Collisions of fast electrons with helium. I. Various forms of the second Born approximation

Various forms of the second Born approximation are applied to electron collisions with helium in the energy range 200 to 500 eV. In each case all intermediate states up to 3 1 P are included explicitly, and a closure approximation used for higher states, the energy parameter being chosen to fit the total cross section and dispersion relation values for Re f(0) and Imf(0). Calculations are carried out with and without V 4 terms, and in a (1,1)-Pade approximation for the 1 2 S to 1 1 S, 2 1 S and 2 1 P transitions. Results are compared with experiment and with those of other calculations. The present results cast doubt upon the practice of normalizing experiment to the first Born approximation at intermediate energies.