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We consider the transitions between electromagnetic bound states, such as theexclusive 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 theatomic wavefunctions are crucial for determining the rate. In the case of heavyatoms, the exclusive channel branching ratios exceed $10^{-6},$ possiblybringing the study of these rare decays within experimental reach. Suchprocesses thus provide a detailed laboratory for studying the high momentumtail of wavefunctions in atomic physics; in addition, they provide a simple toymodel for investigating analogous exclusive heavy hadronic decays in quantumchromodynamics such as $B \to \pi e \nu.$Comment: 16 pages and 5 Figures, SLAC-PUB-648

Atomic alchemy: Weak decays of muonic and pionic atoms into other atoms