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Effects of hyperfine interaction on the circular polarization of the Sc XX x-ray lines

The x-ray lines emitted from highly charged ions collisionally excited by longitudinally polarized electrons can be strongly circularly polarized for ions with no nuclear spin. In the present work, we have theoretically investigated the effects of hyperfine interaction on the circular polarization of the 1s2l → 1s2 lines of helium-like scandium, for which the nuclear spin is large. The hyperfine splitting of the excited levels and the transition probabilities for the hyperfine-induced E1 decays 23P0 → 11S0 and 23P2 F = 5/2 − 9/2 → 11S0 have been calculated by diagonalizing the complete Hamiltonian including both the spin-orbit interaction and the magneticdipole hyperfine interaction. The collision strengths for transitions to the individual magnetic sublevels of the target ion have been computed in two distorted-wave methods, one semi-relativistic and the other fully relativistic. It is shown that the hyperfine effects result in drastic decreases of the degree of circular polarization for the lines 23P2, 1 → 11S0 (labeled x and y, respectively and 23S1 → 11S0 (labeled z). The interference effects between the E1 and M2 transitions for the line x and those between the hyperfine components F = 5/2, 7/2 and 9/2 of the upper level for the line y are considered.