Data of electron elastic scattering cross-sections calculated by numerically solving the Dirac equation for a central electrostatic field, and using the relativistic partial wave expansion method (RPWEM), are presented. After that, an analytical expression is proposed to approximate the RPWEM results. It is an approximation that is used to expedite the calculations in applications such as Monte Carlo simulation. It depends on a parameter à which is a function of the target characteristics and on the electron energy E. Typically, during a Monte Carlo simulation, à is calculated by cubic spline interpolation of previously tabulated data. This Letter proposes an analytical approximation that allows to calculate à , for selected oxides (MgO, SiO2, Al2O3) in the primary energy range from 50 eV to 10 keV, avoiding the cubic spline interpolation and, therefore, reducing the computation time. A comparison between the approximated and the RPWEM computations of the differential and the transport elastic scattering cross-section is presented. Then some applications are proposed.
An analytical approximation of the differential elastic scattering cross-section for electrons in selected oxides
Dapor, Maurizio
2004-01-01
Abstract
Data of electron elastic scattering cross-sections calculated by numerically solving the Dirac equation for a central electrostatic field, and using the relativistic partial wave expansion method (RPWEM), are presented. After that, an analytical expression is proposed to approximate the RPWEM results. It is an approximation that is used to expedite the calculations in applications such as Monte Carlo simulation. It depends on a parameter à which is a function of the target characteristics and on the electron energy E. Typically, during a Monte Carlo simulation, à is calculated by cubic spline interpolation of previously tabulated data. This Letter proposes an analytical approximation that allows to calculate à , for selected oxides (MgO, SiO2, Al2O3) in the primary energy range from 50 eV to 10 keV, avoiding the cubic spline interpolation and, therefore, reducing the computation time. A comparison between the approximated and the RPWEM computations of the differential and the transport elastic scattering cross-section is presented. Then some applications are proposed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
