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 ω in the range of 25 − 50 MeV is presented to next-to-next-to-leading order, i.e. to an accuracy of ∼ 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 α0 and β0 enter as free parameters with a theoretical uncertainty of about 20%. Using data at ωLab = 49 MeV we find α0 = 8.4 ± 3.0(exp) ± 1.7(theor), β0 = 8.9 ± 3.9(exp) ± 1.8(theor), each in units of 10−4 fm. With the experimental constraint for the iso-scalar Baldin sum rule, α0 = 7.2 ± 2.1(exp) ± 1.6(theor), β0 = 6.9∓2.1(exp)∓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. Suggested PACS numbers: 13.60.Fz, 14.20.Dh, 21.30.Fe, 25.20.-x Suggested