Streamlined eigenchannel treatment of open-shell spectra

Abstract

An energy-independent transformation of the generalized eigensystem used in eigenchannel calculations is shown to give the energy dependence of the $R$ matrix in semianalytic form. The transformation gives insight into the energy dependence of the short-range parameters used in multichannel quantum-defect theory. We present a simple method for setting up the many-electron basis set which integrates naturally with the noniterative eigenchannel method. The approach is used to calculate energy-dependent quantum defects for the $^{1}S^{e}$ and $^{3}P^{e}$ symmetries of silicon near the first ionization threshold, with spin-orbit effects described by a frame transformation.