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We report observables for elastic Compton scattering from $^3$He in ChiralEffective Field Theory with an explicit $\Delta(1232)$ degree of freedom($\chi$EFT) for energies between 50 and 120 MeV. The $\gamma\,{}^3$He amplitudeis complete at N3LO, $\mathcal{O}(e^2\delta^3)$, and in general converges wellorder by order. It includes the dominant pion-loop and two-body currents, aswell as the Delta excitation in the single-nucleon amplitude. Since the crosssection is two to three times that for deuterium and the spin of polarised$^3$He is predominantly carried by its constituent neutron, elastic Comptonscattering promises information on both the scalar and spin polarisabilities ofthe neutron. We study in detail the sensitivities of 4 observables to theneutron polarisabilities: the cross section, the beam asymmetry and two doubleasymmetries resulting from circularly polarised photons and a longitudinally ortransversely polarised target. Including the Delta enhances those asymmetriesfrom which neutron spin polarisabilities could be extracted. We also correctprevious, erroneous results at N2LO, i.e.~without an explicit Delta, andcompare to the same observables on proton, neutron and deuterium targets. Aninteractive Mathematica notebook of our results is available fromhgrie@gwu.edu.

Elastic Compton Scattering from 3He and the Role of the Delta