= Rutherford scattering
{c}
{tag=Atomic nucleus}
{wiki}
Rutherford scattering is <elastic scattering> by a <Coulomb potential>. In the repulsive classical case, a positively charged projectile bends around a positively charged <atomic nucleus>. A close approach can turn it backwards without a contact collision. The calculation connects an invisible <impact parameter> with a measurable outgoing <angle>, then with a <differential scattering cross-section> and a detector count.
Assume a projectile of <mass> $m$ and <electric charge> $ze$, a stationary point <atomic nucleus> of <electric charge> $Ze$, and positive $z,Z$. Here $e$ is the <elementary charge>. Neglect <nuclear recoil>, <Electron> <screening effect>, <energy> loss, and the <nuclear force>. With <vacuum permittivity> $\varepsilon_0$, define
$$
V(r)=\frac{\kappa}{r},\qquad
\kappa=\frac{zZe^2}{4\pi\varepsilon_0}>0,\qquad
E=\frac12mv^2,\qquad L=mvb.
$$
Here $E$ and $v$ are the incident <kinetic energy> and <speed> far from the <atomic nucleus>, $b\geq0$ is the <impact parameter>, and $L$ is the magnitude of <angular momentum>. The <nonrelativistic limit> requires $v\ll c$, with $c$ the <speed of light>. The fixed-target approximation requires the target <mass> to be much greater than $m$. In <SI>, $\kappa$ has units $\mathrm{J\,m}$, $E$ has units $\mathrm J$, and $b$ has units $\mathrm m$.
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