  The Mu2e and COMET collaborations will search for nucleus-catalyzed muon
conversion to positrons ($\mu^-\rightarrow e^+$) as a signal of lepton number
violation. A key background for this search is radiative muon capture where
either: 1) a real photon converts to an $e^+ e^-$ pair "externally" in
surrounding material, or 2) a virtual photon mediates the production of an
$e^+e^-$ pair "internally". If the $e^+$ has an energy approaching the signal
region then it can serve as an irreducible background. In this work we describe
how the near end-point internal positron spectrum can be related to the real
photon spectrum from the same nucleus, which encodes all non-trivial nuclear
physics.
