The interaction of a fast electron penetrating a spherical target is studied, in the frame of the classical dielectric theory. Expressions for ω the Fourier component of the induced scalar field and energy loss probability are obtained. The reduction in the bulk loss probability due to the surface boundary correction is calculated to all orders in a multipole expansion. The dependence of this correction on the impact parameter and on the radius of the sphere is also studied and compared with the results for films.
Rivacoba, A. and Echenique, P. M.
"Surface Corrections to Bulk Energy Losses in Scanning Transmission Electron Microscopy of Spheres,"
Scanning Microscopy: Vol. 4
, Article 7.
Available at: https://digitalcommons.usu.edu/microscopy/vol4/iss1/7