Positrons and Cloud Chambers - HOW?

Question

Ok so as I understand it, cloud chambers function because the electrostatic forces generated by fast energetic charged particles interacting with (or colliding with) the molecules of gas in the chamber along its path strips the gas of electrons, with the resulting ions acting as nucleation sites for the supersaturated alcohol vapor to condense on. With an external magnetic field of a known strength and direction, the type/energy/charge/etc of the particle can be determined by the direction and radius of curvature, track length, etc.

In 1932, C.D. Anderson recorded the first proof of antimatter, capturing an image of what looked like an electron track, only curving in the opposite direction - a positron.

There have been many more images of antimatter tracks in cloud chambers, bubble chambers, ionization chambers, etc since then but my question is this:

HOW/WHY do we see a track AT ALL?

A particle track is on the order of several cm long meaning the energetic particle in question must interact/collide with a HUGE number of gas molecules along its path, and strongly enough to strip them of electrons, otherwise it wouldn’t leave a continuous track. This makes perfect sense for a normal-matter particle interacting with normal-matter gas molecules, and would make sense for an anti-matter particle interacting with anti-matter gas molecules, but for an anti-matter particle and normal-matter gas molecules? Why wouldn’t a positron passing through a chamber of normal-matter just annihilate with the first electron it encountered along its path? How could a positron interact with a full tracks worth of normal-matter molecules strongly enough to strip them of electrons them without annihilating?

Answer 1

The range at which the electric field of the positron interacts with matter (thus forming the track), is many magnitudes greater than the range at which it will interact with the matter itself and annihilate on contact.

Think of it like a rogue planet whizzing through the solar system. Its gravity will affect the whole system, disrupting orbits all over the place. But what's the chance of it actually meeting a planet and colliding? Very Very low.

Answer 2

The calculations of the crossection of electron-positron scattering need Feynman diagrams, but one can estimate it qualitatively, since we know that when the electron and positron are almost at rest, they form the positronium atom, where the positron has the role of the proton in the hydrogen atom.

As we know, for an electron to be captured by the proton potential and form hydrogen it should have zero momentum at the center of mass, and then it will start falling to lower energy levels releasing photons. The same is true for the positron to capture an electron and finally annihilate on it. As one sees a track for the positron, the momentum is so much higher than capture, that only elastic scattering at the center of mass "electron positron" can happen. In the lab frame the electrons form the dots in the chambers.

This is qualitative. If one went into the trouble of doing the Feynman diagram crossection calculations it is possible that a probability exists for annihilation even at the MeV energies of the tracks seen in the chambers, but it will be many orders of magnitude smaller than elastic.