is the initial energy of the neutrino in the mass eigenstate with mass $m_k$, and: $$\label{eq:xi}
\xi_{jk} \; \equiv \;  \frac{\gamma}{16\pi^{3/2}r_{C}^{3}m_{0}^{2}c^{4}}\left(\frac{m_{j}^{2}c^{4}}{E_{i}^{\left(j\right)}}-\frac{m_{k}^{2}c^{4}}{E_{i}^{\left(k\right)}}\right)^{2}$$ is the decay-rate of neutrino oscillations, as predicted by collapse models. Note that the frequency of the oscillations is the same as the one predicted by quantum mechanics[^1]. The prediction of the CSL model differs from the standard formula only for a damping factor in front of the oscillating term, with a decay rate given by Eq. . Eqs.  and , which will be derived in Sections V-VIII are significant because they allow to precisely quantify the collapse effect on neutrino oscillations. Since collapse master equations have the same structure as decoherence master equations for open quantum systems, it does not come as a surprise that Eq.  is in agreement with general arguments, which fix the form that the damping terms coming from decoherence effect should take [@floreanini; @deco1; @deco2].

Having the above equations at hand, we can give a quantitative estimate the CSL effect on neutrino oscillations, by computing the damping factor in Eq. . We consider the stronger value $\gamma\simeq \; 10^{-22}\text{cm}^{3}\text{s}^{-1}$ for the collapse parameter, suggested in [@adlerphoto]. Substituting the numeric values of the constants in 