Solving 4-Momentum Problem: Determining Threshold for Triplet Production

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The discussion centers on understanding the conservation of 4-momentum in determining the threshold for triplet production from a photon and an electron. The initial energy is expressed as E1^2 = (pc)^2 + (m0c^2)^2, while the threshold energy after collision is given as E2^2 = (3m0c^2). The user struggles with the calculation, noting that E1 should equal E2, but their substitution does not yield correct results. They acknowledge the need to incorporate 4-momentum into their approach. Clarification on the problem's requirements is also sought to better address the calculation issues.
coregis
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I'm having trouble understanding conservation of 4-momentum. My problem is about dertermining the threshold for triplet production from a photon and an electron using 4-momentum conservation. The answer is 4m0c^2. So far, I say the initial energy is:

E1^2=(pc)^2 + (m0c^2)^2=(hv)^2+(m0c^2)^2

At threshold energy after collision, three particles with no momentum are produced, so

E2^2=(3m0c^2)

E1=E2, but substituting and solving for hv does not work out correctly, and I have not used 4-momentum at all anyhow. What am I doing wrong/forgetting? Help!
 
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It might help to know what the question actually asks.
 
David said:
It might help to know what the question actually asks.
verbatim- "Show the threshold for triplet production is 4m0c^2 using the concept of conservation of 4-momentum." Sorry for the paraphrase.
 
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