Multipole analysis of pion photoproduction based on fixed t dispersion relations and unitarity

We have analysed pion photoproduction imposing constraints from fixed t dispersion relations and unitarity. Coupled integral equations for the S and P wave multipoles were derived from the dispersion relations and solved by the method of Omnes and Muskhelishvili. The free parameters were determined by a fit to the most recent data for \pi^{+} and \pi^{0} production on the proton as well as \pi^{-} production on the neutron, in the energy We have analysed pion photoproduction imposing constraints from fixed t dispersion relations and unitarity. Coupled integral equations for the S and P wave multipoles were derived from the dispersion relations and solved by the method of Omnes and Muskhelishvili. The free parameters were determined by a fit to the most recent data for \pi^{+} and \pi^{0} production on the proton as well as \pi^{-} production on the neutron, in the energy range 160 MeV \leq E_{\gamma} \leq 420 MeV. The lack of high precision data on the neutron and of polarization observables leads to some limitations of our results. Especially the multipole M_{1-} connected with the Roper resonance P_{11}(1440) cannot be determined to the required precision. Our predictions for the threshold amplitudes are in good agreement with both the data and chiral perturbation theory. In the region of the \Delta(1232) we have determined the ratio of electric quadrupole and magnetic dipole excitation. The position of the resonance pole is obtained in excellent agreement with pion-nucleon scattering, and the complex residues of the multipoles are determined with the speed-plot technique.Comment: 46 pages LATEX including 29 postscript figure

New gadolinium-substituted lead sodium apatite structure

The substitution of gadolinium by lead in the compound Pb₈-xNa₂Gdx(PO₄)₆Ox/₂, in accordance with the scheme 2Pb²⁺ + • ↠ 2Gd³⁺ + O2- was studied by means of powder X-ray diffraction (including the Rietveld refinement). It was established that solid solutions apatite samples are synthesized at 900 °C between the range from x = 0.0 up to x = 1.0. Rietveld method shows that Gd³⁺ is located in positions Pb(2), resulting in the distance in a polyhedron Pb(2) where the structure of apatite decreased

Sol-Gel Synthesis, X-Ray Diffraction Studies, and Electric Conductivity of Sodium Europium Silicate

Sodium europium silicate, NaEu9(SiO4)6O2, with apatite structure has been obtained and studied using X-ray diffraction and SEM. It has been shown that sodium sublimation does not take place upon synthesis by the sol-gel method. Rietveld refinement has revealed that sodium atoms are ordered and occupy the 4f position. O(4) atoms not related to silicate ions are placed at the centers of Eu(2) triangles. DC and AC electric conductivity and activation energy have been determined for the compound studied