Abstract. Theory and prospects of Compton scattering on nucleons and light nuclei below 500 MeV are outlined; cf. [1][2][3]. Invited contribution at the WORKSHOP TO
WHY COMPTON SCATTERING?In Compton scattering γX → γX, the electric and magnetic fields of a real photon induce radiation multipoles by displacing the charged constituents and currents inside the target. The energy-and angle-dependence of the emitted radiation explores the interactions of its constituents. In Hadronic Physics, it elucidates the distribution, symmetries and dynamics of the charges and currents which constitute the low-energy degrees of freedom inside the nucleon, and -for few-nucleon systems -the interactions between nucleons; see a recent review for details [1]. The 2007 NSAC and 2010 NuPECC Long-Range Plans emphasise therefore the pivotal rôle of the nucleon's temporal two-photon response below 1 GeV to complement the information accessible in one-photon experiments like form-factor measurements. As a consequence, a number of experiments are presently being pursued at MAMI (Mainz) [4], HIγS at TUNL [5], and MAX-Lab at Lund [6]. For the next generation, Aron Bernstein and Rory Miskimen have shown at this workshop how to use high-intensity electron beams like MESA for "near-real" photon experiments [4,7].In contradistinction to many electro-magnetic processes, such structure effects have only recently been subjected to a multipole-analysis. The Fourier transforms of the corresponding temporal response functions are the proportionality constants between incident field and induced multipole. These energy-dependent polarisabilities parametrise the stiffness of the nucleon N (spin σ 2 ) against transitions Xl → Y l ′ of given photon multipolarity at fixed frequency. Up to 500 MeV, the relevant terms are:The two spin-independent polarisabilities α E1 (ω) and β M1 (ω) parametrise electric and magnetic dipole transitions.Of particular interest are at present the four dipole spin-polarisabilitiesThey encode the response of the nucleon spin-structure, i.e. of the spin constituents. Intuitively interpreted, the electromagnetic field associated with the spin degrees causes bi-refringence in the nucleon, just like in the classical Faraday-effect. Only the linear combinations γ 0 and γ π of scattering under 0 • and 180 • are somewhat constrained by data or phenomenology, with conflicting results for the proton (MAMI, LEGS) and large error-bars for the neutron. The values α E1 (ω = 0) etc. are often called "the (static) polarisabilities"; but the ω-dependence reveals more. Since the polarisabilities are the parameters of a multipole decomposition, they contain not more information than the full amplitudes, but characteristic signatures in specific channels are easier to interpret. For example, the significant ω-dependence of β M1 (ω) and γ M1M1 (ω) already for ω 100 MeV comes from the strong para-magnetic γN∆(1232) transition. The ∆(1232) enters thus dynamically well below the resonance region. The electric polarisabilities exhibit a pronounced c...