Radiative Cascade Repopulation of 1s2s2p 4P States Formed by Single Electron Capture in 2–18 MeV Collisions of C4+ (1s2s 3S) with He

This study focuses on the details of cascade repopulation of doubly excited triply open-shell C3+(1s2s2p)4P and 2P± states produced in 2–18 MeV collisions of C4+(1s2s3S) with He. Such cascade calculations are necessary for the correct determination of the ratio R of their cross sections, used as a measure of spin statistics [Madesis et al. PRL 124 (2020) 113401]. Here, we present the details of our cascade calculations within a new matrix formulation based on the well-known diagrammatic cascade approach [Curtis, Am. J. Phys. 36 (1968) 1123], extended to also include Auger depopulation. The initial populations of the 1s2snℓ4L and 1s2snℓ2L levels included in our analysis are obtained from the direct nℓ single electron capture (SEC) cross sections, calculated using the novel three-electron close-coupling (3eAOCC) approach. All relevant radiative branching ratios (RBR) for n≤4 were computed using the COWAN code. While doublet RBRs are found to be very small, quartet RBRs are found to be large, indicating cascade feeding to be important only for quartets, consistent with previous findings. Calculations including up to third order cascades, extended to n→∞ using an n−3 SEC model, showed a ∼60% increase of the 1s2s2p4P populations due to cascades, resulting, for the first time, in R values in good overall agreement with experiment.