The dynamics of a quantum system with internal degrees of freedom undergoing spontaneous collapse in the position basis are analysed; e.g., neutral mesons or neutrinos. Surprisingly, the value of the Heaviside function θ(x) at x=0 that can in general be chosen in the interval [0,1] leads to different physical predictions. For the QMUPL (Quantum Mechanics with Universal Position Localization) model only a single value leads to probabilities conserving the particle number. Herewith the physical properties of the noise field can be constrained. This opens a road to study the physical properties of the noise field essential for collapse models.