  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 $\theta(x)$ 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.
