Numerical solution of single mode gyrotron equation

In this paper we study numerical problems arising in solving the single mode gyrotron equation. Using the method of finite differences analytical and numerical solutions are obtained. Quasistationary solutions and corresponding eigenvalues and eigenfunctions of this problem are investigated. Girotrono lygties vienos modos skaitiniai sprendimai Santrauka Straipsnyje nagrinėjami skaitiniai sprendiniai gauti tiriant girotrono lygties vieną modą. Analitiniai ir skaitiniai sprendiniai gauti taikant baigtinių skirtumų metodą. Ištirti kvazistacionarieji sprendiniai ir atitinkamos tokio uždavinio tikrinės reikšmės ir tikrinės funkcijos. First Published Online: 14 Oct 201

Error estimates for pi-pi scattering threshold parameters in Chiral Perturbation Theory to two loops

Using the analysis of ChPT to two loops, we perform an error analysis of the threshold and low energy parameters, based on the uncertainties for the one loop low energy parameters and the resonance saturation mechanism. Different sets of one loop low energy constants have been considered.Thus, the predictive power of the effective field theory is quantified on the basis of the present experimental uncertainties.Comment: 12 pages, 2 tables, 3 figures. Numerics upgraded to v2 of ref.(8). New reference added. Typos corrected. New figure for SU(3) parameters include

pp→ppωpp\to pp\omega reaction near threshold

We analyze the total cross section data for $pp \to pp\omega$ near threshold measured recently at SATURNE. Using an effective range approximation for the on-shell $pp$ S-wave final state interaction we extract from these data the modulus $|\Omega| = 0.53$ fm$^4$ of the threshold transition amplitude $\Omega$. We present a calculation of various (tree-level) meson exchange diagrams contributing to $\Omega$. It is essential that $\omega$-emission from the anomalous $\omega\rho\pi$-vertex interferes destructively with $\omega$-emission from the proton lines. The contribution of scalar $\sigma$-meson exchange to $\Omega$ turns out to be negligibly small. Without introducing off-shell meson-nucleon form factors the experimental value $|\Omega|=0.53$ fm$^4$ can be reproduced with an $\omega N$-coupling constant of $g_{\omega N}=10.7$. The results of the present approach agree qualitatively with the J\"ulich model. We also perform a combined analysis of the reactions $pp\to pp\pi^0, pn\pi^+, pp\eta, pp\omega$ and $pn\to pn\eta$ near threshold.Comment: Latex-file 6 pages, 2 Figure