トムソン散乱

${\displaystyle {\frac {d\sigma _{\text{T}}}{d\Omega }}=\left({\frac {q^{2}}{4\pi \varepsilon _{0}mc^{2}}}\right)^{2}\cdot {\frac {1}{2}}(1+\cos ^{2}\theta )}$

${\displaystyle \sigma _{\text{e}}=6.652~458~7051(62)\times 10^{-29}\ {\text{m}}^{2}}$

${\displaystyle {\begin{aligned}\sigma _{\text{e}}&=\left({\frac {e^{2}}{4\pi \varepsilon _{0}m_{\text{e}}c^{2}}}\right)^{2}\cdot \int _{0}^{2\pi }d\phi \int _{0}^{\pi }{\frac {1}{2}}(1+\cos ^{2}\theta )\sin \theta \,d\theta \\&={\frac {8\pi }{3}}\left({\frac {e^{2}}{4\pi \varepsilon _{0}m_{\text{e}}c^{2}}}\right)^{2}\end{aligned}}}$

${\displaystyle \alpha ={\frac {e^{2}}{4\pi \varepsilon _{0}\hbar c}},~R_{\infty }={\frac {\alpha ^{2}m_{\text{e}}c}{2h}},~a_{0}={\frac {\alpha }{4\pi R_{\infty }}},~r_{\text{e}}=\alpha ^{2}a_{0}}$

${\displaystyle \sigma _{\text{e}}={\frac {8\pi }{3}}{r_{\text{e}}}^{2}}$