Introduction to Classical Mechanics · Problem 12.34
4-vectors — Morin
Physics — Mechanics · particle-physics-units
Problem
Maximum energy **
(a) A particle of mass M decays into a number of particles, some of which may be photons. If one of the particles has mass m, and if the sum of the masses of all the other products is μ, what is the maximum possible energy that m can have? Hint: Write the conservation of energy and momentum statements as PM−Pm=Pμ, where Pμ is the total 4-momentum of the other products, and then square. The technique of Problem 12.5 may be useful.
(b) In beta decay, a neutron decays into a proton, an electron, and a neutrino (which is essentially a photon, for the present purposes). The rest energies are En=939.6\,MeV, Ep=938.3\,MeV, Ee=0.5\,MeV, and Eν≈0. What is the maximum energy that the electron can have? The neutrino? Interpret your results.