How do escape peaks from gamma rays occur in annihilation processes?

[Angelos K]

How do escape peaks occure?

I mean peaks originating from a gamma ray located at the Energy value of $$\ E_{peak} \equiv E_{gamma}-511KeV$$.

I read that an annihilation process takes place and one of the annihilation photons escapes detection.To arive at detecting an Energy of $$E_{peak}$$ the undetected annihilation photon must have had the energy of 511KeV.

Is there any reason why the particle system before annihilation (electron/positron) had a vanishing total momentum, so that two photons of 511KeV were emitted? Why did the incident photon interact with a nucleus in a way such that the produced particle/antiparticle pair had vanishing momentum?

I'd appreciate help.

 

[mfb]

The annihilation cross section is small at high energies, so most of the time positrons slow down in matter before annihilating.
PET scans use that, too - most of their photons are 511 keV and back-to-back, even though the original positron from beta decays can have a large momentum.