And Big Apple Splits...

And this is how a big particle might split,

The resulting smaller particles spin in opposite sense.  One of the particle spins in increasing radius because the particles interact as particles and repel each other.  The initial split to a distance beyond their interaction as waves could occur with the impact of a photon with one of the particles (in the big particle).

With

$F_{\rho}=tanh(x)$,

the split occurs beyond,

$x=\pi$

exactly.

Have a nice day.