Electron scattering in Fourier reciprocal space maps the scattering potential

Diffraction-like fringe structures appear in the differential cross-section (DCS) of elastic electron–atom scattering [1]. A recent investigation of e–C₆₀ scattering [2] revealed that such diffraction can be probed in two ways: (i) through the angular DCS of scattering at a fixed impact energy and (ii) through the energy DCS at a fixed scattering angle, the latter promising applications in ultrafast electron diffraction studies. In the current theory-experiment joint research, we present a novel analysis of diffraction in DCS of atomic targets to establish a connection to the scattering potential. Scattering parameters are calculated using the Dirac–Partial wave formalism [3]. Employing a Fourier transform (FT) method, we process the oscillations (fringes) in DCS to gain insights of its relationship with the overall interaction potential [4]. We show that the effective diffracting length, derived from the transform of angular DCS into reciprocal space, as a function of energy can delineate the scattering potential, a quantity which is a fundamental collision parameter, not merely a mathematical entity, but directly inaccessible to experimental observation. The approach may find applications in large-volume, multiscale modelling.

[1] B. P. Marinković, V. Vujcić, G. Sushko, D. Vudragović, D. P. Marinković, S. Dorjević, S. Ivanović, M. Nesvić, D. Jevremović, A. V. Solov’yov, and N. J. Mason, Nucl. Instr. Meth. Phys. Res. B 354, 90 (2015). 

[2] R. Aiswarya, R. Shaik, J. Jose, H. R. Varma, and H. S. Chakraborty, Phys. Rev. Lett. 133, 033002 (2024).

[3] F. Salvat, A. Jablonski, and C. J. Powell, Comput. Phys. Commun. 165, 157 (2005).

[4] R. Aiswarya, J. Jose, N. Simonović, B. P. Marinković, and H. S. Chakraborty, Phys. Rev. A Lett. 113, L010801 (2026)