Elastic Compton Scattering from 3He

We study elastic Compton scattering on $^3$He using chiral effective field theory ($\chi$EFT) at photon energies from 60 MeV to approximately 120 MeV. Experiments to measure this process have been proposed for both MAMI at Mainz and the HI$\gamma$S facility at TUNL. I will present the revised results of a full calculation at third order in the expansion ($\mathcal{O}(Q^3)$). The amplitude involves a sum of both one- and two-nucleon Compton-scattering mechanisms. We have recently computed the fourth-order two-nucleon diagrams. The numerical impact they have on the cross-section results will be discussed. I will also present results in which amplitudes used so far are augmented by the leading effects from $\Delta(1232)$ degrees of freedom, a step which has already been performed for the proton and deuteron processes. Both cross sections and doubly-polarized asymmetries will be presented, and the sensitivity of these observables to the values of neutron scalar and spin polarizabilities will be assessed.