\, .$$

Attention is needed when deriving the TCS for the scattering of neutrini of the same flavour from the result of Eq. (\[eq:EQ160\]). Owing to the fact that the final state comprises indistinguishable particles, the integration of the DCS between the $\theta$ limits of $0$ and $\pi$ yields an erroneous result! The outgoing particles are indistinguishable and it is fallacious to attach labels to them [^2], e.g., by identifying particle (1) as the one scattered at angle $\theta$ and particle (2) as the one scattered at $\pi-\theta$. The indistinguishability of the particles in the final state requires that the integration be performed over the solid angle of $2 \pi$, i.e., over a hemisphere, thus yielding the TCS result $$\sigma_{\rm tot} = \sigma_0 \, \, \, .$$

To be able to compare the DCS of this section with those obtained for the other neutrino-induced processes, one may proceed in either of two ways:

-   by making use of the DCS of Eq. (\[eq:EQ160\]), also bearing in mind that the corresponding TCS must involve an integration over a hemisphere,

-   by halving the DCS of Eq. (\[eq:EQ160\]) and integrating over $4 \pi$.

I will follow the latter option. Of course, all 