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A complete set of linearly independent observables in Compton scattering with arbitrarily polarised real photons off an arbitrarily polarised spin-1 target is introduced, for the case that the final-state polarisations are not measured. Adopted from the one widely used, e.g., in deuteron photo-dissociation, it consists of 18 terms: the unpolarised cross section, the beam asymmetry, 4 target asymmetries and 12 asymmetries in which both beam and target are polarised. They are expressed by the helicity amplitudes and —where available— related to observables discussed by other authors. As application to deuteron Compton scattering, their dependence on the (isoscalar) scalar and spin dipole polarisabilities of the nucleon is explored in Chiral Effective Field Theory with dynamical Δ(1232) degrees of freedom at order e2δ3. Some asymmetries are sensitive to only one or two dipole polarisabilities, making them particularly attractive for experimental studies. At a photon energy of 100MeV, a set of 5 observables is identified from which one may be able to extract the spin polarisabilities of the nucleon. These are experimentally realistic but challenging and mostly involve tensor-polarised deuterons. Relative to Compton scattering from a nucleon, sensitivity to the “mixed” spin polarisabilities γE1M2 and γM1E2 is increased because of the interference with the D wave component of the deuteron and with its pion-exchange current. An interactive Mathematica 9.0 notebook with results for all observables at photon energies up to 120MeV is available from hgrie@gwu.edu.
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