Problem 1.384

A neutron with kinetic energy $T=2 m_{0} c^{2},$ where $m_{0}$ is its rest mass, strikes another, stationary, neutron. Determine: (a) the combined kinetic energy $\widetilde{T}$ of both neutrons in the frame of their centre of inertia and the momentum $\tilde{p}$ of each neutron in that frame; (b) the velocity of the centre of inertia of this system of particles. Instruction. Make use of the invariant $E^{2}-p^{2} c^{2}$ remaining constant on transition from one inertial reference frame to another $(E$ is the total energy of the system, $p$ is its composite momentum).