Past exam of the particle and nuclear physics course of the University of Cambridge / 2012 / Paper 1 / 4 / Solution

For projectile velocity $v$ and a resting target, let $M=m_x+m_X$, $\mu =m_x{m}_X/M$, and $V=m_{x}v/M$. Subtract the kinetic energy of the centre of mass from the laboratory kinetic energy:In the centre-of-momentum frame the two momenta are opposite with equal magnitude, soFor masses quoted in $\mathrm{MeV}/c^2$, use $p^{\ast }c=\sqrt{2(\mu c^2)T^{\ast }}$. These are the nonrelativistic relations stipulated for this question; no relativistic correction should be silently mixed into the numerical results.