My class has recently been studying gamma-ray coincidence and PET. Na-22 decays into $\beta^+$ (plus a neutrino), which then travels along in the material of a sample until it annihilates with an electron around one of the other atoms in the sample bulk. When that happens, two gamma rays are released at an energy of 0.511 MeV; they show up in a spectrum, can be used in coincidence tomography, etc.
These gamma rays are emitted back-to-back: this is because the primary source of energy for the coincident gamma rays is the rest mass energy of the electron and positron, not their pre-collision 3-momenta, because we are in a "low energy" situation. If we were to have a relatively high 3-momentum of the positron, the resultant gamma rays would be emitted at some angle deviating from $180^\circ$ to conserve 3-momentum.
The way this effect is presented is that this (high-energy situation) doesn't in fact happen naturally in Na-22: the gamma rays are emitted almost perfectly back-to-back, and this is the backbone of the entirety of PET. However, when I try to look up just much of a deviation can occur, it seems as though the (kinetic) energies of $\beta$ radiated out from Na-22 are in fact comparable to their rest masses ($\sim0.215$ MeV up to $1.820$ MeV from http://www.nucleide.org/DDEP_WG/Nuclides/Na-22_tables.pdf and http://nrv.jinr.ru/nrv/webnrv/map/nucleus.php?q=Na22 if I understand the sources correctly).
So what am I missing? Does the $\beta$ lose effectively all of its energy through other forms of radiation (Bramsstrahlung, etc.) before interacting with an electron? If so, why do we not observe it interacting "sooner"? Or am I confused about something more fundamental?