Nucleon Spin-Polarisabilities from Polarisation Observables in Low-Energy Deuteron Compton Scattering

We investigate the dependence of polarisation observables in elastic deuteron Compton scattering below the pion production threshold on the spin-independent and spin-dependent iso-scalar dipole polarisabilities of the nucleon. The calculation uses Chiral Effective Field Theory with dynamical Delta(1232) degrees of freedom in the Small Scale Expansion at next-to-leading order. Resummation of the NN intermediate rescattering states and including the Delta induces sizeable effects. The analysis considers cross-sections and the analysing power of linearly polarised photons on an unpolarised target, and cross-section differences and asymmetries of linearly and circularly polarised beams on a vector-polarised deuteron. An intuitive argument helps one to identify kinematics in which one or several polarisabilities do not contribute. Some double-polarised observables are only sensitive to linear combinations of two of the spin-polarisabilities, simplifying a multipole-analysis of the data. Spin-polarisabilities can be extracted at photon energies \gtrsim 100 MeV, after measurements at lower energies of \lesssim 70 MeV provide high-accuracy determinations of the spin-independent ones. An interactive Mathematica 7.0 notebook of our findings is available from [email protected]: 30 pages LaTeX2e, including 22 figures as 66 .eps file embedded with includegraphicx; three errors in initial submission corrected. This submission includes ot the erratum to be published in EPJA (2012) and the corrections in the tex

Nucleon Polarizabilities from Deuteron Compton Scattering within a Green's-Function Hybrid Approach

We examine elastic Compton scattering from the deuteron for photon energies ranging from zero to 100 MeV, using state-of-the-art deuteron wave functions and NN-potentials. Nucleon-nucleon rescattering between emission and absorption of the two photons is treated by Green's functions in order to ensure gauge invariance and the correct Thomson limit. With this Green's-function hybrid approach, we fulfill the low-energy theorem of deuteron Compton scattering and there is no significant dependence on the deuteron wave function used. Concerning the nucleon structure, we use Chiral Effective Field Theory with explicit \Delta(1232) degrees of freedom within the Small Scale Expansion up to leading-one-loop order. Agreement with available data is good at all energies. Our 2-parameter fit to all elastic $\gamma d$ data leads to values for the static isoscalar dipole polarizabilities which are in excellent agreement with the isoscalar Baldin sum rule. Taking this value as additional input, we find \alpha_E^s= (11.3+-0.7(stat)+-0.6(Baldin)) x 10^{-4} fm^3 and \beta_M^s = (3.2-+0.7(stat)+-0.6(Baldin)) x 10^{-4} fm^3 and conclude by comparison to the proton numbers that neutron and proton polarizabilities are essentially the same.Comment: 47 pages LaTeX2e with 20 figures in 59 .eps files, using graphicx. Minor modifications; extended discussion of theoretical uncertainties of polarisabilities extraction. Version accepted for publication in EPJ