フランク＝タムの公式
E 2 ( ω ) → z e v λ b e − λ b {\displaystyle E_{2}(\omega )\rightarrow {\frac {ze}{v}}{\sqrt {\frac {\lambda }{b}}}e^{-\lambda b}}
B 3 ( ω ) = ε ( ω ) β E 2 ( ω ) {\displaystyle B_{3}(\omega )=\varepsilon (\omega )\beta E_{2}(\omega )}
と求めることができ、結果として
( d E d x ) r a d = Re ( ∫ 0 ∞ z 2 e 2 c 2 ( − i λ ∗ λ ) ω ( 1 − 1 β 2 ε ( ω ) ) e − ( λ + λ ∗ ) a d ω ) {\displaystyle \left({\frac {\mathrm {d} E}{\mathrm {d} x}}\right)_{rad}={\text{Re}}\left(\int _{0}^{\infty }{\frac {z^{2}e^{2}}{c^{2}}}\left(-i{\sqrt {\frac {\lambda ^{*}}{\lambda }}}\right)\omega \left(1-{\frac {1}{\beta ^{2}\varepsilon (\omega )}}\right)e^{-(\lambda +\lambda ^{*})a}\mathrm {d} \omega \right)}