  We study direct energy transfer by multipolar or exchange interactions
between diffusive excited donor and diffusive unexcited acceptors. Extending
over the case of long-range transfer of an excitation energy a non-perturbative
approach by Bray and Blythe [Phys. Rev. Lett. 89, 150601 (2002)], originally
developed for contact diffusion-controlled reactions, we determine exactly
long-time asymptotics of the donor decay function in one-dimensional systems.
