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).