Question

Two beams of particles consisting of n bunches with N1 and N2 particles in each circulate in a collider and make head-on-collisions. A, the crosssectional area of the beam and f is the frequency with which the particles circulate, obtain an expression for the luminosity L.

Answer 1

In the colliding beam experiments, for two colliding beams the reaction rate is written in terms of the “luminosity” L. The number of interactions per second is

N = Lσ

where σ is the interaction cross-section in question.

If N1 or N2 = number of particles/bunch in each beam

A = area of cross-section of intersecting beams

N = number of bunches/beam and f = frequency of revolution then luminosity is simply given by

L = n N1N2f/A