Consider the reaction ? + e -> p+ + p- + e with the electron initially free at r

Question

Consider the reaction ? + e -> p+ + p- + e with the electron initially free at rest (with this frame designated as lab frame). a) What is a minimum photon energy for this reaction to proceed? b) Assuming that the photon energy is the determine in a), What is the velocity of either of the pions after the reaction? c) Assume the pion then decays to a muon and neutrino p -> µ + v. In the lab frame, what is maximum energy of the muon produced in the pion decay assuming the photon energy determined in a). Give your answers in terms of the pion, muon, and electron masses while setting the photon and neutrino masses to 0. Consider the reaction ? + e -> p+ + p- + e with the electron initially free at rest (with this frame designated as lab frame). a) What is a minimum photon energy for this reaction to proceed? b) Assuming that the photon energy is the determine in a), What is the velocity of either of the pions after the reaction? c) Assume the pion then decays to a muon and neutrino p -> µ + v. In the lab frame, what is maximum energy of the muon produced in the pion decay assuming the photon energy determined in a). Give your answers in terms of the pion, muon, and electron masses while setting the photon and neutrino masses to 0.

Explanation / Answer

Given ? + e -> p+ + p- + e (a)Rest mass energy of the photon is zero rest mass energy of electron and positron is 0.511 MeV Rest mass energy of pions is 140 MeV In lab frame The the minimum kinetic energy of photon for this reaction is               K = (initial rest mass enegy - final rest mass energy)                K = (0.511 MeV - (140 MeV + 140 MeV + 0.511 MeV)                 K = -280 MeV Here negative sign indicates that this reaction is endothermic reaction (b) if the photon energy is 280 MeV this energy only useful to produce the pions because the total rest mass energy of the pions is equals to 280 MeV. hence the kinetic energy of the pions is zere the velocity of either of the pions is zero (c) p -> µ + v the energy of the each pion in the decay (a) is 140 MeV The rest mass energy of the µ is 106 MeV the maximum energy of the µ is (140 - 106) MeV .i.e 34 MeV

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