line of table I, the error due to the ultra-relativistic approximation is bigger. This is the reason why we did not make such an approximation.

                       cosmogenic               solar                laboratory
  -------------- ---------------------- ---------------------- ----------------------
      E(eV)            $10^{19}$               $10^{6}$              $10^{10}$
       t(s)       $3.15\times10^{18}$       $5\times10^2$       $2,13\times10^{-2}$
   $\xi_{ij} t$   $2.31\times10^{-55}$   $3.66\times10^{-45}$   $1.56\times10^{-57}$

  : We consider three types of neutrinos: cosmogenic, solar and laboratory neutrinos. For each type, the table shows: the typical order of magnitude of the energies (first line), the time of flight (second line) and the damping factor as predicted by the mass proportional CSL model (third line).

Comparison with the Diosi-Penrose gravity-induced collapse model
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As mentioned in the introduction, the damping of neutrino oscillations due to gravitational collapse, as described by the Diosi-Penrose model, was first studied in [@Ch]. In this work, the author argued that the decaying factor (the analog of $\xi_{jk} t$ for the CSL model) has the following form: $$\Lambda_{G}^{j,k}\equiv \int_{D}^{L}\triangle E_{G}^{j,k}\left(L'\right)dL'\,,$$ where $D$ is the distance such that $\triangle E_{G}^{j,k}\left(D\right)=0$, $L$ is the distance traveled by the neutrino, and $$\triangle E_{G}^{j,k}=4\pi\bar{\xi}\int\int\frac{\left[\rho_{j}\left(\mathbf{r}\right)-\rho_{k}\left(\mathbf{r}\right)\right]\left[\rho_{j}\left(\mathbf{r}'\right)-\rho_{k}\left(\mathbf{r}'\right)\right]}{\left|\mathbf{r}-\mathbf{r}'\right|}d\mathbf{r}d\mathbf{r}'\,,$$ where $\bar{\xi}$ is a parameter that we will set equal to $-G$, with $G$ the gravitational constant, like in the original paper by Penrose [@Pd1]. Moreover, $\rho_{1}\left(\mathbf{r}\right)$ and 