Positron - electron annihilation

In summary: If the photons have a higher energy in one frame than the other, then they will have a lower frequency in the other frame.
  • #1
tnho
31
0

Homework Statement


A positron having a kinetic energy equal to its rest mass energy mec^2 collides with a stationary electron. The positron and the electron annihilate in the process and two photons are created. What is the maximum possible energy of a photon produced in the annihilation process??

Homework Equations


4-momentum vectors(??)
CM frame can help ??

The Attempt at a Solution

 
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  • #2
4-momentum vectors, absolutely. Though it's hard to be sure until you write some down and try them out. CM may help (at least to think about) but I suggest you try first in the rest frame of the electron since it seems that is the frame in which they want an answer.
 
  • #3
I'll definitely get a boost to the CM frame so that the two final photons travel at opposite direction.

then look at momentum 4 vectors of each objects, take the 4 vector dot product. and you'll get something involving the usual dot product of the two momentum vector (of the photons). simplify things (put everything in terms of energy of the two photons, E1, E2) (the dot products can be simplified since the photons travel at opposite direction). then work some inequality out (complete the squares, work out AM-GM or Cauchy if you know those).

formulas to use:
recall:
[tex]E=pc=hf[/tex] for photons

and the CM frame moves at:
[tex]\vec{V}_{\text{CM}}=\frac{\sum_i{\vec{p}_ic^2}}{\sum_i E_i}[/tex]
 
Last edited:
  • #4
in fact, i don't know under what physical conditions, the energy of photon is at its maximum.

If the energy of photon is maximum in one frame (says CM frame), it is also maximum in another frame (says Rest frame), isn't it??

Thx
 
  • #5
tnho said:
in fact, i don't know under what physical conditions, the energy of photon is at its maximum.

If the energy of photon is maximum in one frame (says CM frame), it is also maximum in another frame (says Rest frame), isn't it??

Thx

Not true at all. This why I suggested you stay in the rest frame. There is such a thing as a doppler shift.
 

What is positron-electron annihilation?

Positron-electron annihilation is a process in which a positron (a positively charged particle) and an electron (a negatively charged particle) collide and annihilate each other, producing two gamma rays.

How does positron-electron annihilation occur?

Positron-electron annihilation occurs when a positron and an electron interact through the electromagnetic force. The two particles approach each other, and when they get close enough, they annihilate, releasing energy in the form of gamma rays.

What is the significance of positron-electron annihilation in science?

Positron-electron annihilation is significant in science because it allows us to study the interactions between matter and antimatter. It also has practical applications in medical imaging, such as positron emission tomography (PET) scans.

What happens to the energy released during positron-electron annihilation?

The energy released during positron-electron annihilation is converted into two gamma rays. These gamma rays can be detected and measured, providing information about the annihilation process and the particles involved.

Can positron-electron annihilation be reversed?

No, positron-electron annihilation is an irreversible process. Once the particles have annihilated, they cannot be brought back to their original state. However, new positrons and electrons can be created through other processes, such as pair production.

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