THE EGS5 CODE SYSTEM

and〈cos 2 Θ〉 GS = 1 3 [1 + 2 exp(−t/λ 2)] . (2.361)These expressions can be used to check the accuracy of the calculated Goudsmit-Saunderson distribution.The Goudsmit and Saunderson expansion of the multiple scattering distribution given in Equation2.355 is exact for pure elastic scattering without energy loss. To compute it for a given singlescattering DCS, we have to evaluate the transport coefficients g l as defined in Equation 2.352. Thenumber of terms needed to make the Goudsmit-Saunderson series converge increases as the pathlength becomes shorter. In the case of small path lengths, the convergence of the series can beimproved by separating the contributions from electrons that have had no collisions,δ(cos Θ − 1)F GS (Θ; t) ≡ exp(−t/λ)2π+∞∑l=02l + 14π [exp(−tg l/λ) − exp(−t/λ)] P l (cos Θ). (2.362)The first term on the right-hand side represents unscattered electrons. In the current implementation,angular distributions are expressed in terms of the variableWe haveF GS (µ; t) = exp(−t/λ)δ(µ) +µ ≡ (1 − cos Θ)/2. (2.363)∞∑(2l + 1) [exp(−tg l /λ) − exp(−t/λ)] P l (2µ − 1). (2.364)l=0Differential cross sections for elastic scattering of electrons and positrons by neutral atoms havebeen calculated for the elements Z =1-95 and projectile kinetic energies from 100 eV to 100 MeV.The calculations were performed by using the Dirac partial-wave program ELSEPA. The scatteringpotentials were obtained from self-consistent atomic electron densities calculated with Desclaux’smulticonfiguration Dirac-Fock program. A finite nucleus, with Fermi model charge distribution,was assumed. Exchange effects in electron scattering were described by means of the local exchangepotential of Furness and McCarthy. The DCSs computed in this way account for screening, finitenuclear size, exchange, spin and relativistic effects in a consistent way.Electron and positron elastic DCS data is presented in tabulated form using a mesh of kineticenergies and scattering angles that is dense enough to allow cubic spline interpolation of ln(dσ/dΩ)in ln T and µ. The size of the complete data set, referred to as DCSLIB, is about 125 MB. A seriesof new PEGS subroutines (ELASTINO being the main one) evaluates elastic DCSs for electronsand positrons in elements and compounds (using the additivity approximation) and computesGoudsmit-Saunderson multiple scattering distributions for specified path lengths. The transportcoefficients g l are obtained by means of Gauss-Legendre quadrature, with the angular range splitinto a number of subintervals to improve accuracy.94