Nuclear Excitation by Free Muon Capture

Several ingredients have to come together for the NEEC process to occur and to be efficient: (i) the presence of vacancies in which the capture can occur; (ii) a good match between atomic binding energies and nuclear transition energies (i.e., \(E_\textrm{b}\sim E_\textrm{n}\) ); and (iii) a significant overlap between bound and continuum wavefunctions. While the first (i) and third (iii) requirements can be considered somewhat accessible, the range of nuclear levels efficiently reachable through NEEC is limited by the K-shell binding energy of a given nuclide. This is due to the inverse proportionality of the NEEC cross-section with the energy of the free particle that has to be captured, that is \(\sigma _\textrm{NEEC}\propto \nicefrac {1}{(E_\textrm{n}-E_\textrm{b})}\) . Considering that \(E_\textrm{b}^\textrm{K}\) is approximately \( {110\,\mathrm{\text {k}\text {eV}}}\) for \(Z=90\) , it becomes increasingly less probable to excite nuclear levels substantially higher in energy due to the growing energy mismatch. Moreover, \(~{100\,\mathrm{\text {k}\text {eV}}}\) nuclear transitions could already be very challenging to achieve for much lighter atoms.