RESUMEN
A precise measurement of the differential cross sections dσ/dΩ and the linearly polarized photon beam asymmetry Σ_{3} for Compton scattering on the proton below pion threshold has been performed with a tagged photon beam and almost 4π detector at the Mainz Microtron. The incident photons were produced by the recently upgraded Glasgow-Mainz photon tagging facility and impinged on a cryogenic liquid hydrogen target, with the scattered photons detected in the Crystal Ball/TAPS setup. Using the highest statistics Compton scattering data ever measured on the proton along with two effective field theories (both covariant baryon and heavy-baryon) and one fixed-t dispersion relation model, constraining the fits with the Baldin sum rule, we have obtained the proton electric and magnetic polarizabilities with unprecedented precision: α_{E1}=10.99±0.16±0.47±0.17±0.34, ß_{M1}=3.14±0.21±0.24±0.20±0.35; in units of 10^{-4} fm^{3} where the errors are statistical, systematic, spin polarizability dependent, and model dependent.
RESUMEN
The double-polarization observable E and helicity-dependent cross sections σ_{1/2}, σ_{3/2} have been measured for the photoproduction of π^{0} pairs off quasifree protons and neutrons at the Mainz MAMI accelerator with the Crystal Ball/TAPS setup. A circularly polarized photon beam was produced by bremsstrahlung from longitudinally polarized electrons and impinged on a longitudinally polarized deuterated butanol target. The reaction products were detected with an almost 4π covering calorimeter. The results reveal for the first time the helicity- and isospin-dependent structure of the γNâNπ^{0}π^{0} reaction. They are compared to predictions from reaction models in view of nucleon resonance contributions and also to a refit of one model that predicted results for the proton and for the neutron target. The comparison of the prediction and the refit demonstrates the large impact of the new data.