Re: Why does Positronium decay via the particles spiraling into eachother?

Some people call positronium an "atom", since it really does behave just like a weird ultralight atom: a positive positron (instead of a nucleus) with a negative electron orbiting it. So, you're right! It really does behave exactly like an atom, with strictly quantized energy levels of different shapes and sizes.

Just like in ordinary atoms, the electron and positron actually exist in fuzzy "wavefunctions", blurry clouds of probability-density, which define where the particle is likely (or unlikely) to be found. For any particular energy level, you can figure out the probability for the two particles to be very close to each other, or very far apart, or whatever. In an atom, for example, there's always a small probability that an electron is actually inside of the nucleus, instead of orbiting outside of it. In some atoms, this enables something called a "K-capture" decay, in which an electron crashes into a proton and turns it into a neutron.

Anyway, the electron and positron are unlikely to annihilate unless they are very close together. This is most probable when the "positronium atom" is in its lowest-energy state. Therefore, if you create a positronium atom in some high-energy state, it will fall into lower and lower energy states, step by step, while emitting photons. This is exactly how an ordinary atom loses energy! (It cannot annihilate while in the high-energy states, since the electron and positron tend to be far apart.) When the positronium reaches its lowest energy level, the two particles are likely to find themselves close together, and they can finally annihilate.

You can see why this is sometimes described as "spiraling in"! But it is indeed not quite accurate.

There are also some "spin" considerations; you start with two particles with spin=1/2, trapped in energy levels with spin=0, or 1, or 2,3,4,etc., and the final state (two photons from the annihilation) consists of two particles each with spin=1, and the decay has to conserve angular momentum. These considerations make it even more difficult for positronium to annihilate from something other than the ground state.

Hope this helps!

-Ben Monreal