Nonradiative and radiative F\"orster energy transfer between quantum dots

We study theoretically nonradiative and radiative energy transfer between two localized quantum emitters, donor one (i.e. initially excited) and acceptor one (i.e. receiving the excitation). The rates of nonradiative and radiative processes are calculated depending on the spatial and spectral separation between donor and acceptor states and for different donor and acceptor lifetimes for typical parameters of semiconductor quantum dots. We find that the donor lifetime can be significantly modified only due to the nonradiative F\"orster energy transfer process at donor-acceptor separations $\sim 10~$nm (depending on the acceptor radiative lifetime) and for the energy detuning not larger than 1$\div$2 meV. The efficiency of the nonradiative F\"orster energy transfer process under these conditions is close to unity and decreases rapidly with the increase of donor-acceptor distance or energy detuning. At large donor-acceptor separations $>40~$nm the radiative corrections to the donor lifetime are comparable with nonradiative ones but are relatively weak.