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When an electron and a positron meet, they annihilate each other, converting into two gamma rays. Unless all of them hit in a straight line (very unlikely), they should emit Bremsstrahlung before the collision, but I think this is not observed. Can someone explain why the Bremsstrahlung is missing?

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  • $\begingroup$ Would be hard to measure against the background of Compton radiation from the annihilation gammas. $\endgroup$ – Pieter Feb 13 '18 at 12:01
  • $\begingroup$ Any spectrometer should be able to distinguish the gamma rays from other radiation. Why should this be hard? $\endgroup$ – Johannes Maria Frank Feb 13 '18 at 12:37
  • $\begingroup$ Because of the overlap with the Compton continuum caused by the annihilation gammas. At te same energy, spectroscopy cannot help you to distinguish these from a bremsstrahlung continuum. $\endgroup$ – Pieter Feb 13 '18 at 12:47
  • $\begingroup$ Even if this is the case, the Bremsstrahlung should be emitted before the gamma rays are emitted. Thus it should be detectable. $\endgroup$ – Johannes Maria Frank Feb 13 '18 at 12:50
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Thinking of the interaction in terms of Bremsstralung is equivalent to treating each particle as acting independently in an external field, but as the particle interact under the field of their partner a better point of view is to consider the system as (excited or even unbound) state of positronium.

That is the dynamics of the system is better understood in terms of the relaxation of excited atomic states. And indeed the atomic spectrum of positronium can be measured.

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  • $\begingroup$ This is an interesting one. It would imply almost every annihilation is preceded by a Positronium. And the spectrum of this should be detectable. Do we actually see this? $\endgroup$ – Johannes Maria Frank Feb 13 '18 at 15:43
  • $\begingroup$ @JohannesMariaFrank No. This is shown by the angular correlation of the gammas (ACAR). This is a way to measure electron momentum distributions in solids. For example the Fermi surface of metals. $\endgroup$ – Pieter Feb 13 '18 at 18:44
  • $\begingroup$ @Pieter I appreciate your answers, but they miss the point. We are talking on effects BEFORE the annihilation and not after. Also I asked if we actually see the spectrum of the Positron, which is also referring to BEFORE the annihilation. You also pull the compton continuum out of your hat, but this isn't even referenced in the standard wikipedia article. You are welcome to amend the article or be a little more verbose. $\endgroup$ – Johannes Maria Frank Feb 13 '18 at 19:37
  • $\begingroup$ @dmckee Thank you for pointing me to the Positronium. But it only adds more questions to the question. What is happening before the annihilation. If we think in terms of relaxation we should see a spectrum. If we think in isolated particles we should see Bremsstrahlung. So before the gamma rays, there should be something. Just changing the vantage point does not change the facts. So do we see something before the annihilation and if not why? $\endgroup$ – Johannes Maria Frank Feb 13 '18 at 19:46
  • $\begingroup$ @JohannesMariaFrank My understanding is that observing the Rydberg spectrum of positronium is a tricky measurement, but it has certainly been done. But you shouldn't think that there is some fixed set of decay steps that must occur before annihilation. The hydrogen-like wave-function is non-zero for zero separation in all s-states, which means that annihilation can occur for any value of $n$ or even for an un-bound pair. $\endgroup$ – dmckee Feb 13 '18 at 19:47

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