Excitation of Highly Ionized Atoms by Electron Impact

We use the Coulomb-Born approximation to calculate the total cross section for the electron-impact excitation of ionized atoms which have one electron outside their closed shells. When the incident energy is high and the atom is highly ionized, we can use the eikonal and classical approximations in conjunction with the Coulomb-Born approximation. Then, the scattering amplitude reduces to a one-dimensional path integral. The path integral, in turn, can be reduced, to any desired accuracy, to a sum over integrals which can be evaluated analytically. Using this procedure, we have calculated the total cross sections for the heavily ionized atoms ${\mathrm{Fe}}^{15+}$, ${\mathrm{Co}}^{16+}$, ${\mathrm{Ni}}^{17+}$, and ${\mathrm{Cu}}^{18+}$.