# 汤姆孙散射

## 汤姆孙散射的描述

$\epsilon_t = \frac{\pi \sigma }{2}~I\,n$
$\epsilon_r = \frac{\pi \sigma }{2}~I\,n\,\cos^2(\chi)$

$\sigma \equiv \left(\frac{q^2}{mc^2}\right)^2=\left(\frac{q^2}{4\pi\epsilon_0mc^2}\right)^2$

$\sigma = \left(\frac{ \alpha \lambda_e }{2\pi} \right)^2 = \left( \frac{\alpha \hbar}{m_e c} \right)^2$
 $\sigma = \left( \frac{\alpha \hbar}{m_e c} \right)^2$
$\sigma = 7.9407875\ldots\times 10^{-26}~\textrm{cm}^2$

$\int_0^{2\pi}d\phi \int_0^\pi d\chi \left(\epsilon_t+\epsilon_r\right) \sin \chi = I\,\sigma_T\,n$

$\lambda_e = \frac{h}{m_e c}$
$\sigma_T = \frac{8 \pi}{3} \sigma = \frac{8 \pi}{3} \left(\frac{\alpha \lambda_e}{2\pi}\right)^2 = \frac{8 \pi}{3} \left( \frac{\alpha \hbar}{m_e c} \right)^2$
 $\sigma_T = \frac{8 \pi}{3} \left( \frac{\alpha \hbar}{m_e c} \right)^2$

$\sigma_T =6.6524586\ldots\times 10^{-25}~\textrm{cm}^2$

## 参考文献

• Jackson, John D. Classical Electrodynamics 3rd. New York: Wiley. 1998. ISBN 0-471-30932-X.
• Billings, Donald E., A Guide to the Solar Corona, Academic Press, New York 1966.