Resonance contributions to collision strengths for transitions between magnetic sublevels in highly charged ions by impact with an electron beam

A fully relativistic approach is described for obtaining the resonance contribution to the cross sections for transitions between magnetic sublevels in highly charged ions due to impact with an electron beam. We derive the relativistic distorted-wave cross section for the ion in a lower N-electron magnetic sublevel to capture a directive electron and form a doubly excited (N + 1)-electron magnetic sublevel. Also the autoionization rate from this magnetic sublevel to an N-electron magnetic sublevel is derived. The resonances are then treated as the two-step process of electron capture followed by autoionization to the final sublevel with the effects of autoionization to a different final level or radiative decay of the doubly excited sublevels included. These resonance contributions are added to the relativistic distorted-wave results for the "direct" contribution to give the complete cross section. Numerical results expressed in terms of the collision strengths are calculated and studied for He-like oxygen and iron and for Be-like oxygen. These are of interest for electron beam ion trap experiments and population alignment analysis.