Energy transfer from dark states: a relativistic approach

Recently, a relativistic theory of energy transfer has been developed and shown to give rise to highly-important long-range phenomena for very large transferred energies where relativistic effects are crucial to include. Being general, the theory is also applicable for small and intermediate sized excess energies, where it describes retardation and magnetic effects. In this work we consider mainly energy transfer from dark states of the donor, i.e., states which cannot decay radiatively by a dipole transition. Starting from the general full relativistic expressions for the various asymptotic contributions, we derive the leading terms describing the energy transfer for small and intermediate sized excess energies. It becomes evident that at small excess energies retardation and magnetic effects are essentially negligible compared to the impact of the bare Coulomb interaction. The situation can change drastically if one considers the transfer of intermediate sized energies as possible in the case of interatomic and intermolecular coulombic decay (ICD). Already a transfer of several hundreds of eV makes retardation effects similarly relevant as the Coulomb interaction at internuclear distances typical for equilibrium distances of weakly bound systems. Increasing the transferred energy further, the impact of retardation effects can overtake that of the bare Coulomb interaction between the donor and acceptor and even magnetic effects may become relevant. At such intermediate sized energies, a standard non-relativistic description of the participating donor and acceptor systems themselves is expected to suffice in computing the energy transfer, while the description of the energy transfer needs to take into account the relativistic effects as done here.