Relativistic energy transfer

Energy transfer processes are ubiquitous in nature and intensely investigated. The investigations concentrate on the transfer of small to intermediate sized energies. Here, we pose the question of whether the transfer of large energies, where relativistic effects play a central role, can be efficient. At large energies, the process leads to ionization of the environment, i.e., it is the interatomic (or intermolecular) Coulombic decay (ICD) process. To that end, we derive asymptotic expressions for the ICD amplitude by employing the Dirac-Breit Hamiltonian and expanding the frequency dependent Coulomb-Breit interaction between the electrons of the donor and those of the acceptor in powers of the inverse distance between their centers of mass. Expressions are separately derived for the two popular Feynman and Coulomb gauges. At long range, the two expressions have a different appearance but are proven to be equivalent. The derived energy transfer rate at long range shows that when the donor is embedded in an environment, the transfer can be highly efficient. A key is that the radiative lifetime of the donor is extremely short (it can be in the attosecond, 10-18 s, regime), and the x-ray emission typically dominates by far Auger decay (also called Auger-Meitner decay), and the ICD can quench this emission. This contrasts with the situation at small to intermediate sized energies, where the radiative lifetime is much smaller and Auger decay (if the channel is open) dominates. In these cases, the major contribution to ICD comes from the neighbors nearby.