Problem 6.302

A relativistic particle with rest mass \(m\) collides with a stationary particle of mass \(M\) and activates a reaction leading to formation of new particles: \(m+M \rightarrow m_{1}+m_{2}+\ldots,\) where the rest masses of newly formed particles are written on the right-hand side. Making use of the invariance of the quantity \(E^{2}-p^{2} c^{2},\) demonstrate that the threshold kinetic energy of the particle \(m\) required for this reaction is defined by Eq. (6.7c).