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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/213506
Inelastic collisions of fast charged particles with atoms: Bethe asymptotic formulas and shell corrections
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The relativistic plane-wave Born approximation is applied to the study of inelastic collisions of charged particles with atoms, by considering atomic wave functions calculated from the independent-electron approximation with the self-consistent Dirac-Hartree-Fock-Slater potential. A database of longitudinal and transverse generalized oscillator strengths (GOSs) has been computed by using accurate numerical methods for all the subshells of the ground-state configurations of the elements with atomic numbers from 1 (hydrogen) to 99 (einsteinium). The calculated GOS do not satisfy the Bethe sum rule; departures from the sum rule are in accordance with previous theoretical estimates. Asymptotic high-energy formulas for the total cross section, the stopping cross section, and the energy-straggling cross section are derived with proper account of the relativistic departure from the Bethe sum rule. The shell correction is calculated as the energy-dependent term that, when added to the asymptotic formula, reproduces the value of the atomic cross section calculated by integrating the energy-loss differential cross section. Shell corrections to the stopping cross section obtained from the present approach are presented and compared with previous estimates.
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SALVAT GAVALDÀ, Francesc, BARJUAN BALLABRIGA, Laia and ANDREO LILLO, Patricia. Inelastic collisions of fast charged particles with atoms: Bethe asymptotic formulas and shell corrections. Physical Review A. 2022. Vol. 105. ISSN 2469-9926. [consulted: 11 of August of 2026]. Available at: https://hdl.handle.net/2445/213506