A Query about Pair Production and Electron-Positron Annihilation

[Cambienta]

After an electron-positron pair is produced by a high-energy photon hitting the nucleus of an atom, is it possible for the produced positron to annihilate with a bound electron from the very same atom it was produced in? In this situation, what would happen to the produced electron--would it be captured by the atom to replace the lost electron?

I've been wondering about this for a while, and I've only ever been able to reason that the first scenario would be possible under extremely rare circumstances. Really rare. But I'm not entirely sure that such a thing would be possible under ANY circumstances. I've asked around and done searches, but have only been able to find that it is possible for a positron to annihilate with a bound electron, and that the produced particles don't necessarily have to annihilate with each other, not necessarily that the two processes can be linked and occur subsequently.

I'm wondering what you all might think on the matter?

 

[Spinnor]

After an electron-positron pair is produced by a high-energy photon hitting the nucleus of an atom, is it possible for the produced positron to annihilate with a bound electron from the very same atom it was produced in? In this situation, what would happen to the produced electron--would it be captured by the atom to replace the lost electron?

I've been wondering about this for a while, and I've only ever been able to reason that the first scenario would be possible under extremely rare circumstances. Really rare. But I'm not entirely sure that such a thing would be possible under ANY circumstances. I've asked around and done searches, but have only been able to find that it is possible for a positron to annihilate with a bound electron, and that the produced particles don't necessarily have to annihilate with each other, not necessarily that the two processes can be linked and occur subsequently.

I'm wondering what you all might think on the matter?

Draw the Feynman Diagrams for both cases, they are not the same, one is more complected, less probable?

On the other hand a large Z atom will have lots of electrons which increases likelihood of the more complicated event?

 

[bcrowell]

The half-life of positronium is on the order of nanoseconds or longer. In a nanosecond, a relativistic electron will travel ~10 cm. Since this is 10^9 times greater than the size of an atom, I would think that the probability of annihilation before it left the vicinity of the original atom would be on the order of 10^-9.

 

[Bob S]

After an electron-positron pair is produced by a high-energy photon hitting the nucleus of an atom, is it possible for the produced positron to annihilate with a bound electron from the very same atom it was produced in? In this situation, what would happen to the produced electron--would it be captured by the atom to replace the lost electron?

Sure. Why not. The probability of positron annihilation in flight is plotted on page 385 of Heitler "Quantum Theory of Radiation" 3rd edition. Also read Section 27 on page 268. The atomic electron is close by, so it could annihilate in the same atom. It is not necessary to stop positrons and create positronium for them to annihilate. The other electron is going too fast to get captured in an atomic bound state.
Bob S

 

[Cambienta]

Thanks! Gosh, I thought I'd replied to this. I really appreciate the answers. Bob, I picked up the book you mentioned (I found it quite cheap online), and it's been helpful.

Thank you again for your replies.