Nucleon polarisabilities from Compton scattering on the deuteron

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.