a finite radius $R$. In [@Dg] it was proposed to take $R \sim 10^{-15}$m, i.e. the nuclear size. However in [@Gpd] it was shown that also in this case the model is consistent with known facts (the energy increase of isolated systems, due to the collapse, is too large), and proposed a much larger radius, namely $R \sim 10^{-5}$cm, in order to restore compatibility. On the contrary, in [@Ch] the radius ($a_j$, according to the paper’s notation) $R \sim G_F m / \hbar^2 \sim 10^{-31\pm1}$m (where the uncertainty depends on the chosen value for the neutrino’s mass) was considered. This cutoff is too small, therefore the result cannot be trusted.

Decoherence effects
===================

While traveling through the Universe and in particular through the atmosphere, neutrinos interact with the surrounding environment and scatter with other particles, mainly protons, electrons and other neutrinos. These interactions give rise to decoherence effects which also modify neutrino oscillations. Since protons interact with neutrinos only via the neutral weak current, both neutrino families[^2] are affected in the same way by this kind of interaction and neutrino oscillations are not modified. Unlike protons, electrons and neutrinos interact with the incoming neutrino both via neutral and charged weak 