Calculation of muonic Coulomb-capture probabilities from electron binding energies

Muonic Coulomb-capture probabilities are calculated assuming that electrons with binding energies less than a given limit (about 80 eV) contribute with a weight which is a function of the electron binding energy, the electron quantum numbers $n$ and $l$, and $Z$. This functional dependence is suggested by a quantum-mechanical calculation. By fitting few free parameters, good agreement with experimental capture probabilities is obtained; in particular, the periodicity with $Z$ of these values is well reproduced.