How much energy would a fixed-target proton accelerator require to match the energy available in the LHC for a p+\bar{p} reaction?
Strategy The energy available in the LHC is the sum of the colliding beams, or 14 TeV. We use Equation (14.10) to determine the kinetic energy K needed for a fixed-target experiment.
E_{ cm }=\sqrt{\left(m_{1} c^{2}+m_{2} c^{2}\right)^{2}+2 m_{2} c^{2} K} (14.10)