Past exam of the physics 1 paper of the University of Oxford / 2014 / 10 / b / Solution

For fixed-target electron-Positron formation, set $m_1=m_2=m_e$ in a and solve for the incident total energy:The incident kinetic energy is smaller by another $m_e{c}^2$, a negligible relative change here. Most of the fixed-target energy becomes motion of the final rho meson in the laboratory.

With equal and opposite incoming momenta, the centre-of-momentum frame is the laboratory. Each incoming particle has the same total energy, and there is no final translational kinetic energy at formation:This large contrast illustrates the invariant-energy advantage of colliding beams. The given $768\mathrm{MeV}/c^2$ resonance mass is used rather than replacing it with a modern tabulated value.