Test of isospin symmetry via low energy 1^1H(π−\pi^-,πo\pi^o)nn charge exchange

We report measurements of the $\pi^- p \to \pi^o n$ differential cross sections at six momenta (104-143 MeV/c) and four angles (0-40 deg) by detection of $\gamma$-ray pairs from $\pi^o \to \gamma \gamma$ decays using the TRIUMF RMC spectrometer. This region exhibits a vanishing zero-degree cross section from destructive interference between s-- and p--waves, thus yielding special sensitivity to pion-nucleon dynamics and isospin symmetry breaking. Our data and previous data do not agree, with important implications for earlier claims of large isospin violating effects in low energy pion-nucleon interactions.Comment: 5 pages, 3 figures, submitted to Physical Review Letter

Multi-wavelength Stellar Polarimetry of the Filamentary Cloud IC5146: I. Dust Properties

We present optical and near-infrared stellar polarization observations toward the dark filamentary clouds associated with IC5146. The data allow us to investigate the dust properties (this paper) and the magnetic field structure (Paper II). A total of 2022 background stars were detected in $R_{c}$-, $i'$-, $H$-, and/or $K$-bands to $A_V \lesssim 25$ mag. The ratio of the polarization percentage at different wavelengths provides an estimate of $\lambda_{max}$, the wavelength of peak polarization, which is an indicator of the small-size cutoff of the grain size distribution. The grain size distribution seems to significantly change at $A_V \sim$ 3 mag, where both the average and dispersion of $P_{R_c}/P_{H}$ decrease. In addition, we found $\lambda_{max}$ $\sim$ 0.6-0.9 $\mu$m for $A_V>2.5$ mag, which is larger than the $\sim$ 0.55 $\mu$m in the general ISM, suggesting that grain growth has already started in low $A_V$ regions. Our data also reveal that polarization efficiency (PE $\equiv P_{\lambda}/A_V$) decreases with $A_V$ as a power-law in $R_c$-, $i'$-, and $K$-bands with indices of -0.71$\pm$0.10, -1.23$\pm$0.10 and -0.53$\pm$0.09. However, $H$-band data show a power index change; the PE varies with $A_V$ steeply (index of -0.95$\pm$0.30) when $A_V < 2.88\pm0.67$ mag but softly (index of -0.25$\pm$0.06) for greater $A_V$ values. The soft decay of PE in high $A_V$ regions is consistent with the Radiative Aligned Torque model, suggesting that our data trace the magnetic field to $A_V \sim 20$ mag. Furthermore, the breakpoint found in $H$-band is similar to the $A_V$ where we found the $P_{R_c}/P_{H}$ dispersion significantly decreased. Therefore, the flat PE-$A_V$ in high $A_V$ regions implies that the power index changes result from additional grain growth.Comment: 31 pages, 17 figures, and 3 tables; accepted for publication in Ap

On the Convergence of Ritz Pairs and Refined Ritz Vectors for Quadratic Eigenvalue Problems

For a given subspace, the Rayleigh-Ritz method projects the large quadratic eigenvalue problem (QEP) onto it and produces a small sized dense QEP. Similar to the Rayleigh-Ritz method for the linear eigenvalue problem, the Rayleigh-Ritz method defines the Ritz values and the Ritz vectors of the QEP with respect to the projection subspace. We analyze the convergence of the method when the angle between the subspace and the desired eigenvector converges to zero. We prove that there is a Ritz value that converges to the desired eigenvalue unconditionally but the Ritz vector converges conditionally and may fail to converge. To remedy the drawback of possible non-convergence of the Ritz vector, we propose a refined Ritz vector that is mathematically different from the Ritz vector and is proved to converge unconditionally. We construct examples to illustrate our theory.Comment: 20 page