# 汤姆孙散射

## 汤姆孙散射的描述

${\displaystyle \epsilon _{t}={\frac {\pi \sigma }{2}}~I\,n}$
${\displaystyle \epsilon _{r}={\frac {\pi \sigma }{2}}~I\,n\,\cos ^{2}(\chi )}$

${\displaystyle \sigma \equiv \left({\frac {q^{2}}{mc^{2}}}\right)^{2}=\left({\frac {q^{2}}{4\pi \epsilon _{0}mc^{2}}}\right)^{2}}$

${\displaystyle \sigma =\left({\frac {\alpha \lambda _{e}}{2\pi }}\right)^{2}=\left({\frac {\alpha \hbar }{m_{e}c}}\right)^{2}}$
 ${\displaystyle \sigma =\left({\frac {\alpha \hbar }{m_{e}c}}\right)^{2}}$
${\displaystyle \sigma =7.9407875\ldots \times 10^{-26}~{\textrm {cm}}^{2}}$

${\displaystyle \int _{0}^{2\pi }d\phi \int _{0}^{\pi }d\chi \left(\epsilon _{t}+\epsilon _{r}\right)\sin \chi =I\,\sigma _{T}\,n}$

${\displaystyle \lambda _{e}={\frac {h}{m_{e}c}}}$
${\displaystyle \sigma _{T}={\frac {8\pi }{3}}\sigma ={\frac {8\pi }{3}}\left({\frac {\alpha \lambda _{e}}{2\pi }}\right)^{2}={\frac {8\pi }{3}}\left({\frac {\alpha \hbar }{m_{e}c}}\right)^{2}}$
 ${\displaystyle \sigma _{T}={\frac {8\pi }{3}}\left({\frac {\alpha \hbar }{m_{e}c}}\right)^{2}}$

${\displaystyle \sigma _{T}=6.6524586\ldots \times 10^{-25}~{\textrm {cm}}^{2}}$

## 参考文献

• Billings, Donald E., A Guide to the Solar Corona, Academic Press, New York 1966.