= Coulomb head-on closest approach with target recoil
{c}
{title2=$r_{\min}=k_eq_1q_2(m_1+m_2)/(m_2K_{\rm lab})$}
A projectile of <mass> $m_1$, <electric charge> $q_1$, and nonrelativistic laboratory <kinetic energy> $K_{\rm lab}$ approaches an initially stationary free target of <mass> $m_2$ and like-sign <electric charge> $q_2$. The relative-motion <kinetic energy> is $K_*=m_2K_{\rm lab}/(m_1+m_2)$. At a head-on turning point it is converted to the repulsive <Coulomb potential> $k_eq_1q_2/r_{\min}$, proving the displayed separation. The remaining laboratory <kinetic energy> is the translation of the <centre of mass>; it cannot be converted into the pair's separation energy. An externally fixed target is the infinite-target-mass limit.
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