Year: 1995
Type: article
Abstract: The rates of weak transitions between electromagnetic bound states, for example, (${\mathrm{\ensuremath{\pi}}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$)\ensuremath{\rightarrow}(${\mathrm{\ensuremath{\mu}}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$)${\ensuremath{\nu}}_{\mathrm{\ensuremath{\mu}}}$, and the exclusive weak decay of a muonic atom into an electronic atom, (Z${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$)\ensuremath{\rightarrow}(${\mathit{Ze}}^{\mathrm{\ensuremath{-}}}$)${\ensuremath{\nu}}_{\mathrm{\ensuremath{\mu}}}$\ensuremath{\nu}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{e}}$, are calculated. For Z=80, relativistic effects are shown to increase the latter rate by a factor of 50 compared to the results of a nonrelativistic calculation. It is argued that the conditions for producing the muonic decay in neon gas (Z=10), where the branching ratio for the decay per captured muon is 1.7\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$, can be realized using cyclotron traps, though the prospect for a practical experiment seems remote. In lead the same ratio would be approximately \ensuremath{\sim}1\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$. In addition to providing detailed information on the high momentum tail of the wave functions in atomic physics, these decays of QED bound states provide a simple toy model for investigating kinematically analogous situations in exclusive heavy hadronic decays in quantum chromodynamics, such as B\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{*}}$\ensuremath{\gamma} or B\ensuremath{\rightarrow}\ensuremath{\pi}e\ensuremath{\nu}.
Authors: C. Greub, D. Wyler, S. J. Brodsky, C. T. Munger
Institutions: University of Zurich, Institute for Theoretical Physics
Language: English
Topic: Atomic and Molecular Physics
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2051823856