Excitation of positive ions in Coulomb-Born approximation

We have presented a method for the evaluation of the Coulomb-Born matrix element between arbitrary initial and final Slater orbitals. Since for the two- or more-electron ionic target the wave functions may be constructed by the combination of the Slater orbitals of various angular momenta, one can easily apply this method to calculate the cross sections for the electron-impact excitation of a complex ion from an arbitrary initial state to an arbitrary final state. As an example we have calculated the excitation cross sections of the He⁺ ion from the ground state to the $4f$ state at several energies.