Almanzo said:
Its probability of doing so would be the cross section of the particles divided by the cross section of the atom. Roughly 1/100.000 squared or one in ten billion.
That would be a very high cross section, and if that were the case, then, per astrophysical argument, not just all neutron stars, but probably even all asteroids would already have been transformed into black holes. First of all, it is usually wrong to use the "geometrical" cross sections for this kind of interactions, but even then, you took the geometrical cross section of the nucleus (which is of the order of a 1 fm) - while you should take the geometrical cross section of the black hole - which is of the order of 10^-30 m (I should check but it is the Schwarzschild radius of the mass of 10 000 protons). Now, that gives you a tiny surface: about 30 orders of magnitude smaller than the nucleus surface. So if we can use geometrical arguments, it should interact about 10^30 times less than your estimation here. That said, we don't know what is the real cross section of a micro BH, because in order to even create one at the very low LHC energies (for gravitational phenomena), spacetime has to be very special, and theoretical speculation is abound.
So it might be as large as you say. Or it might be even much smaller than I say. Anyone's bet is ok. In fact, we have no theoretical model of such a BH at all, because all theoretical BH we know should emit Hawking radiation.
Also, your argument about it being charged and hence gobbling up the whole atom is not correct. It would simply become an ionizing particle. Otherwise, your argument would also stop any possibility of ionizing an atom with any radiation, as the "rest of the charge would follow". But again, it might be possible for very peculiar BH (as they aren't of the kind theorists have thought up, everything is possible now).
To devour one atom it would have to pass through ten billion layers of atoms, or roughly 10 centimeters of solid material. Passing once through the Earth, say ten thousand kilometers of material, it would devour one hundred million atoms, and multiply its original mass by ten thousand. If it started at nearly lightspeed, it would still have a speed larger than 10 km/s. But if it started at nonrelativistic speed, it might not re-emerge.
Again, if it had such enormous cross section in its interaction with matter, any such freely traveling BH would immediately transform each stellar body into a BH. We wouldn't be here in the first place.
EDIT: ah, I think I see your argument now: you seem to think that if a BH crosses a nucleus, it "must" absorb it, no matter how small the hole. But on the BH's scale, the nucleus is not a "massive filled thing", in the same way as for a fast electron, the atom is not a massive filled thing".
What you estimated was roughly the probability of a NEUTRON to interact in matter.
be my guest !