Horizon Quantum Mechanics of collapsing shells

We study the probability that a horizon appears when concentric shells of matter collide, by computing the horizon wave-function of the system. We mostly consider the collision of two ultra-relativistic shells, both shrinking and expanding, at the moment their radii are equal, and find a probability that the system is a black hole which is in qualitative agreement with what one would expect according to the hoop conjecture and the uncertainty principle of quantum physics, and parallels the results obtained for simpler sources. One new feature however emerges, in that this probability shows a modulation with the momenta of the shells and the radius at which the shells collide, as a manifestation of quantum mechanical interference. Finally, we also consider the case of one light shell collapsing into a larger central mass.