  We study lepton number violating (LNV) process of muon-positron conversion in
nuclei mediated by the exchange of light and heavy Majorana neutrinos. Nuclear
structure calculations have been carried out for the case of experimentally
interesting nucleus 48Ti in the framework of renormalized proton-neutron
Quasiparticle Random Phase Approximation. We demonstrate that the imaginary
part of the amplitude of light Majorana neutrino exchange mechanism gives an
appreciable contribution to the muon-positron conversion rate. This specific
feature is absent in the allied case of neutrinoless double beta decay. Using
the present neutrino oscillations, tritium beta decay, accelerator and
cosmological data we derived the limits on the effective masses of light
<m>_{\mu e} and heavy <M_N^{-1}>_{\mu e} neutrinos. The expected rates of
muon-positron nuclear conversion, corresponding to these limits, were found to
be so small that even within a distant future the muon-positron conversion
experiments will hardly be able to detect the neutrino signal. Therefore,
searches for this LNV process can only rely on the presence of certain physics
beyond the trivial extension of the Standard Model by inclusion of massive
Majorana neutrinos.
