Electron impact excitation of atomic systems

Abstract

Starting from the usual partial wave method, we present a theoretically exact formulation for the calculation of differential and total cross sections corresponding to electron impact excitation in atomic systems. For transitions involving an s state the derived formulae are very simple, free of Racah or Clebsch-Gordan coefficients, so that for computational purposes they are more convenient than the usual expressions. In particular, we have considered monopole, dipole and quadrupole transitions from (or to) an s state. In comparison with the usual formulation, the present one also has the advantage that it allows us to separate out the scattering amplitudes corresponding to excitation of individual magnetic substates: electron-photon coincidence parameters for dipole and quadrupole transitions from an s state can be obtained directly. For the total differential cross section an alternative formulation is derived and compared with the previous one. Both formulations given here are very general because they can be employed using any non-relativistic T-matrix, and are valid for both neutral and charged targets. In the weak coupling approximation and for alkali-like systems, the resulting formulae are compared with others of the literature; as an illustration the Coulomb Bethe approach is described. Finally, expressions for the integrated cross sections corresponding to excitation of individual magnetic substates are also given and it is shown how, for charged targets, the Coulomb phase must be included in all calculations except in those which give the total integrated cross section.