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14 Nov 2019
An experimenter sets up a beam of protons which impacts a stationary liquid hydrogen target. We will call this frame of reference, in which the target is not moving, the lab frame. The protons in the beam interact with the protons in the hydrogen nuclei via the reaction : 1H + 1H rightarrow2 D + e+ + ve For the purposes of this problem, you can neglect the small momentum and energy carried by the electron neutrino ve. The rest mass energy of the proton is mpc2 = 938 MeV, the deuteron mD = 1876 MeV, and the electron mec2 = 511 keV. The rest mass energy of the proton is mpc2 = 938 MeV. Consider the same collision in the center-of-mass reference frame, in which the net momentum of particles before and after the collision is zero. What are the momentum and energies of the 2D and e+ in the lab frame? Give your answer in GeV/c and GeV. (Hint : Use the fact that the invariant s2 = (E1 + E2)2 - c2(p1 + p2)2 remains the same both in the lab and center-of-mass frames, before and after the collision.)
An experimenter sets up a beam of protons which impacts a stationary liquid hydrogen target. We will call this frame of reference, in which the target is not moving, the lab frame. The protons in the beam interact with the protons in the hydrogen nuclei via the reaction : 1H + 1H rightarrow2 D + e+ + ve For the purposes of this problem, you can neglect the small momentum and energy carried by the electron neutrino ve. The rest mass energy of the proton is mpc2 = 938 MeV, the deuteron mD = 1876 MeV, and the electron mec2 = 511 keV. The rest mass energy of the proton is mpc2 = 938 MeV. Consider the same collision in the center-of-mass reference frame, in which the net momentum of particles before and after the collision is zero. What are the momentum and energies of the 2D and e+ in the lab frame? Give your answer in GeV/c and GeV. (Hint : Use the fact that the invariant s2 = (E1 + E2)2 - c2(p1 + p2)2 remains the same both in the lab and center-of-mass frames, before and after the collision.)