An analytic calculation of the differential cross section for elastic Compton scattering on the deuteron at photon energies omega in the range of 20-50 MeV is presented to next-to-next-to-leading order, i.e., to an accuracy of similar to3. 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. We argue that a window exists at omega similar to 20-50 MeV in which nucleon polarisabilities can be extracted in a model-independent way without having to know detailed pion dynamics. In a feasibility study, we use data at omega(Lab) = 49 MeV to find alpha(0) = 8.4 +/- 3.0(exp) +/- 1.7(theor), beta(0) = 8.9 +/- 3.9(exp) +/- 1.8(theor), each in units of 10(-4) fm(3). With the experimental constraint for the iso-scalar Baldin sura rule, alpha(0) = 7.2 +/- 2.1(exp) +/- 1.6(theor), beta(0) = 6.9 -/+ 2.1(exp) -/+ 1.6(theor). A more ad curate result can be achieved (i) predominantly by better experimental data, and (ii) by a higher order theoretical calculation including contributions from so far undetermined four-nucleon-two-photon operators. (C) 2002 Elsevier Science B.V. All rights reserved. References: 29
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