system
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human
What happens when an electron hits a positron when they both have different momentum?

I know that after the annihilation when they have the same momentum, or no momentum there are 2 photons emmited in 2 different directions, due to conservation of momentum, but what happens when they hit eachother with different momentums?
Will they be emmited at an angle other than 180deg to each other, or will one have higher frequency than the other, or something completely different?
gpt
There are a number of possible processes that can happen, regardless of their momenta.

At high energies, they will just scatter elastically off of each other. This is called Bhabha scattering.

At lower energies, they can combine to form a bound system called positronium, which will eventually decay, or they can just annihilate each other outright.

The probability that they annihilate is largest when they are not moving relative to each other.