PHY 3101 “Introduction to Modern Physics” Fall 2009 18 September 2009 Professor Mark W. Meisel Problem 2.21 from the textbook: (recall drawing from class), where the notation is m o,p = 938 MeV is the rest mass of the proton, m o,π = 135 MeV is the rest mass of the π0 , the neutral pion, and “ in ” will mean “incident” for the proton that is moving in the lab frame prior to the collision. Recall E 2 = p 2 c 2 + m o c 2 , (1) E = mc 2 , (2) and the invariant is ( m o c 2 ) 2 = E 2-p 2 c 2 . (3) So, the lab frame invariant before collision is the left-hand-side (LHS) and the center-of-mass (CM) frame immediately after collision at threshold is the right-hand-side (RHS) of an equation that sets the invariants to be equal, i.e. E 2 in-p 2 in c 2 = E 2-p 2 c 2 (4) n m in c 2 + m o,p c 2 o 2-p 2 in c 2 = ± 2 m o,p c 2 + m o,π c 2 ² 2 , (5) where we need to keep in mind that m in is the relativistic mass used in Eq. (2) and where we have used the fact that there is no momentum in the CM frame at threshold so any “
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