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9.5: Optical Theorem

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The differential scattering cross-section f(θ) . The total cross-section is given by

=dΩ|f(θ)|2 $ = \frac{1}{k^2} \oint d\varphi \int_{-1}^{1} d\mu \sum_l \sum_{l'...
...elta_l-\delta_{l'})]\, \sin\delta_l \,\sin\delta_{l'}\, P_l(\mu)\, P_{l'}(\mu),$ ???

where σtotal=4πk2l=0,(2l+1)sin2δl, ???

where use has been made of Equation ???. A comparison of this result with Equation ??? yields

Pl???=1 . This result is known as the optical theorem. It is a reflection of the fact that the very existence of scattering requires scattering in the forward (σtotal=l=0,σl, ???

where

l
th partial cross-section: i.e., the contribution to the total cross-section from the l th partial cross-section occurs when the phase-shift π/2 .

Contributors

  • Richard Fitzpatrick (Professor of Physics, The University of Texas at Austin)


This page titled 9.5: Optical Theorem is shared under a not declared license and was authored, remixed, and/or curated by Richard Fitzpatrick.

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