What Is the Minimum Beam Energy for Proton-Proton Collisions?

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Homework Help Overview

The discussion revolves around calculating the minimum beam energy required for proton-proton collisions to initiate a specific reaction involving the production of a neutral pion. The subject area includes particle physics and energy conservation principles in collisions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between beam energy and rest energy, questioning whether to include the rest energy of the protons in their calculations. There is also discussion on the interpretation of "beam energy" and its components.

Discussion Status

The conversation includes attempts to clarify the calculations needed for the minimum beam energy, with some participants confirming the necessity of including the rest energy of the protons. There is an ongoing exploration of the correct approach to the problem without a definitive consensus yet.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information available or the methods they can use. The rest energy values provided for the particles are also a point of focus in the discussion.

J_M_R
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Homework Statement



Calculate the minimum beam energy in a proton-proton collider to initiate the p+p→p+p+n0 reaction. The rest energy of the no is 547.3MeV.

Homework Equations



For a head on collision between particles a and b, from conservation of total energy: Ex = Ep + Ep' = 2Ep

so that mx^2c^4 = Ex^2 - px^2c^2 = (2Ep)^2

The Attempt at a Solution


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Rearranging the above, gives mx = 2Ep/c^2

So using the values I have been provided: Ep = (547.3MeV)/2 = 0.2737Gev

I am not sure if my method is correct?
 
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I guess "beam energy" means the total energy, including the rest energy of the protons.
For the additional energy: yes it is correct. The lab frame is also the center of mass frame, so both protons simply contribute half of the n0 energy plus their rest energy.
 
So to get Ep, I am also required to add the rest energy of the two protons?:

Ep = (547.3MeV + 2(938.3MeV))/2 = 1.212GeV

If rest energy of a proton is 938.3Mev.
 
Right.
 
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