@cea.fr Communicated by V.V. Anisovich     

Sharp Estimates for the Size of Balls in the Complement of a Hypersurface

In this paper, we make estimates for the radius of balls contained in some component of the complementary of a complete hypersurface into a space form, generalizing and improving analogous radius estimates for embedded compact hypersurfaces obtained by Blaschke, Koutroufiotis and the authors. The results are obtained using an algebraic lemma and a tangency principle related with the length of the second fundamental form. The algebraic lemma also is used to improve a result for graphs due to Hasanis–Vlachos. The first author dedicates this work to his parents José (in memoriam) and Herondina     

Variational Formula for Dirichlet Forms and Estimates of Principal Eigenvalues for Symmetric α-stable Processes

In this paper, we prove a variational formula for Dirichlet forms generated by general symmetric Markov processes. As its applications, we obtain lower bound estimates of the bottom of spectrum for symmetric Markov processes. Moreover, for a positive measure charging no set of zero capacity, we give a new proof of an L²()-estimate of functions in Dirichlet spaces. Finally, we calculate the principal eigenvalues for absorbing and time changed -stable processes and obtain conditions for some measures being gaugeable. Mathematics Subject Classifications (2000) Primary 31C25; Secondary 34L15, 60G52.