Two beams of particles consisting of n bunches with ni and n2 particles in each circulate in a collider and make head-on-collisions. a, the cross sectional area of the beam and f is the frequency with which the particles circulate, obtain an expression for the luminosity l in an electron-positron collider the particles circulate in short cylindrical bunches of radius 1.2 mm. the number of particles per bunch is 6 x 101 the bunches collide at a frequency of 2 mhz. the cross-section for ut creation at 8 gev total energy is, 1.4 x 10-3 cm2: how many t pairs are created per second? (a) show that in a head-on-collision of a beam of relativistic particles energy e1 with one of energy e2, the square of the energy in the cms is ei e2 and that for a crossing angle e between the beam this is reduced by a factor (1+cose)/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 fixed hydrogen target. (courtesy d. h. perkins, cambridge university press) head-on collisions are observed between protons each moving with velocity (relative to the fixed observer) corresponding to 1010 ev. if one of the protons were to be at rest relative to the observer, what would the energy of the other need to be so as to produce the same collision energy as before. the rest energy of the proton is 10 ev