Low-Energy Compton Scattering of Polarized Photons on Polarized Nucleons

The general structure of the cross section of $\gamma N$ scattering with polarized photon and/or nucleon in initial and/or final state is systematically described and exposed through invariant amplitudes. A low-energy expansion of the cross section up to and including terms of order $\omega^4$ is given which involves ten structure parameters of the nucleon (dipole, quadrupole, dispersion, and spin polarizabilities). Their physical meaning is discussed in detail. Using fixed-t dispersion relations, predictions for these parameters are obtained and compared with results of chiral perturbation theory. It is emphasized that Compton scattering experiments at large angles can fix the most uncertain of these structure parameters. Predictions for the cross section and double-polarization asymmetries are given and the convergence of the expansion is investigated. The feasibility of the experimental determination of some of the struture parameters is discussed.Comment: 41 pages of text, 9 figures; minor revisions prior to publication in Phys. Rev.

Dispersion Effects in Nucleon Polarisabilities

We present a formalism to extract the dynamical nucleon polarisabilities defined via a multipole expansion of the structure amplitudes in nucleon Compton scattering. In contradistinction to the static polarisabilities, dynamical polarisabilities gauge the response of the internal degrees of freedom of a composed object to an external, real photon field of arbitrary energy. Being energy dependent, they therefore contain additional information about dispersive effects induced by internal relaxation mechanisms, baryonic resonances and meson production thresholds of the nucleon. We give explicit formulae to extract the dynamical electric and magnetic dipole as well as quadrupole polarisabilities from low energy nucleon Compton scattering up to the one pion production threshold and discuss the connection to the definition of static nucleon polarisabilities. As a concrete example, we examine the results of leading order Heavy Baryon Chiral Perturbation Theory for the four leading spin independent iso-scalar polarisabilities of the nucleon. Finally, we consider the possible r{\^o}le of energy dependent effects in low energy extractions of the iso-scalar dipole polarisabilities from Compton scattering on the deuteron.Comment: 17 pages LaTeX2e with 2 figures, using includegraphicx (5 .eps files). Minor corrections, references updated. Contents identical to version to appear in Phys. Rev. C 65, spelling differen

Measurement of the Electric and Magnetic Polarizabilities of the Proton

The Compton scattering cross section on the proton has been measured at laboratory angles of 90$^\circ$ and 135$^\circ$ using tagged photons in the energy range 70--100 MeV and simultaneously using untagged photons in the range 100--148~MeV. With the aid of dispersion relations, these cross sections were used to extract the electric and magnetic polarizabilities, $\bar{\alpha}$ and $\bar{\beta}$ respectively, of the proton. We find $$\bar{\alpha}+\bar{\beta} = ( 15.0 \pm 2.9 \pm 1.1 \pm 0.4 ) \times 10^{-4} \: {\rm fm}^3,$$ in agreement with a model-independent dispersion sum rule, and $$\bar{\alpha}-\bar{\beta} = ( 10.8 \pm 1.1 \pm 1.4 \pm 1.0 ) \times 10^{-4} \: {\rm fm}^3,$$ where the errors shown are statistical, systematic, and model-dependent, respectively. A comparison with previous experiments is given and global values for the polarizabilities are extracted.Comment: 35 pages, 11 PostScript figures, uses RevTex 3.

Photon- and meson-induced reactions on the nucleon

In an unitary effective Lagrangian model we develop a unified description of both meson scattering and photon-induced reactions on the nucleon. Adding the photon to an already existing model for meson-nucleon scattering yields both Compton and meson photoproduction amplitudes. In a simultaneous fit to all available data involving the final states $\gamma N$, $\pi N$, $\pi\pi N$, $\eta N$ and $K \Lambda$ the parameters of the nucleon resonances are extracted.Comment: 57 pages, 14 figures, LaTex (uses Revtex and graphicx). Submitted to Phys. Rev. C. References updated, Fig. 14 change