Equivalent exchange potentials in electron scattering

Development of a new Geant4-DNA electron elastic scattering model for liquid-phase water using the ELSEPA code

“…This is expected as the exchange potential cannot accurately predict the interaction of electrons below 1 Hartree energy (27.21 eV). 102 Moreover, the DCSs at 0°are overestimated, considering the expected difference between vapour and liquid water data above 500 eV. Globally, the DCSs calculated in this study are closer to the measurements than the default ICRU 77 recommendation, SR, USR, Champion, and CPA-100 models over the entire Bethe formula 65 for the collision energy loss with the Sternheimer density-effect correction 66 Cross section generated by the Koch-Motz formula 67 68 Continuous slowing down approximation (CSDA) range 70,a Modified Bethe theory given in ICRU 37 69 > 10 keV Deduction based on the theoretical results of Ashley 70 and empirical evaluations 71 CSDA range 69 with and without exchange Inelastic cross section based on dielectric theory 74 and elastic cross sections based on partial wave analysis 75,76 Liquid water MCTS code (MOCA) 81,82 and CSDA range 69 Elastic cross section based on partial wave method [83][84][85] Inelastic cross sections based on experimental dipole oscillator strength 86,87 Liquid water MCTS code (PITS) 88 Inelastic cross section based on dielectric theory (Dingfelder-GSF model) for liquid water 13 and elastic cross section based on the experiments and NIST data for vapour water 89 Liquid water MCTS code (KURBUC) 44 Water vapour cross sections for ionization and excitation 1 are compiled from different sources and elastic cross section based on the Rutherford formula for vapour water with a screening parameter 44 Vibrational excitation and multi-step thermalization process are taken into account 42 Vapour water 55 and DCSs proposed by Brenner and Zaider below 200 eV, 96 and Rutherford cross section above 200 eV 44 Vibrational excitation, 55 dissociative attachment,…”

Electron- and positron-impact ionization of inert gases

“…In the approximation (2) the electron-electron interaction occurs exactly once and no account is taken of PCI between the two final-state electrons. In our calculations below, the full nonlocal exchange potential is not used but rather a localized version [19,[28][29][30][31] is employed. Its use greatly simplifies the static-exchange calculations in that one needs only solve differential equations rather than integrodifferential equations.…”

Energy-sharing(e,2e)collisions: Ionization of the inert gases in the perpendicular plane

“…In actual calculations, it is not usual to work with the full nonlocal exchange potential; rather, one employs a localized version [5][6][7][8][9]. Its use greatly simplifies the static exchange calculations in that one needs to solve only differential equations rather than the integro-differential equations.…”

“…Because we treat each of the exiting electrons as moving in the field of a spin-1 2 ion, there is an inherent ambiguity in the choice of exchange potential in the final channels; we could chose it to be singlet or triplet [5,10]. For most energies there is little or no difference between results calculated with the singlet and triplet potentials [5,8], but at low energies there is a weakness in the singlet form because for some energies it can become complex. A method has been proposed in [7] to make the potential real again if this happens, but this method results in a discontinuous singlet potential and generally gives results in poorer agreement with experiment than the equivalent triplet calculation (see [5]).…”