Piece-Wise Analytic Evaluation Of The Radiative Tail From Elastic And Inelastic Electron-Scattering

We consider here the calculation of the radiative tail from the elastic peak in medium and high energy scattering as well as from a discrete inelastic level of the recoiling nucleus. We examine the method generally used for this calculation, viz., a numerical integration of the differential cross section over the angles of the unobserved photon, and discuss the difficulties inherent in this numerical integration due to the sharp peaking of the integrand. We present an alternative method for calculating the radiative tail, in which the region of integration is divided into an arbitrary number of subintervals, the structure functions are filled by cubic spline functions in each subinterval, and the integrations are then performed analytically in closed form. This method has the advantages of greatly increased accuracy and a reduction of the computation time by a factor which can vary between 10 and 10 3 , depending on the kinematics.