Originally posted by sonhouse
So if an anti and a regular come together, it's just a matter of the exact closure velocities and the exact angle of the path. Sometimes the kinetic energy is enough to overcome nuclear forces and they collide to make a gamma but sometimes a slightly deflected angle of closure and just the right kinetic energy will allow quantum forces to take over and 'orb ...[text shortened]... s and what makes them all have the same decay time, like this hydride at half a nanosecond.
Positronium is a short-lived particle, with a lifetime in the region of picoseconds (I think, I cant remember the exact timescale off the top of my head - it may even be as long as microseconds), anyway, it is a split second timescale.
However, it has been studied and its energy levels have been observed to match with predicted levels. The different spin states have also been observed, by means of observed the mean decay rate. Different spin total spin states allow "singlet" and "triplet" states as it can have a spin of either 0 or +1. Parallel spins decay at different rates to antiparalell spins.
You're questions about what governs the lifetimes of particle is very interesting indeed. It has to do with the forces involved. There are 4 fundamental forces in the universe; gravity, coloumb (charge), strong nuclear, and weak nuclear.
Different particles interact via different forces, or a combination of forces. For example, leptons do not feel the Strong nuclear force, they only interact via the Weak force and Gravity. Only charged paricles interact via coloumb forces etc...
We must make the distinction between fundamental particles and composite particles. The nuclei of particles are COMPOSITE, they are made of many fundamental particles. Fundamental particles (like protons, electrons) are not made of anything smaller (forget about quarks for this discription, and just assume that quarks are fundamental, it is not certain they are but that doesnt matter here).
FUNDAMENTAL PARTICLES:
The decay rate (and thus lifetime) of these particles is goverent by the number of possible decay paths they have and the strength of the forces involved in each path. Each of the 4 forces have an assocated strength, and a coefficent of reaction that has been experimentally determined. A particle with many decay paths (like a high energy electron, which can decay into any of the lepton pairs) will decay faster then one which has less decay paths. Each of the paths is weighted by the strength of the force that governs that particular interaction. The strength of the forces, in decreasing order is: Strong, Coloumb, Weak, Gravity. So decay paths involving Strong force have a higher probability of happening then ones what involve the Weak force.
COMPOSITE PARTICLES:
The life time of Nuclei is a bit more complicated. The nucleus can be modeled a bit like a water droplet, with terms analogous to surface tension and internal pressure, but there are some quantum terms in the equations which have no classical analogy. The stability of the nucleus is governed by its internal energy and the energy per nucleon (proton of neutron). Imagin there is a large nucleus. There may be a combination of two smaller nuclei that can be made from the large nucleu's nucleons. If the two smaller nuclei have a lower combined internal energy then it is energetically favourable for the large particle to decay. The rate of decay depends on the difference between the total energy of the possible states and the energy avilable to the particle to decay.
Sorry if this is a bit muddled, I hope it is helpful ๐