Atomic Alchemy

We consider the transitions between electromagnetic bound states, such as the exclusive weak decay of a muonic atom into an electronic atom: (µ − Z) → (e − Z)¯ ν e ν µ. We show that relativistic effects in the atomic wave-functions are crucial for determining the rate. In the case of heavy atoms, the exclusive channel branching ratios exceed 10 −6 , possibly bringing the study of these rare decays within experimental reach. Such processes thus provide a detailed laboratory for studying the high momentum tail of wavefunctions in atomic physics; in addition, they provide a simple toy model for investigating analogous exclusive heavy hadronic decays in quantum chromodynamics such as B → πeν.