Antimatter and bubble chambers?

Why should there be immediate annihilation? Or more quantitatively, how "immediate" do you think it should be, and why? (Remember, if it lasts a microsecond, it will travel 1000 feet)

 

You are right this does seem difficult to google. I thought about just writing down the cross section for e+e- to two photons, but actually I am not sure that that captures everything since at low energies the e+e- pair usually form the bound state positronium before they annihilate. I also seem to recall there is a thing called the "impact parameter", b, which gives the cross-section a dependence which I think is something like [itex]e^{-b.k}[/itex], so that it goes down as the impact is less "head on" and as the momentum goes up. That doesn't give any hint of the scale that matters though. Also I think it is for two approximately plane wave initial states, which is probably not very reasonable if the target electrons are bound in atoms.

But the overall picture is that the positrons are not very likely to annihilate while they are fast-moving, they need to slow down first by scattering off things.