= Nuclear radius bound from a Coulomb turning point
{title2=$r_{\min}=zZe^2/(4\pi\varepsilon_0E_{\rm cm})$}
For a head-on repulsive <Rutherford scattering> encounter, relative <kinetic energy> becomes <Coulomb potential> energy at closest approach. With projectile charge $ze$ and target charge $Ze$, <conservation of energy> gives the displayed separation. If the Coulomb description remains valid down to that separation, it bounds the target's interaction radius from above, treating the projectile as pointlike. For a stationary target of mass $M$ and incident projectile mass $m$, use centre-of-mass energy $E_{\rm cm}=ME_{\rm lab}/(M+m)$; neglecting <nuclear recoil> amounts to $M\gg m$.
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