First Measurement of the Gerasimov-Drell-Hearn Sum Rule for 1H from 0.7 to 1.8 GeV at ELSA

To verify the fundamental Gerasimov-Drell-Hearn (GDH) sum rule for the first time experimentally, we measured the helicity dependent total photoabsorption cross section with circularly polarized real photons and longitudinally polarized nucleons in the photon energy range 0.68-1.82 GeV with the tagged photon facility at ELSA. The experiment was carried out with a 4pi detection system, a circularly polarized tagged photon beam, and a frozen spin polarized proton target. The contribution to the GDH sum rule in this photon energy range is [49.9+/-2.4(stat)+/-2.2(syst)] microb.     

Measurement of the G asymmetry for the γp↦Nπ channels in the Δ(1232) resonance region

The G asymmetry of the γp↦Nπ reaction has been measured for the first time for E_γ = 340±14 MeV. This observable, for which very scarce published data exist, plays an important role to disentangle the contributions of the various nucleon resonances. The experiment, performed at the Mainz microtron MAMI, used a 4π-detector system, a linearly polarized, tagged photon beam, and a longitudinally polarized proton target.     

On Hahn polynomial expansion of a continuous function of bounded variation

We consider the well-known method of least squares (cf., e.g., [1, p. 217]) on an equidistant grid with N + 1 nodes on the interval [−1, 1]. We investigate the following problem: For which ratio N/n, do we have pointwise convergence of the least square operator LS^N_n : C[−1,[1][→[P_n? To solve this problem we investigate the relation between the Jacobi polynomials P^α,β_k (cf., e.g., [2, p. 216]) and the Hahn polynomials Q_k (·; α, β, N) (cf., e.g., [2, p. 204]). In particular, we present the following result: Let f ∈ {g ∈ C¹[−1, 1] : g′∈ BV [−1, 1]} and let (N_n)_n be a sequence of natural numbers with n⁴/N_n → 0. Then the least square method LS^N_n [f] converges for each x ∈ [−1, 1]. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hydrophilicity and the viscosity of interfacial water

We measure the viscosity of nanometer-thick water films at the interface with an amorphous silica surface. We obtain viscosity values from three different measurements: friction force in a water meniscus formed between an oxide-terminated W tip and the silica surface under ambient conditions; similar measurements for these interfaces under water; and the repulsive "drainage" force as the two surfaces approach at various speeds in water. In all three cases, we obtain effective viscosities that are approximately 10(6) times greater than that of bulk water for nanometer-scale interfacial separations. This enhanced viscosity is not observed when we degrade the hydrophilicity of the surface by terminating it with -H or -CH3. In view of recent results from other interfaces, we conclude that the criterion for the formation of a viscous interphase is the degree of hydrophilicity of the interfacial pair.