# Conservation of angular momentum in positron-electron annihilation

• A
• Simon Bridge
In summary, the conversation discusses the question of whether spins need to be opposite in order to conserve angular momentum for two-photon annihilation to occur in electron-positron pairs. The speaker initially thought that this seemed reasonable, but upon further research, found that there is no clear conclusion on the matter. They mention that standard texts do not cover the spin aspect, and ask for direction on understanding this concept more clearly. The conversation then delves into the idea of spin states and the possibility of using a thought experiment to explore this concept further.
Simon Bridge
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TL;DR Summary
if we have spin polarized electrons and positrons, how is the annihilation probability affected by spin orientation?
Pretty much in a nutshell... fielded a question about how spin affects electron positron annihilation... ie do the spins have to be opposite in order to conserve angular momentum for two-photon annihilation to happen?

Intuitively I figured that looks reasonable ... but decided to check, and found lots of discussions of electron-positron scattering re spin polarization, but nothing that seemed to come definitely to a clear conclusion on this. Standard texts on the matter to hand do not cover the spin part... so I am probably forgetting something obvious.

It's been a while.
Someone want to point me in the right direction?

I'll want to understand this fairly solidly (A), but be able to give a description to intermediate level (I).

Creation of electron positron pairs by photons conserved but Wikipedia e-p anhiliation article says conserved. But electron and positron are spin 1/2 and both emitted photons are spin 1.

The e-p pair must be in a spin zero state. The two photons cannot be in a spin one state, because the spin addition 1+1=1 is antisymmetric, and the photons are bosons.

ie. if the e-p pair had aligned spins, then the probability of 2-photon annihilation is zero?
Is there a paper to back this up?

I am thinking of thought experiment where the spins of both particles are deliberately polarized.
They could have prepared initial polarization angles to whatever angle we want.

If randomly aligned, could I argue that the particles interact magnetically so establishing a spin 1 or spin 0 measured combined state?

Spin 1 allowing odd-photon annihilation and spin 0 allowing even-photon annihilation?

I'm trying to get my head clear on this.

## 1. What is conservation of angular momentum in positron-electron annihilation?

Conservation of angular momentum in positron-electron annihilation refers to the fundamental law of physics that states that the total angular momentum of a system remains constant in the absence of external torques. In the case of positron-electron annihilation, the total angular momentum of the system before and after the annihilation event must be equal.

## 2. How is angular momentum conserved in positron-electron annihilation?

Angular momentum is conserved in positron-electron annihilation through the principle of conservation of momentum. This means that the total angular momentum of the system before the annihilation event, which is the sum of the individual angular momenta of the positron and electron, must be equal to the total angular momentum of the system after the event, which is the angular momentum of the resulting photons.

## 3. Why is conservation of angular momentum important in positron-electron annihilation?

Conservation of angular momentum is important in positron-electron annihilation because it is a fundamental law of physics that must hold true in all physical interactions. It allows us to predict the behavior of the system before and after the annihilation event, and it also helps us to understand the underlying principles of the annihilation process.

## 4. What happens to the angular momentum of the positron and electron in positron-electron annihilation?

In positron-electron annihilation, the angular momentum of the positron and electron are both converted into the angular momentum of the resulting photons. This is because the total angular momentum of the system must remain constant, so any change in the angular momentum of one component must be balanced by an equal and opposite change in the other component.

## 5. Is conservation of angular momentum violated in any other physical processes?

No, conservation of angular momentum is a fundamental law of physics that applies to all physical processes. It has been extensively tested and has been found to hold true in all cases. Violations of this law would require a fundamental change in our understanding of the laws of physics.

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