Atomic Alchemy

Abstract

We consider the transitions between electromagnetic bound states, such as the exclusive weak decay of a muonic atom into an electronic atom: $({\mu }^{-}Z)\to (e^{-}Z){\bar{\nu }}_e{\nu }_{\mu }.$ We show that relativistic effects in the atomic wavefunctions 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 $B\to \pi e\nu .$

Comments: 16 pages and 5 Figures, SLAC-PUB-6487