Small-angle scattering and quasiclassical approximation beyond leading order

Understand

In the present paper we examine the accuracy of the quasiclassical approach on the example of small-angle electron elastic scattering.

• Using the quasiclassical approach, we derive the differential cross section and the Sherman function for arbitrary localized potential at high energy.
• These results are exact in the atomic charge number and correspond to the leading and the next-to-leading high-energy small-angle asymptotics for the scattering amplitude.
• Using the small-angle expansion of the exact amplitude of electron elastic scattering in the Coulomb field, we derive the cross section and the Sherman function with a relative accuracy $\theta^2$ and $\theta^1$, respectively ($\theta$ is the scattering angle).