Why KE of Annihilation Electrons Differs?

[cemtu]

TL;DR Summary

When electron-positron pair is created their KE is not necessarily shared equally, for example, if the energy of the incoming gamma ray is 1022 keV the pair of positron and electron does not have to be 511 keV each; one can be 501 keV while the other can have 521 keV. Why is that?

We know that when a high energy gamma ray(E >= 1022 keV because the total energy of 1 electron at rest and 1 positron at rest is 511 keV) passes near a high Z(atomic weight) atomic nucleus interacts with the electrical field of the nucleus and there is a probability that this high energetic gamma-ray will create positron and electron pairs in order to conserve the linear momentum.

However, when the total energy of the incoming gamma ray is bigger than 1022 keV, this pair is created their total energy is not necessarily shared equally, there can be a difference in the KE shared by the electron-positron pair. For example, if the total energy of the incoming gamma ray is 1044 keV the pair of positron and electron does not have to be 522 keV each; one can be 523 keV while the other can have 521 keV. Why is that?

What does determine which particle will have which value for total energy for pair of electron and positron?

(Any remaining energy of more than 1022 keV will be given to each particle of pair as KE.)

My source(free): https://www.nrc.gov/docs/ML1122/ML11229A667.pdf (62th page of 110)

 

[malawi_glenn]

Recoil of nucleus, pair creation is a 2 -> 3 body process

 

[cemtu]

Recoil of nucleus, pair creation is a 2 -> 3 body process

Okay? What should I infer from this?

 

[malawi_glenn]

Okay? What should I infer from this?

You tagged the thread "A"-level, which means I assume that you are a grad student or similar. I can give you a hint, have you ever studied beta decay?

 

[cemtu]

You tagged the thread "A"-level, which means I assume that you are a grad student or similar. I can give you a hint, have you ever studied beta decay?

I graduated from "engineering physics" and am about to start my graduate education on "medical physics". I did not study beta decay specifically, no. But I am currently reading about photon-matter interactions which are needed for radiotherapy physics.

 

[malawi_glenn]

I am about to start my graduate education on medical physics. I did not study beta decay specifically, no.

Kids don't study beta decay in under grad education these days? I teach it to 17 y old kids in my country.

However, when this pair is created their KE is not necessarily shared equally, for example, if the energy of the incoming gamma ray is 1022 keV the pair of positron and electron does not have to be 511 keV each; one can be 501 keV while the other can have 521 keV. Why is that?

This is not true, because the threshold energy is $2m_e$. You are mixing up total energy with kinetic energy here. The total energy of the electron/positron will always be greater than or equal to $m_e$. Their individual kinetic energy can vary because the recoiling nuclei can carry away some momentum. Thus, the magnitude of the momentum for the electron/positron does not have to be equal.

 

[malawi_glenn]

I think this is what you are looking for (the example at the bottom of this page)
https://phys.libretexts.org/Bookshelves/Modern_Physics/Book:_Spiral_Modern_Physics_(D'Alessandris)/4:_The_Photon/4.3:_Pair_Production
as you'll see the effect of nucleus recoil is very small, of the order 0,01 keV

 

[cemtu]

Kids don't study beta decay in under grad education these days? I teach it to 17 y old kids in my country.

This is not true, because the threshold energy is $2m_e$. You are mixing up total energy with kinetic energy here. The total energy of the electron/positron will always be greater than or equal to $m_e$. Their individual kinetic energy can vary because the recoiling nuclei can carry away some momentum. Thus, the magnitude of the momentum for the electron/positron does not have to be equal.

Thank you I fixed my question.

 

[malawi_glenn]

Thank you I fixed my question.

If you want to know the details of how the kinetic energy is distributed you'll need some quantum field theory know how the matrix element for the process looks like.

 

[PeroK]

Okay? What should I infer from this?

Energy is frame dependent. Energy will be equal in the resulting centre of momentum frame. But, of course, not in every frame.

That's a B-level answer, by the way.

 

[cemtu]

Kids don't study beta decay in under grad education these days? I teach it to 17 y old kids in my country.

This is not true, because the threshold energy is $2m_e$. You are mixing up total energy with kinetic energy here. The total energy of the electron/positron will always be greater than or equal to $m_e$. Their individual kinetic energy can vary because the recoiling nuclei can carry away some momentum. Thus, the magnitude of the momentum for the electron/positron does not have to be equal.

Is the reason for kinetic energy difference about how the nucleus was positioned relative to the newly created electron-positron pair in the instance that pair came to be? Is that the reason why you said "Recoil of nucleus, pair creation is a 2 -> 3 body process"?

 

[malawi_glenn]

Is the reason for kinetic energy difference about how the nucleus was positioned relative to the newly created electron-positron pair in the instance that pair came to be? Is that the reason why you said "Recoil of nucleus, pair creation is a 2 -> 3 body process"?

Not positioned rather what the recoil momentum of the nucleus will be. Hint: look up beta decay electron energy distribution it is more or less the same phenomena.

In the process "photon + nucleus -> electron + positron + nucleus" there are an infinitely many ways you can arrange the momentum of the final particles while conserving momentum and energy.