# 1-photon emission possible from electron-positron annihilation?

• B
• Puffer Fish
In summary, the result of electron-positron annihilation can be either one photon or three photons, depending on the spin orientation of the particles before the annihilation.
Puffer Fish
I was reading about electron-positron annihilation. Typically it results in two photons, each with an energy of 511 keV, that go shooting out in opposite directions. But I read that in some instances three photons can result. Electrons have an intrinsic spin of ½, while photons have a spin of 1. So if the electron and positron have spins of +½ and -½, you will get two photons with spins +1 and -1. If, on the other hand, the electron and positron have the same spin orientation, say +½ and +½, then three photons will result, with spins +1, +1, and -1.

Well what I’m wondering is, is it possible for only one photon to result from an electron-positron annihilation? This outcome could still abide by the laws of spin conservation. Suppose the positron was traveling with a kinetic energy of 600 keV, and then a faster moving electron was shot from directly behind, say with a kinetic energy of 1.2 MeV, on an intercept course to annihilate with it. Because the kinetic energy of the system outweighs the rest masses of the two particles, any resulting photons from the annihilation would be directed in the forward vector.

You might also have to magnetically polarize the particles before shooting them out, to make sure they had the proper spin orientation for an odd-number multiple photon creation.

I thought about this and I am thinking what would tend to happen is you would have a cone of radiation with a specifically defined angle of emission. But as the kinetic energy was increased, the angle would become narrower and narrower until coherence effects started to predominate. Obviously at some extreme narrow angle you can’t have multiple photons streaming out from the same annihilation point, or at least that’s not statistically favorable.

Puffer Fish said:
I read that in some instances three photons can result.

Puffer Fish said:
Well what I’m wondering is, is it possible for only one photon to result from an electron-positron annihilation?

This is not possible, as energy-momentum cannot be conserved in this case. See, for example:

https://en.wikipedia.org/wiki/Electron–positron_annihilation

Dale
Puffer Fish said:
is it possible for only one photon to result from an electron-positron annihilation?

No. It is impossible for such a process to conserve both energy and momentum.

PeterDonis said:
No. It is impossible for such a process to conserve both energy and momentum.
Can you explain why it would be impossible?

I do not see why it would not be possible under these special conditions.

The outgoing particle will still have the same overall vector and energy of the two beginning particles.

Unless I'm missing something very obvious, it seems both of your answers are very lazy and you didn't bother to really stop for more than a moment to think about this.

Puffer Fish said:
The outgoing particle will still have the same overall vector and energy of the two beginning particles.
Not in the centre-of-momentum frame of the original particles!

This question, as an exercise for the student, is in most textbooks on Special Relativity.

PeroK said:
Not in the centre-of-momentum frame of the original particles!
I wonder though, is it possible to have a different outcome depending on the reference frame?

It's well established in quantum theory that two different outcomes can simultaneously occur and it depends on your reference frame.

Puffer Fish said:
I wonder though, is it possible to have a different outcome depending on the reference frame?
There is either one resultant photon or two. A change of reference frame can't change that.

PeroK said:
There is either one resultant photon or two. A change of reference frame can't change that.
A correction to your statement: You mean one photon or three. Remember the spin polarization in this situation.

Puffer Fish said:
The outgoing particle will still have the same overall vector and energy of the two beginning particles.
If it did then it would also have the same mass as the system of the two original particles together.

Dale said:
If it did then it would also have the same mass as the two original particles.
How does that mean anything?

That would be the same case in normal annihilation too.

Yes, obviously the energy of the outgoing photon would be the same sum as the input in rest mass plus the energy of velocity of the two ingoing particles.

Puffer Fish said:
A correction to your statement: You mean one photon or three. Remember the spin polarization in this situation.
Okay, I meant whether there is one photon or not is an invariant outcome of the experiment.

Well, as many people said, this annihilation in vacuum is forbidden by 4-momentum conservation, maybe if the annihilation occurs inside some material, it could be possible for they to decay to 1 photon, I don't know.

PeroK said:
Okay, I meant whether there is one photon or not is an invariant outcome of the experiment.
One of the most glaringly obvious examples of what I am talking about is in very high energy particle physics, where an electron can scatter off a photon as if the photon were a hadron composed of separate point-like quarks.

Because the electron is moving at such high energies, from the frame of reference of the electron it looks like the photon has an ultra-short wavelength, and thus can take on gigantic hadron-like energies, even though from our frame of reference (and that of the photon) the photon does not have an energy anywhere close to that.

Puffer Fish said:
Can you explain why it would be impossible?

Do the math and see.

Puffer Fish said:
The outgoing particle will still have the same overall vector and energy of the two beginning particles.

No, it won't. It can't, because a single photon has zero invariant mass but the electron-positron pair has non-zero invariant mass, so those two systems can't possibly be described by the same 4-vector.

Puffer Fish said:
One of the most glaringly obvious examples of what I am talking about is in very high energy particle physics, where an electron can scatter off a photon as if the photon were a hadron composed of separate point-like quarks.
We were talking about electron-positron annihilation!

Anyway, an elementary result of SR is that two massive particles cannot annhiliate to a single photon. As energy-momentum cannot be conserved.

PeroK said:
Not in the centre-of-momentum frame of the original particles!

You don't have to use any frame at all. The key observation, which I made in post #15, is frame-independent.

PeroK said:
We were talking about electron-positron annihilation!
We were talking about two different reference frames and seemingly separate incompatible outcomes.

I gave an example that could be analogous to this.

Puffer Fish said:
I wonder though, is it possible to have a different outcome depending on the reference frame?

No.

Puffer Fish said:
It's well established in quantum theory that two different outcomes can simultaneously occur and it depends on your reference frame.

No, it isn't. I have no idea where you are getting this from.

Puffer Fish said:
How does that mean anything?

He was saying the same thing I said in post #15, just not as explicitly.

Puffer Fish said:
One of the most glaringly obvious examples of what I am talking about is in very high energy particle physics, where an electron can scatter off a photon as if the photon were a hadron composed of separate point-like quarks.

This is irrelevant to the point @PeroK was making. Not just because we were talking about electron-positron annihilation, but because the photon in your example is only observed as a single photon; you get one electron plus one photon in, and one electron plus one photon out. The "as if it were a hadron composed of separate point-like quarks" is a heuristic model invoked to make predictions about the scattering cross section; it is not a statement about how many particles are actually measured. How many particles are actually measured is an invariant outcome of any particular experiment, just as @PeroK said.

PeroK
Puffer Fish said:
It's well established in quantum theory that two different outcomes can simultaneously occur and it depends on your reference frame.
There is no reference frame in which your laws of physics apply! Quantum theory or no quantum theory.

@Puffer Fish you've used more energy in arguing than it would take to just do the calculation.

mattt
Puffer Fish said:
We were talking about two different reference frames and seemingly separate incompatible outcomes.

I gave an example that could be analogous to this

You have given no such example. Nor have you given a substantive response to any of the posts pointing out what you are missing. At this point your question has been thoroughly answered.

In view of that, this thread is closed.

## 1. What is electron-positron annihilation?

Electron-positron annihilation is a process in which an electron and a positron (the antimatter counterpart of an electron) collide and produce two or more photons. This process is governed by the laws of quantum mechanics.

## 2. How is 1-photon emission possible from electron-positron annihilation?

In electron-positron annihilation, the total energy of the electron and positron is converted into electromagnetic energy in the form of photons. Due to the conservation of energy and momentum, the resulting photons must have a combined energy equal to the total energy of the colliding particles. In some cases, this results in the production of a single photon.

## 3. Can 1-photon emission from electron-positron annihilation be observed?

Yes, 1-photon emission from electron-positron annihilation has been observed in various experiments, including particle accelerators. The photons produced in this process have specific energies and can be detected by specialized equipment.

## 4. What is the significance of 1-photon emission from electron-positron annihilation?

The production of a single photon in electron-positron annihilation is important in understanding the fundamental interactions between particles. It also has practical applications in medical imaging techniques such as positron emission tomography (PET) scans.

## 5. Is 1-photon emission from electron-positron annihilation a common occurrence?

No, 1-photon emission from electron-positron annihilation is a rare occurrence and depends on the energy of the colliding particles. In most cases, the annihilation results in the production of multiple photons. However, with high enough energies, the production of a single photon becomes more likely.

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