Matter effects on the mixing of the neutrinos mass eigenstates, also know as the Mikheyev-Smirnov-Wolfenstein effect, seem to be well established in describing the propagation of the neutrino from the source to detecting devices. These effects were mostly considered in bulk matter, but not inside the atoms. Here we consider the effect of the high electron densities existing in the atomic nuclei. We investigate if these effects can affect the known neutrino phenomenology. It was reported that the mixing of the neutrino in high density matter, such as inside a supernova, can affect the Majoron decay probabilities. We investigate if the neutrino mixing effects in the high electron density inside the atomic nuclei can change the neutrinoless double beta decay half-life formula. In both cases we found that the standard results stand. The results look simple, but the road to them is complex and it opens the possibility that the neutrino mixing in atomic nuclei may affect other observables, such as the neutrinoless double beta Majoron decays.