1-photon emission possible from electron-positron 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.

 

[PeterDonis]

I read that in some instances three photons can result.

Where have you read this? Please give a specific reference.

 

[PeroK]

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

 

[PeterDonis]

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.

 

[Puffer Fish]

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.

 

[PeroK]

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.

 

[Puffer Fish]

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.

 

[PeroK]

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.

 

[Puffer Fish]

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.

 

[Dale]

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.

 

[Puffer Fish]

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.

 

[PeroK]

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.

 

[Gaussian97]

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.

 

[Puffer Fish]

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.

 

[PeterDonis]

Can you explain why it would be impossible?

Do the math and see.

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.

 

[PeroK]

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.

 

[PeterDonis]

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.

 

[Puffer Fish]

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.

 

[PeterDonis]

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

No.

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.

 

[PeterDonis]

How does that mean anything?

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

 

[PeterDonis]

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]

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.

 

[Vanadium 50]

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

 

[PeterDonis]

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.