(a) Show that in a head-on-collision of a beam of relativistic particles of energy E1 with one of energy E2, the square of the energy in the CMS is 4 E1 E2 and that for a crossing angle θ between the beam this is reduced by a factor (1+cosθ)/2, (neglect the masses of beam particles in comparison with the energy)
(b) Show that the available kinetic energy in the head-on-collision with two 25 GeV protons is equal to that in the collision of a 1,300 GeV proton with a fixed hydrogen target. (Courtesy D.H. Perkins, Cambridge University Press)
