Pozitron-Electron interaction(anihilation)

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Homework Statement


A given pozitron with T kinetic energy is approaching an electron bound to a hard nucleus(in the K energy level, and the ionization energy for this level, Ek(>0), is given).
The energy of the two resulting photons is to be determined.


Homework Equations


Conservation of energy.

The Attempt at a Solution


So I wrote the conservation of energy as follows:
2m0c2 + T = 2ε + Ek ( ε is the energy of one photon )
Let me explain my way of thinking: After the anihilation, the electron has vanished, so the atom has become a ion(so it's energy has increased by Ek).

However, the proposers of the problem consider the conservation of energy as follows:
2m0c2 + T + Ek = 2ε;

So who is right?
 

Answers and Replies

  • #2
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If Ek is defined to be positive, it should be subtracted on the left side (or added on the right side).
Otherwise you can violate energy conservation: Take a free electron, let it get caught by a nucleus (emitting energy). Add a free positron, and get more than 2*511keV as energy => you gained the binding energy two times.
 

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