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Hi everyone,

I'm looking at the following problem from C. Bertulani's Ch.1, Problem 6. The problem statement is:

"Using relativistic expressions for momentum and energy conservation, show that a proton must have energy greater than 5.6 GeV to produce a proton-antiproton pair in a collision with another proton at rest."

My first question is why does this reaction occur? It seems to violate charge conservation the way it stands.

My second question is, if I use energy conservation, and let initial p of the moving proton be my unknown, and assume the minimum energy required of this incoming proton is when both final momenta are zero, I get that

[tex] p=0 [/tex]... which is setting my unknown to zero which I don't want. So there must be a mistake in my reasoning. Here is how I get this result:

1. Requiring energy conservation yields:

[tex] E_1 + E_2 = E'_1 + E'_2 [/tex]

2. For the minimum incoming momentum, p, we would require that both final particles have zero momentum, so the above reduces to:

[tex] m_p + sqrt(m_p^2+ p^2) = m_p + m_\bar p [/tex]

3. And if we just rearrange the above we get: [tex] p=0 [/tex] since the mass of a particle and its antiparticle are equal.

I appreciate any clarifications on this problem, thanks!

iman

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# P+p -> p + (anti)p

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