Continuity-equation constraint in the two-vertex nuclear processes: Radiative muon capture on ¹⁶O and ⁴⁰Ca

Abstract

A modified form of the impulse-approximation effective hamiltonian of the nuclear radiative muon capture (RMC) is developed. In the derivation we have used the electromagnetic current-continuity equation; the procedure is actually an extension for the nonzero momentum transfer of the Siegert theorem. Radiative capture rates and spectra of the emitted photons for RMC on ¹⁶O and ⁴⁰Ca are analysed by using the nuclear shell-model wave functions for the calculation of the partial RMC transition rates. The spectra obtained are strongly reduced in comparison with the standard impulse-approximation calculations and agree with the phenomenological results. The main contradiction of recent RMC theoretical works has been resolved in this way.