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Pair Production, electron and positron from isolated photon 
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#1
Apr1014, 03:21 AM

P: 106

I don't completely understand why an electron positron pair cannot be created from an isolated photon. I understand it must have something to do with 4 momentum conservation, but I really can't see a problem given the photon has enough energy for the mass to energy vice versa conversion.\
The only seemingly sound argument I could seem to convince myself with is that if 4 momentum is conserved and we say pf=pi. And we take pi of the photon in the photons rest frame we have (0,0,0,E/c), but the electrons can never move at the speed of light and hence the 4 momentum of any two of the electrons will have a negative momentum value (x,0,0,E/c) and hence it is therefore impossible. But I don't believe this is correct. Any suggestions appreciated thanks! 


#2
Apr1014, 03:54 AM

P: 386

Pretty simple and trivial argument: equality of reference frames. You can always pick a reference frame where the isolated photon is Doppler shifted to have too little energy for pair production. Since the event must happen in all reference frames or in none of them, and there are frames where it is impossible, therefore it is impossible in all frames.
Even simpler argument: an isolated photon has no time whatsoever and therefore no events whatsoever can happen to it. Splitting a photon into several photons of lower energy travelling in the same initial direction would not violate conservation of momentum (unlike production of particles with rest mass) but it is still impossible because of no time at the speed of light. 


#3
Apr1014, 03:56 AM

P: 106

Cheers. What i'm really looking for though is a rigorous violation of the conservation of 4 momentum.



#4
Apr1014, 05:27 AM

Mentor
P: 16,356

Pair Production, electron and positron from isolated photon
You won't find a "rigorous violation", since it is conserved.



#5
Apr1014, 05:30 AM

P: 106

No it isn't as an isolated photon cannot produce and electron and an anti electron, therefore writing the 4 momentum before and after will produce a violation in conservation of 4 momentum, which I know occurs, I just don't know the proof and i've been trying for a while.



#6
Apr1014, 05:59 AM

P: 899

Can't photons of energy E>~1MeV lead to pair production?



#7
Apr1014, 06:32 AM

P: 106

Yep, but apparently in the presence of a nucleus or something, not an isolated photon which is why i'm trying to prove it mathematically.



#9
Apr1014, 07:13 AM

Sci Advisor
Thanks
P: 4,160




#10
Apr1014, 07:57 AM

P: 93




#11
Apr1014, 07:59 AM

P: 93




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