Basic physics of mixed electron-positron systems

1 Basic physics of mixed electron-positron systems 

The most interesting quantities of mixed systems that can be both calculated and measured today are binding energies, annihilation rates, and momentum distributions of the annihilation photons. A system has a binding energy in some state if it is chemically stable in that state, meaning that it stays in that state until it annihilates. More properly, we say that a system is chemically stable in some state if its annihilation rate is greater than the sum of the rates of all other processes that depopulate that state. 

Of course, all mixed systems are unstable in a broader sense because they ultimately annihilate. This implies that each pre-annihilation system is in reality a metastable state or a resonance embedded in a continuum that embraces one less electron, one less positron, and two or three more photons. If we perform calculations on the pre-annihilation system while ignoring the coupling to this continuum and then include the coupling as a second step in the calculation, our energies will be shifted and broadened on account of the coupling. Fortunately, the coupling is quite weak [2], and 

When an accurate wave function is calculated by some effective method, we can calculate an accurate annihilation rate with the use of an effective annihilation operator [5]  

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