Final state interaction in spin asymmetry and GDH sum rule for incoherent pion production on the deuteron

The contribution of incoherent single pion photoproduction to the spin response of the deuteron, i.e., the asymmetry of the total photoabsorption cross section with respect to parallel and antiparallel spins of photon and deuteron, is calculated over the region of the $\Delta$-resonance with inclusion of final state $NN$- and $\pi N$-rescattering. Sizeable effects, mainly from $NN$-rescattering, are found leading to an appreciable reduction of the spin asymmetry. Furthermore, the contribution to the Gerasimov-Drell-Hearn integral is explicitly evaluated by integration up to a photon energy of 550 MeV. Final state interaction reduces the value of the integral to about half of the value obtained for the pure impulse approximation.