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• W2083994920 abstract "Screening effects are important to understand various aspects of ion-solid interactions and, in particular, play a crucial role in the stopping of ions in solids. In this paper the phase shifts and scattering amplitudes for the quantum-mechanical elastic scattering within up to the second-order Born (B2) approximation are revisited for an arbitrary spherically-symmetric electron-ion interaction potential. The B2 phase shifts and scattering amplitudes are then used to derive the Friedel sum rule (FSR) involving the second-order Born corrections. This results in a simple equation for the B2 perturbative screening parameter of an impurity ion immersed in a fully degenerate electron gas which, as expected, turns out to depend on the ion atomic number $Z_{1}$ unlike the first-order Born (B1) screening parameter reported earlier by some authors. Furthermore, our analytical results for the Yukawa, hydrogenic, Hulth'{e}n, and Mensing potentials are compared, for both positive and negative ions and a wide range of one-electron radii, to the exact screening parameters calculated self-consistently by imposing the FSR requirement. It is shown that the B2 screening parameters agree excellently with the exact values at large and moderate densities of the degenerate electron gas, while at lower densities they progressively deviate from the exact numerical solutions but are nevertheless more accurate than the prediction of the B1 approximation. In addition, a simple Pad'{e} approximant to the Born series has been developed that improves the performance of the perturbative FSR for any negative ion as well as for $Z_{1}=+1$." @default.
• W2083994920 created "2016-06-24" @default.
• W2083994920 creator A5017159893 @default.
• W2083994920 creator A5071705606 @default.
• W2083994920 date "2013-09-01" @default.
• W2083994920 modified "2023-10-18" @default.
• W2083994920 title "Second-order Born approximation for the scattering phase shifts: Application to the Friedel sum rule" @default.
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• W2083994920 doi "https://doi.org/10.1016/j.nimb.2013.06.023" @default.
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