Study the differential cross-section of scattering by using Gaussian potential in presence of laser

Abstract

The study of electron–atom scattering provides fundamental insights into particle interactions and quantum dynamics. The differential cross-section (DCS) is a key quantity that quantifies the probability of scattering at specific angles and energies. Modeling the target potential accurately is essential for precise predictions, and the Gaussian potential offers a smooth and well-defined representation of atomic fields. When combined with external laser fields, the scattering behavior becomes more complex, as the laser modifies the interaction dynamics and introduces polarization dependent effects. The aim of this work is understood how polarization type, scattering angle, momentum, photon energy and distance separation effect the interaction of electron-atom in laser field. For this study, a theoretical model was developed using Volkov wavefunctions, Gaussian potentials, the S-matrix formalism, and Bessel functions within the framework of the Kroll–Watson approximation. The resulting model was implemented in MATLAB to analyze and compare the behavior of the newly derived equations. The observations show, elliptical polarization produces the highest DCS, followed by circular and linear polarizations, and that zero-order Bessel functions yield higher magnitudes than first-order. Equilibrium occurs when electrostatic interaction energy equals particle rest energy, with resonance phenomena observed around specific energies and momentum transfers. Limitations include the challenge of experimentally measuring DCS for higher order Bessel functions due to reduced magnitudes. Future work is recommended to extend the study to multi-photon and higher-order interactions and to explore experimental validation of theoretical predictions. Overall, the results provide insight into controlled scattering processes in laser modulated fields.