Electron inelastic scattering by atoms of helium

We discuss the evaluation of inelastic differential cross sections. The method we use is the Born series throught second order to calculate the direct and exchange terms of the scattering amplitudes. In the second order terms we applied the simplifies second Born approximation, in which an average energy is introduced in order to employ a closure relation to sum to all the intermediate states. This approximation is improved including the exact form of the first terms in the sum. Algebraic results for inelastic scattering with helium are presented as an application of the method discussed. We consider the excitation of the 2'p state. We also show some numerical results for this process. (author)