  A detailed study of the muonic analogue of neutrinoless double beta decay,
(muon^-,muon^+) conversion, has been carried out for the A=44 nuclear system.
We studied several lepton number violating (LNV) mechanisms potentially
triggering this process: exchange by light and heavy Majorana neutrinos as well
as exchange by supersymmetric particles participating in R-parity violating
interactions. The nuclear structure has been taken into account within the
renormalized Quasiparticle Random Phase Approximation method. To our knowledge,
this is the first realistic treatment of nuclear structure aspects of the
(muon^-,muon^+) conversion. We estimated the rate of this process utilizing the
existing experimental constraints on the parameters of the underlying LNV
interactions and conclude that the (muon^-,muon^+) conversion is hardly
detectable in the near future experiments.
