"When a positron emitted in beta+ decay annihilates with an electron, the combined mass of the two particles, m = 2me, is converted into an amount of energy 2mec^2 in the form of two 511 keV gamma rays. Momentum conservation requires that the two gamma ray photons are emitted in opposite directions from the point of annihilation. Positron emission tomography exploits the fact that the detection of two oppositely-directed gamma rays defines a line on which the point of annihilation occurs."(adsbygoogle = window.adsbygoogle || []).push({});

I haven't put this in college homework because this was just a side note in my textbook and is not something I imagine I will get asked about. As such, I imagine there are some details skimmed over. What these are will hopefully get cleared up with answers to the following questions. I'm an undergrad, and we've only studied QM to a relatively low level, so please don't baffle me with stuff there's no chance I'll understand.

1. If the total momentum of the photons MUST be zero, then the total momentum of the electron-positron pair must also be zero. Why do such pairs only annihilate when they have equal and opposite momenta? What would happen if an electron and positron met with unequal momenta, either in magnitude or direction?

2. If the total momentum of the pair must be equal and opposite, and we can determine the position of annihilation from the trajectories of the photons, where is the uncertainty?

3. Presupposing an answer to the last question, I assume that proximity, and so precise position, is not an issue for pair annihilation, and that maybe the pair will annihilate if they are in the same quantum state. If so, what is the meaning of the point of annihilation?

Thanks to all in advance.

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# Conservation of momentum and HUP in PET

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