collapse of the wave function. The fact that the collapse mechanism acts on the spatial part of the wave function implies that we have to consider the whole Hilbert space of the system, not just the part related to the flavour degrees of freedom. Technical details about this issue are given in Sec.V.

The paper is organized as follows: in Section II we state the main result of the computation and quantify the damping of neutrino oscillation, as predicted by the mass proportional CSL model. In Section III we compare our result with that of [@Ch]. In Section IV we discuss decoherence effects on neutrino oscillation and compare them with the collapse effects. The remaining sections of the paper are devoted to computing the formulas, which are used in Section II.

The CSL prediction for neutrino oscillation
===========================================

According to the mass proportional CSL model, the transition probability of finding a neutrino in a flavour eigenstate $\beta$, when it was initially in the flavour state $\alpha$, is: $$\label{eq:dfggkdse}
P_{\alpha\rightarrow\beta}
=
\sum_{k=1}^{n}\text{U}_{\alpha k}\text{U}_{\beta k}\text{U}_{\alpha k}\text{U}_{\beta k}+\sum_{{k \neq j}}^{n}\text{U}_{\alpha k}\text{U}_{\beta k}\text{U}_{\alpha j}\text{U}_{\beta j} \; e^{-\xi_{jk}t} \; \cos\left[\frac{1}{\hbar}(E_{i}^{\left(k\right)}-E_{i}^{\left(j\right)})t\right].$$ $\text{U}$ is the $n\times n$ mixing matrix, which relates the flavour and mass bases, $E_i^{(k)}$ 