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The nuclear aspects of flavour changing neutral current (FCNC) processes,predicted by various new-physics models to occur in the presence of nuclei, areexamined by computing the relevant nuclear matrix elements within the contextof the quasi-particle RPA using realistic strong two-body forces. One of ouraims is to explore the role of the non-standard interactions (NSI) in theleptonic 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 concretenuclear systems we have chosen the stopping targets of $\mu^-\rightarrow e^-$conversion experiments, i.e. the $^{48}\mathrm{Ti}$ nucleus of the PRIME/PRISMexperiment at J-PARC and the $^{27}\mathrm{Al}$ of the COMET at J-PARC as wellas of the Mu2e at Fermilab. These experiments have been designed to reduce thesingle event sensitivity down to $10^{-16}$--$10^{-18}$ in searching forcharged lepton mixing events. Our goal is, by taking advantage of our detailednuclear structure calculations and using the present limits or the sensitivityof the aforementioned exotic $\mu^- \rightarrow e^-$ experiments, to putstringent constraints on the parameters of NSI Lagrangians.

Nuclear aspects of neutral current non-standard $\nu$-nucleus reactions and the role of the exotic $\mu^-\to e^{-}$ transitions experimental limits