Calculation of resonant effects in electron-impact excitation of positive ions: Application to oxygen vii

The general reaction theory of Feshbach is applied to the calculation of resonant effects in near-threshold electron-positive-ion excitation. The theory divides configuration space into open- and closed-channel parts, resonance effects being described by the closed-channel part. The open-channel part is handled in a distorted-wave approximation to the set of open-channel coupled equations. We suggest various methods for handling the closed-channel part. However, we explicitly use an "attached-excited-target approximation," which we further approximate by a set of uncoupled closed-channel equations. As an example, we calculate the $1{}_{}{}^1{}_{}{}^{}S\to 2{}_{}{}^1{}_{}{}^{}P$ excitation cross section of O vii below the $3{}_{}{}^3{}_{}{}^{}S$ threshold. Various distorted-wave approximations are investigated and results from most of them are quite similar. Resonant effects arising from the attachment of the colliding electron with the $3{}_{}{}^3{}_{}{}^{}S$ state are found to be small, but other close-lying $n=3\mathrm{}$ states have not yet been included.