Moravcsik's theorem on complete sets of polarization observables reexamined

Abstract

We revisit Moravcsik's theorem on the unique extraction of amplitudes from polarization observables, which has been originally published in 1985. The proof is (re-) written in a more formal and detailed way and the theorem is corrected for the special case of an odd number of amplitudes (this case was treated incorrectly in the original publication). Moravcsik's theorem, in the modified form, can be applied in principle to the extraction of an arbitrary number of $N$ helicity amplitudes. The uniqueness theorem is then applied to hadronic reactions involving particles with spin. The most basic example is Pion-Nucleon scattering ($N=2$), the first non-trivial example is pseudoscalar meson photoproduction ($N=4$) and the most technically involved case treated here is given by pseudoscalar meson electroproduction ($N=6$). The application of Moravcsik's theorem to electroproduction yields new results, which for the first time provide insights into the structure and content of complete sets for this particular process. The uniqueness-statements for the various reactions are compared and an attempt is made to recognize general patterns, which emerge under the application of the theorem.

35 pages, 12 figures; Version 2 has been accepted for publication in Phys. Rev. C

References in corpus (12)

• Extended Partial-Wave Analysis of piN Scattering Data
• Partial-Wave Analysis of Nucleon-Nucleon Elastic Scattering Data
• Radiative pi0 photoproduction on protons in the Delta+(1232) region
• The N(1520) 3/2- helicity amplitudes from an energy-independent multipole analysis based on new polarization data on photoproduction of neutral pions
• Information Content of Polarization Measurements
• Differential Cross Section Measurements for $\gamma n\to {\pi }^{-}p$ Above the First Nucleon Resonance Region
• First measurement of the polarization observable $E$ and helicity-dependent cross sections in single ${\pi }^0$ photoproduction from quasi-free nucleons
• Amplitude extraction in pseudoscalar-meson photoproduction: towards a situation of complete information
• Differential cross section and photon beam asymmetry for the gamma p -> pi+ n reaction at forward pi+ angles at Egamma=1.5-2.95 GeV
• Photon asymmetry measurements of $\overrightarrow{\gamma }\mathrm{p}\to {\pi }^0\mathrm{p}$ for E${}_{\gamma }$=320$-$650 MeV
• Complete set of observables for photoproduction of two pseudoscalars on a nucleon
• The complete experiment problem of pseudoscalar meson photoproduction in a truncated partial wave analysis

Cited by in corpus (5)

• Light Baryon Spectroscopy
• Light baryon resonances from a coupled-channel study including $\mathbf{K\Sigma }$ photoproduction
• Coupled-channel analysis of pion- and eta-electroproduction with the Jülich-Bonn-Washington model
• Minimal complete sets for two pseudoscalar meson photoproduction
• New graphical criterion for the selection of complete sets of polarization observables and its application to single-meson photoproduction as well as electroproduction