Nuclear radius bound from a Coulomb turning point ($r_{\min }=zZ{e}^2/(4\pi {\epsilon }_0{E}_{\mathrm{cm}})$)

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 $E_{\mathrm{cm}}=M{E}_{\mathrm{lab}}/(M+m)$; neglecting nuclear recoil amounts to $M\gg m$.