  An analytic calculation of the differential cross section for elastic Compton
scattering on the deuteron at photon energies \omega in the range of 25-50 MeV
is presented to next-to-next-to-leading order, i.e. to an accuracy of \sim 3%.
The calculation is model-independent and performed in the low energy nuclear
Effective Field Theory without dynamical pions. The iso-scalar, scalar electric
and magnetic nucleon polarisabilities \alpha_0 and \beta_0 enter as free
parameters with a theoretical uncertainty of about 20%. Using data at
$\omega_{Lab}=49 MeV$ we find $\alpha_0=8.4\pm 3.0(exp)\pm 1.7(theor)$,
$\beta_0=8.9\pm 3.9(exp)\pm 1.8(theor)$, each in units of $10^{-4} fm^3$. With
the experimental constraint for the iso-scalar Baldin sum rule,
$\alpha_0=7.2\pm 2.1(exp)\pm 1.6(theor)$, $\beta_0=6.9\mp 2.1(exp)\mp
1.6(theor)$. A more accurate result can be achieved by: (i) better experimental
data, and (ii) a higher order theoretical calculation including contributions
from a couple of so far undetermined four-nucleon-two-photon operators.
