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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 (χEFT) with dynamical Δ(1232) degrees of freedom in the Small Scale Expansion (SSE) at next-to-leading order. Resummation of the NN intermediate rescattering states and including the Δ 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 100MeV, after measurements at lower energies of 70MeV provide high-accuracy determinations of the spin-independent ones. An interactive Mathematica 7.0 notebook of our findings is available from hgrie@gwu.edu.
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