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

STUDY OF THE TRANSITION PROCESS OF OPERATION IN THE CONTACT INTERACTION OF THE ROTARY KILN AND THE SUPPORT ROLLERS IN ANSYSMECHANICAL

At first glance, a rotary kiln is a simple structural object, which is very widespread in the industry of processing and obtaining materials, both for construction and for other purposes. However, behind the external simplicity, there are complex chemical processes, mechanical, subtleties of the control system, the technology of manufacturing large-sized parts that are part of the general assembly and directly issues related to the design and modernization stage. The study of various regularities of mechanical processes associated with the theory of elasticity, kinematics and contact interactions is difficult even separately, especially when the processes run together. Studying the contact interaction of the kiln with roller supports allows to see the anomalous effects that can occur if the design is incorrect. In a specific case, it is necessary to observe how, under the action of external forces, time-varying deformations, displacements, of individual structural elements occur, which are of key functional importance in the operation of the equipment, in conditions of contact interaction of its individual parts, taking into account inertial loads and damping. The study of transition processes with changing force factors in time will allow to obtain the response of the structure to external influences</jats:p

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