The First Born Approximation

Abstract

This chapter discusses the calculations using the first Born approximation and compares the theoretical results with experimental data to derive lower limits to the incident system energy. The evaluation of atom–atom cross sections in the Born approximation requires the same matrix elements as are necessary for electron–atom collisions in the first Born approximation, and errors not already inherent in the Born approximation may be introduced through the use of poor wave functions. Comparison of the Born total ionization cross section with the measured cross section suggests that the Born cross section is too large at a proton energy of 50 keV. Comparison of the differential cross section at 50 keV reveals that at this incident energy, the measured differential cross section lies below the Born differential cross section at almost all energies of ejection. For 2s excitation, comparison of the first Born approximation results with both experiment and more sophisticated calculations indicates that it is a satisfactory approximation for impact energies greater than about 10 keV.