Abstract
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 θ2 and θ1, respectively (θ is the scattering angle). We show that the correction of relative order θ2 to the cross section, as well as that of relative order θ1 to the Sherman function, originates not only from the contribution of large angular momenta l≫1, but also from that of l∼1. This means that, in general, it is not possible to go beyond the accuracy of the next-to-leading quasiclassical approximation without taking into account the non-quasiclassical terms.
Highlights
In the high-energy QED processes in the atomic field, the characteristic angles θ between the momenta of final and initial particles are small
The quasiclassical approach allows one to obtain the results for the amplitudes in the leading quasiclassical approximation and with the first quasiclassical correction taken into account [9,10,11,12,13,14]
We are driven to the conclusion that, in general, it is not possible to go beyond the accuracy of the next-to-leading quasiclassical approximation without taking into account the non-quasiclassical terms
Summary
In the high-energy QED processes in the atomic field, the characteristic angles θ between the momenta of final and initial particles are small. The quasiclassical approach provides a systematic method to account for the contribution of large angular momenta It was successfully used for the description of numerous processes such as charged particle bremsstrahlung, pair photoproduction, Delbruck scattering, photon splitting, and others [1,2,3,4,5,6,7,8]. As for the unpolarized cross section dσ0/dΩ, its leading and subleading terms with respect to the scattering angle θ are known for a long time [16]. They can both be calculated within the quasiclassical framework. We are driven to the conclusion that, in general, it is not possible to go beyond the accuracy of the next-to-leading quasiclassical approximation without taking into account the non-quasiclassical terms
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