Proof of two conjectures of Z.-W. Sun on congruences for Franel numbers

For all nonnegative integers n, the Franel numbers are defined as $$f_n=\sum_{k=0}^n {n\choose k}^3.$$ We confirm two conjectures of Z.-W. Sun on congruences for Franel numbers: \sum_{k=0}^{n-1}(3k+2)(-1)^k f_k &\equiv 0 \pmod{2n^2}, \sum_{k=0}^{p-1}(3k+2)(-1)^k f_k &\equiv 2p^2 (2^p-1)^2 \pmod{p^5}, where n is a positive integer and p>3 is a prime.Comment: 8 pages, minor changes, to appear in Integral Transforms Spec. Func

Quasi-Local Density Functional Theory and its Application within Extended Thomas-Fermi Approximation

A generalization of the Density Functional Theory is proposed. The theory developed leads to single-particle equations of motion with a quasi-local mean-field operator, which contains a quasi-particle position-dependent effective mass and a spin-orbit potential. The energy density functional is constructed using the Extended Thomas-Fermi approximation. Within the framework of this approach the ground-state properties of the doubly magic nuclei are considered. The calculations have been performed using the finite-range Gogny D1S force. The results are compared with the exact Hartree-Fock calculations

Structure of the icosahedral Ti-Zr-Ni quasicrystal

The atomic structure of the icosahedral Ti-Zr-Ni quasicrystal is determined by invoking similarities to periodic crystalline phases, diffraction data and the results from ab initio calculations. The structure is modeled by decorations of the canonical cell tiling geometry. The initial decoration model is based on the structure of the Frank-Kasper phase W-TiZrNi, the 1/1 approximant structure of the quasicrystal. The decoration model is optimized using a new method of structural analysis combining a least-squares refinement of diffraction data with results from ab initio calculations. The resulting structural model of icosahedral Ti-Zr-Ni is interpreted as a simple decoration rule and structural details are discussed.Comment: 12 pages, 8 figure

Tensor Correlations Measured in 3He(e,e'pp)n

We have measured the 3He(e,e'pp)n reaction at an incident energy of 4.7 GeV over a wide kinematic range. We identified spectator correlated pp and pn nucleon pairs using kinematic cuts and measured their relative and total momentum distributions. This is the first measurement of the ratio of pp to pn pairs as a function of pair total momentum, $p_{tot}$. For pair relative momenta between 0.3 and 0.5 GeV/c, the ratio is very small at low $p_{tot}$ and rises to approximately 0.5 at large $p_{tot}$. This shows the dominance of tensor over central correlations at this relative momentum.Comment: 4 pages, 4 figures, submitted to PR

Measurement of the nuclear multiplicity ratio for Ks0K^0_s hadronization at CLAS

The influence of cold nuclear matter on lepto-production of hadrons in semi-inclusive deep inelastic scattering is measured using the CLAS detector in Hall B at Jefferson Lab and a 5.014 GeV electron beam. We report the $K_s^0$ multiplicity ratios for targets of C, Fe, and Pb relative to deuterium as a function of the fractional virtual photon energy $z$ transferred to the $K_s^0$ and the transverse momentum squared $p_{T}^2$ of the $K_s^0$. We find that the multiplicity ratios for $K^0_s$ are reduced in the nuclear medium at high $z$ and low $p_{T}^2$, with a trend for the $K^0_s$ transverse momentum to be broadened in the nucleus for large $p_{T}^2$.Comment: Submitted to Phys. Lett.

A Bayesian analysis of pentaquark signals from CLAS data

We examine the results of two measurements by the CLAS collaboration, one of which claimed evidence for a $\Theta^{+}$ pentaquark, whilst the other found no such evidence. The unique feature of these two experiments was that they were performed with the same experimental setup. Using a Bayesian analysis we find that the results of the two experiments are in fact compatible with each other, but that the first measurement did not contain sufficient information to determine unambiguously the existence of a $\Theta^{+}$. Further, we suggest a means by which the existence of a new candidate particle can be tested in a rigorous manner.Comment: 5 pages, 3 figure

Precise Measurements of Beam Spin Asymmetries in Semi-Inclusive π0\pi^0 production

We present studies of single-spin asymmetries for neutral pion electroproduction in semi-inclusive deep-inelastic scattering of 5.776 GeV polarized electrons from an unpolarized hydrogen target, using the CEBAF Large Acceptance Spectrometer (CLAS) at the Thomas Jefferson National Accelerator Facility. A substantial $\sin \phi_h$ amplitude has been measured in the distribution of the cross section asymmetry as a function of the azimuthal angle $\phi_h$ of the produced neutral pion. The dependence of this amplitude on Bjorken $x$ and on the pion transverse momentum is extracted with significantly higher precision than previous data and is compared to model calculations.Comment: to be submitted PL

Measurement of the Nucleon Structure Function F2 in the Nuclear Medium and Evaluation of its Moments

We report on the measurement of inclusive electron scattering off a carbon target performed with CLAS at Jefferson Laboratory. A combination of three different beam energies 1.161, 2.261 and 4.461 GeV allowed us to reach an invariant mass of the final-state hadronic system W~2.4 GeV with four-momentum transfers Q2 ranging from 0.2 to 5 GeV2. These data, together with previous measurements of the inclusive electron scattering off proton and deuteron, which cover a similar continuous two-dimensional region of Q2 and Bjorken variable x, permit the study of nuclear modifications of the nucleon structure. By using these, as well as other world data, we evaluated the F2 structure function and its moments. Using an OPE-based twist expansion, we studied the Q2-evolution of the moments, obtaining a separation of the leading-twist and the total higher-twist terms. The carbon-to-deuteron ratio of the leading-twist contributions to the F2 moments exhibits the well known EMC effect, compatible with that discovered previously in x-space. The total higher-twist term in the carbon nucleus appears, although with large systematic uncertainites, to be smaller with respect to the deuteron case for n<7, suggesting partial parton deconfinement in nuclear matter. We speculate that the spatial extension of the nucleon is changed when it is immersed in the nuclear medium.Comment: 37 pages, 15 figure

Demonstration of a novel technique to measure two-photon exchange effects in elastic e±pe^\pm p scattering

The discrepancy between proton electromagnetic form factors extracted using unpolarized and polarized scattering data is believed to be a consequence of two-photon exchange (TPE) effects. However, the calculations of TPE corrections have significant model dependence, and there is limited direct experimental evidence for such corrections. We present the results of a new experimental technique for making direct $e^\pm p$ comparisons, which has the potential to make precise measurements over a broad range in $Q^2$ and scattering angles. We use the Jefferson Lab electron beam and the Hall B photon tagger to generate a clean but untagged photon beam. The photon beam impinges on a converter foil to generate a mixed beam of electrons, positrons, and photons. A chicane is used to separate and recombine the electron and positron beams while the photon beam is stopped by a photon blocker. This provides a combined electron and positron beam, with energies from 0.5 to 3.2 GeV, which impinges on a liquid hydrogen target. The large acceptance CLAS detector is used to identify and reconstruct elastic scattering events, determining both the initial lepton energy and the sign of the scattered lepton. The data were collected in two days with a primary electron beam energy of only 3.3 GeV, limiting the data from this run to smaller values of $Q^2$ and scattering angle. Nonetheless, this measurement yields a data sample for $e^\pm p$ with statistics comparable to those of the best previous measurements. We have shown that we can cleanly identify elastic scattering events and correct for the difference in acceptance for electron and positron scattering. The final ratio of positron to electron scattering: $R=1.027\pm0.005\pm0.05$ for $=0.206$ GeV$^2$ and $0.830\leq \epsilon\leq 0.943$

First measurement of direct f0(980)f_0(980) photoproduction on the proton

We report on the results of the first measurement of exclusive $f_0(980)$ meson photoproduction on protons for $E_\gamma=3.0 - 3.8$ GeV and $-t = 0.4-1.0$ GeV$^2$. Data were collected with the CLAS detector at the Thomas Jefferson National Accelerator Facility. The resonance was detected via its decay in the $\pi^+ \pi^-$ channel by performing a partial wave analysis of the reaction $\gamma p \to p \pi^+ \pi^-$. Clear evidence of the $f_0(980)$ meson was found in the interference between $P$ and $S$ waves at $M_{\pi^+ \pi^-}\sim 1$ GeV. The $S$-wave differential cross section integrated in the mass range of the $f_0(980)$ was found to be a factor of 50 smaller than the cross section for the $\rho$ meson. This is the first time the $f_0(980)$ meson has been measured in a photoproduction experiment