  We examine elastic Compton scattering off the deuteron for photon energies
between 50 MeV and 100 MeV in the framework of chiral effective field theories
to next-to-leading order. We compare one theoretical scheme with only pions and
nucleons as explicit degrees of freedom to another in which the Delta(1232)
resonance is treated as an explicit degree of freedom. Whereas pion degrees of
freedom suffice to describe the experimental data measured at about 70 MeV, the
explicit Delta(1232) gives important contributions that help to reproduce the
angular dependence at higher energies. The static isoscalar dipole
polarizabilities alpha_E^s and beta_M^s are fitted to the available data,
giving results for the neutron polarizabilities
alpha_E^n=(14.2+-2.0(stat)+-1.9(syst))*10^(-4)fm^3,
beta_M^n=(1.8+-2.2(stat)+-0.3(syst))*10^(-4)fm^3. These values are in good
agreement with previous experimental analyses. Comparing them to the well-known
proton values we conclude that there is currently no evidence for significant
differences between the proton and neutron electromagnetic dipole
polarizabilities.
