  The nuclear aspects of flavour changing neutral current (FCNC) processes,
predicted by various new-physics models to occur in the presence of nuclei, are
examined by computing the relevant nuclear matrix elements within the context
of the quasi-particle RPA using realistic strong two-body forces. One of our
aims is to explore the role of the non-standard interactions (NSI) in the
leptonic sector and specifically: (i) in lepton flavour violating (LFV)
processes involving the neutral particles $\nu_\ell$ and $\tilde{\nu}_\ell$,
$\ell = e,\mu,\tau$ and (ii) in charged lepton flavour violating (cLFV)
processes involving the charged leptons $\ell^-$ or $\ell^+$. As concrete
nuclear systems we have chosen the stopping targets of $\mu^-\rightarrow e^-$
conversion experiments, i.e. the $^{48}\mathrm{Ti}$ nucleus of the PRIME/PRISM
experiment at J-PARC and the $^{27}\mathrm{Al}$ of the COMET at J-PARC as well
as of the Mu2e at Fermilab. These experiments have been designed to reduce the
single event sensitivity down to $10^{-16}$--$10^{-18}$ in searching for
charged lepton mixing events. Our goal is, by taking advantage of our detailed
nuclear structure calculations and using the present limits or the sensitivity
of the aforementioned exotic $\mu^- \rightarrow e^-$ experiments, to put
stringent constraints on the parameters of NSI Lagrangians.
