Two Questions About Positron/Electron Interactions

Having just read the outstanding biography of the great physicist who predicted the existence of the positron (The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom) and having also recently tried to digest the Wiki article on Positron Emission Tomography (PET scanning), I have a couple of basic questions about positron/electron interactions.

Question 1 - when a positron and an electron encounter each other, they are annihilated and photons are emitted (i.e. radiation). Is the frequency of this radiation the same for all positron/electron collision-annihilations? Or does it depend on the energy of the positron/electron pair at the moment of their encounter (or maybe something else)?

Question 2 - how “close” to each other do the positron and electron have to be in order to interact and annihilate? Or does their “successful” interaction depend on factors other than their distance from each other, e.g. angle of approach, their momentum, etc.?

Thanks!

The answer to question one is that the resulting gamma photons always have an energy of 512 KEV.

Why do electrons and positrons annihilate each other?

A positron is an anti-electron. Matter + Antimatter = BOOM.

Excellent. Now I can ask my follow-up question.

In PET scanning why is it so critical, then, to record only temporally coincident photons (at 512 KeV)? Given that their frequency is always going to be fixed (i.e. corresponding to 512 KeV), why can’t you simply tune in to that frequency and ignore all others. Wouldn’t it then be the case that a photon arriving at the detector, and having that unique frequency, has come from the PET scanner? In other words, why fiddle with timing-based detection, when frequency-based would (seem) to do?

Thanks!

  1. The energy of their combined rest mass is 512 Kev, but if they collided with more energy than that there could be other particles (like in a Lepton linear accelerator).

2… In principle electrons and positrons could react at any distance but in practice the chance of their doing so (dictated by quantum physics) drops off to practically zero at distances much greater than their effective wavelength.

  1. Gamma-ray photons aren’t really focusible so imaging with them is a challenge. I believe the timing-based dectection is part of that.

Also, with all due respect to Dirac, I had always read that what he “predicted” was particle-pair production out of the vacuum, rather than the positron as a real particle with positive mass/energy. Slightly different concepts.

Thanks for your very helpful answers.

With respect to Dirac, you are absolutely right. I phrased my “introduction” in the OP the way I did out of laziness.

Too slow a typist to add this as an edit.

Of course, I have a f/u question now that you’ve answered #2 above: given that they only interact when VERY close, I would expect a positron would have to go a LONG way to have a good chance of “finding” an electron with which to interact. Wouldn’t that mean it might often pass right through someone before that happened, and hence not be a useful event re: PET scans (and make the process inefficient? (let alone send positrons flying all over)

I wasn’t clear. I do understand that part. I’m asking more generally why matter and antimatter annihilate each other.

The detectors and electronics have noise. That is, just because they fired does not mean a gamma ray actually went through them. Looking for two coincident signals gives you a much better signal to noise ratio than looking to see if a single detector fired.

Also, the detectors don’t individually provide direction information, which is needed to reconstruct the image. The beauty of the anihillation is that the two photons travel along pretty much a straight line, so when you see the two detection events you can draw a line between the two detectors, and thus start to construct an image of emmision density. Without the timing you would not know which events were paired - and thus would be unable to create a tomographic image. Faster detectors can get some estimate of time of flight as well, which helps improve things a bit - but the primary information that allows image reconstruction is the ability to pair up detection events.

Precisely!

The whole point of PET is to determine the line on which the annihilation occurred and from many events tomographically reconstruct the site of origin.

Question 1: Yes, it depends on the energy of the collision. The total energy of the two gamma rays has to equal twice the rest energy of an electron (512 keV) plus the collision energy. In PET, the collision energy is much smaller than the rest energy, and to conserve momentum, the two photons must have the same energy, i.e. ~512 keV.

Question 2: The cross section for the interaction (essentially the square of “how close they have to come”) is a function of the collision energy. If the relative speed is high, they better hit very close to each other. If the electron and positron start at rest, their electric attraction will eventually cause them to interact and annihilate.

Thanks for all your excellent answers. Things make much more sense now.