Nuclear Instrumentsand Methods in PhysicsResearchB 82 (1993)39-45 ~ / ~ Bl~ North-Holland Beam interactions with Materials & Atoms Cross sections for elastic scattering of fast electrons and positrons by atoms J.M. Fern~indez-Varea, R. Mayol and F. Salvat Facultat de Fisica (ECM), Universitat de Barcelona, Societat Catalana de Fisica (IEC), Diagonal 647, 08028 Barcelona, Spain Received 25 January 1993 In order to provide reliable cross section data needed for Monte Carlo simulation of high-energy electron and positron transport, a simple procedure to evaluate cross sections for elastic scattering of these particles by neutral atoms is described. Our approach starts from the exact Mott cross section for scattering by a bare point nucleus. Screening effects are accounted for by means of the Born approximation. A correction, for which we give a simple analytical expression, is introduced to compensate for the inaccuracies of the Born approximation at low energies. This correction has been determined from an extensive partial wave calculation involving 20 elements within the periodic system and electrons and positrons with kinetic energies from 1 keV to 10 MeV. Finite nuclear size effects are introduced by means of the Born approximation and a simple nuclear charge distribution. The resulting differential cross sections are adequate for describing multiple elastic scattering of electrons and positrons with kinetic energies above ,,~ Z keV, where Z is the atomic number of the target atom. 1. Introduction In many practical circumstances, the interaction of fast electrons and positrons with matter involves multiple scattering processes which can be described through Monte Carlo simulation methods (see, e.g., ref. [ 1] ). The simulation of high-energy electron and positron transport requires accurate differential cross sections (DCS) for the elastic scattering of these par- ticles. The DCS should preferably be obtainable from a numerically simple and computationaUy fast algo- rithm. Accurate elastic DCSs can be evaluated by the method of partial waves, i.e. through the numerical solution of the radial Dirac equation for the electron or positron in the screened nuclear field [2,3]. How- ever, this kind of calculation requires a formidable amount of numerical work when the kinetic energy of the electron exceeds a few hundred keV. The nu- merical effort to obtain the DCS can be reduced at the expense of using approximate scattering fields that allow the calculation of the majority of phase shifts by means of approximate methods which are much faster than the direct solution of the radial Dirac equation. Using this kind of strategy, partial wave calculations are feasible for energies up to ,-~ 10 MeV [4]. Although these partial wave methods yield Correspondence to: F. Salvat, Facultat de Fisica (ECM), Universitat de Barcelona, Diagonal 647, Barcelona E-08028, Spain. reliable numerical DCSs, they are still too compli- cated to be useful in high-energy Monte Carlo simu- lations, where calculation simplicity is as important as reliability. It is therefore necessary to seek simpler, approximate methods to obtain the DCS for energies larger than a few hundred keV. It is well known that multiple scattering distribu- tions are determined by the value of the first transport cross section [5,6] and by the large-angle behaviour of the single scattering DCS (see, e.g., ref. [7 ] ). More- over, realistic simulation procedures can be devised from the knowledge of only the first and second trans- port cross sections [7]. In the present paper we de- scribe a simple procedure to compute these quantities with a modest amount of numerical work. Our start- ing point is the exact Mott DCS for the scattering of electrons and positrons against an unscreened point nucleus [8,9] which, for large enough energies, repro- duces the large-angle behaviour of the actual DCS. Screening effects are introduced by means of the Born approximation, i.e. through the screening factor [ 1 - Fe(q)] 2, where Fe(q) is the atomic form factor [8]. To improve the accuracy of this "screened" Mott DCS we introduce a correction which modifies it at small angles so as to reproduce the first transport cross sec- tion obtained from partial wave calculations. Finally, nuclear size effects, which have an influence for elec- trons and positrons with kinetic energies larger than 10 MeV, are introduced through the Born approxi- mation assuming a simple nuclear charge distribution [ 10]. The DCS so obtained is accurate except for very 0168-583X/93/$ 06.00 (~) 1993 - Elsevier Science Publishers B.V. All rights reserved