hw03.pdf - Physics 5110 Spring 2020 Homework#3 Due in class Wednesday January 29th 1 In a two-body scattering event A B \u2212\u2192 C D it is convenient to

# hw03.pdf - Physics 5110 Spring 2020 Homework#3 Due in class...

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Physics 5110, Spring 2020 Homework #3 Due in class Wednesday January 29 th 1. In a two-body scattering event A + B -→ C + D , it is convenient to introduce the Mandelstam variables s = ( p A + p B ) 2 t = ( p A - p C ) 2 u = ( p A - p D ) 2 where p A , p B ( p C , p D ) are the four-vector momenta of the incident (outgoing) particles. The Mandelstam variables are useful in calculation because they are Lorentz invariants, that is, they have the same value in any inertial system. However experimentally it is more straight- forward to measure three-momenta and scattering angles. Taking e e + e e + to be the s -channel process, verify that s = 4( P 2 CM + m 2 ) t = - 2 P 2 CM (1 - cos θ ) u = - 2 P 2 CM (1 + cos θ ) where θ is the center-of-mass scattering angle and P CM is the magnitude of the 3-momenta of the incident and scattered electrons in the center-of-mass. 2. For this exercise, we are going to use actual experimental data to determine the size of the nucleus of a nickel ( 58 Ni 28 ) atom. On the course web page, I have placed a file containing data from a 1975 experiment 1 in which 449.5 MeV electrons were scattered off of a

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